Simplify the expression

For the relation of times of money , Francine and Tommy start with the amount of money equals to $18 and $3 respectively.

Let 'x' represents the amount of money with Francine .

And 'y' represents the amount of money with Tommy.

In the first condition:

x = 6y __(1)

To purchase baseball cap Francine gave $33 then the given relation is :

y - 33 = 2( x - 33 )

⇒ y - 33 = 2x - 66

⇒y = 2x -66 + 33

⇒ y = 2x -33 __(2)

Substitute the value of 'x' from (1) in (2) we get,

y = 2(6y) - 33

⇒y = 12y - 33

⇒ 12y - y = 33

⇒ 11y = 33

⇒ y = $3

⇒ x = 6(3)

⇒ x = $18

Therefore, the amount of money Francine and Tommy start with is equal to $18 and $3 respectively.

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The number of years that he save this money is 7 years

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

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

Given;

Mike saves $2,000 at a yearly simple interest rate of 2%;

Money he earns in interest= $280

Then the number of years;

$280 = ($2,000 x 2 x T) / 100

$28,000 = $4,000 x T

T = $28,000 / $4,000

T = 7 years

Therefore, numbers of years mike has to pay interest will be 7

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Answer:

  0.4247

Step-by-step explanation:

You want to know the proportion of heights less than 103.1 cm if the population is normal with a mean of 105 cm and a standard deviation of 10 cm.

The proportion can be found using a suitable probability calculator. The one shown in the attachment tells us ...

  the proportion of heights less than 103.1 cm is about 0.4247.

__

Additional comment

The height of interest is less than the mean by approximately 0.2 times the standard deviation. This suggests the proportion will be close to, but less than, 0.5000.

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The Interquartile range of the given set is 1.5.

What is Interquartile range ?

The variation between the third and first quartiles is defined by the interquartile range. The numbers that partition the entire series into four equal sections are known as quartiles. There are therefore 3 quartiles. The lower quartile is represented by the letter Q₁, the higher quartile by the letters Q₁, and the middle quartile by the letter Q₃.

Given set : 81, 82, 83, 83, 84, 84, 84, 85

Here, It is already in increasing order but the number of values is 8 which is even.

So, Q₁ part = 81, 82, 83, 83

Q₁ will be the median of 82 and 83.

So, Q₁ = (82+83)/2

          = 82.5

Similarly, Q₃ part =84, 84, 84, 85

So, Q₃ will be the median of 84 and 84.

hence, Q₃ = (84+84)/2

                 = 84

We know that, Interquartile range = Q₃ - Q₁

                                                          =  84 - 82.5

                                                          = 1.5

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The graphic representation of data points arranged into user-specified ranges is called a histogram. The diagram below that is attached shows the histogram diagram.

A histogram is a figure made up of rectangles with widths equal to the class interval and areas proportionate to the frequency of a variable.

From the given information, we have the following:

Length of time (t)     Frequency

0 ≤ t < 10                        5

10 ≤ t < 25                     24

25 ≤ t < 30                    12

30 ≤ t < 50                    8

So, the image that is attached shows how the table is represented in a histogram.

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The complete question is given below:

The percentage of alcohol in a handy is 3%. 3/5 * 5% = 3% , Since beer is 5% alcohol, then 3/5 of the handy is 5% alcohol.

The ratio of beer to lemonade in a handy is 3:2, which means that 3 parts of the handy is beer and 2 parts of the handy is lemonade. To express it in terms of fractions, 3/5 of the handy is beer and 2/5 of the handy is lemonade. Since beer is 5% alcohol, then 3/5 of the handy is 5% alcohol. Therefore, if you take the proportion of the beer in the handy and multiply it by the alcohol percentage of the beer, you will get the percentage of alcohol in the handy. In this case, 3/5 * 5% = 3%. This means that the percentage of alcohol in a handy is 3%. It's important to note that this assumes that the beer and lemonade are mixed together evenly and there's no spillage or evaporation. Also, it's important to consider the fact that the alcohol percentage of the beer can vary depending on the brand and type of beer.

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The missing angle measure for the following letters are:

a - 65°

b - 115°

c - 115°

d - 65°

e - 65°

Corresponding angles are generated when two parallel lines are crossed by a transversal.

Opening and closing a lunchbox, completing a Rubik's cube, and endless parallel railway tracks are all examples of equivalent angles.

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Answer:

X ≤ -1

How do we know this?

Well, if x = the value of any number in the graph, we can see that it can be equal to negative one, or less than -1, meaning we use the symbol ≤.

The inequality describes the mile marker she would be at this point is:

325 + 2y ≤ 475

Now, According to the question:

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

The fastest driving speed of Willow is 75 miles per hour,

There is a bit of traffic on her route that might slow her speed down,

So, the inequality which represents the speed of the willow is:

y ≤ 75

Hence, the inequality which represents the speed of the driving of willow is y ≤ 75.

Now, the expression 361 + 2y represents what mile marker he is at after 2 hours. We know that the fastest he will drive is 75, so we could replace y=75 in the last expression to know what mile marker he would be seeing at that point. This is:

325 + 2(75) => 325 + 150 = 475

Now, we know that the inequality would be:

325 + 2y ≤ 475

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eeeeeAnswer:

Step-by-step explanation:

Answer:

the answer is A

I hope I help you in this ans and tq.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below for Function A.

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{(-8)}}} \implies \cfrac{4 +5}{10 +8} \implies \cfrac{ 9 }{ 18 } \implies \cfrac{1 }{ 2 }\impliedby \stackrel{\textit{slope of}}{A} \\\\[-0.35em] ~\dotfill[/tex]

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{5}x-1\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}\qquad \stackrel{\textit{slope of}}{B} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} \stackrel{A}{\cfrac{1}{2}} ~~ < ~~ \stackrel{B}{5} \end{array}}~\hfill[/tex]

Answer: 70/13

Step-by-step explanation:

Slope = rise/run

(r-5)/(6-r) = 5/8

30-5r = 8r-40

70 = 13r

70/13 = r

The solution to the expression in this problem is given as follows:

x = -1/3 + 1.7i and x = -1/3 - 1.7i.

The rational expression for this problem is defined as follows:

[tex]\frac{2x}{3x - 5} - \frac{x + 1}{3x + 5} = -\frac{4}{9x^2 - 25}[/tex]

Applying the least common factor at the left side, we have that:

[tex]\frac{2x(3x + 5) - (x + 1)(3x - 5)}{9x² - 25} = -\frac{4}{9x^2 - 25}[/tex]

[tex]\frac{6x^2 + 10x - 3x^2 + 5x - 3x + 5}{9x^2 - 25} = -\frac{4}{9x^2 - 25}[/tex]

As the denominators are equal, the solution is obtained equaling the denominators, hence:

3x² + 2x + 5 = -4

3x² + 2x + 9 = 0.

Which is a quadratic function with coefficients given as follows:

a = 3, b = 2, c = 9.

Inserting these coefficients into a calculator, the solutions are given as follows:

x = -1/3 + 1.7i and x = -1/3 - 1.7i.

The rational expression is given by the image presented at the end of the answer.

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For given frequency table the relative frequency table with percentage is given in image.

What is a frequency table ?

A frequency table consists of the lists of items in a given data set and the number of times each item occurs in the data set and The number of times a particular data value occurs in a given data set is referred to as its frequency.

e.g.

A, A, A, B, B, B, B, C, C, D

Count the number of times each grade occurs in the above series. Yes, ‘A’ occurs thrice, ‘B+’ occurs four times, ‘C’ occurs twice, and ‘D’ occurs once. Now, according to the definition of frequency, we can note the frequency of each grade as follows:

Frequency of A = 3

Frequency of B = 4

Frequency of C = 2

Frequency of D = 1

Let us list the grades obtained by the students in the above example, in a frequency table. Table is in image.

Now,

To find the percentage for relative frequency table we used (given value/Total people)*100.

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Answer: (e) (i) To represent the inequalities graphically on a coordinate plane, you can use a scale of 2cm to represent 5 units on each axis. To shade the unwanted regions, you can start by drawing the coordinate plane and labeling the x and y axes. Then, you can graph the inequalities by plotting the lines and shading the regions that do not satisfy the inequalities.

(b) 2x + 3y ≤ 30

This inequality represents a line with the equation 2x + 3y = 30. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.

(c) x - 2y ≥ -10

This inequality represents a line with the equation x - 2y = -10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or above the line satisfy the inequality.

(d) y ≤ -2x + 10

This inequality represents a line with the equation y = -2x + 10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.

The set of points that satisfy all three inequalities is the area that is not shaded in the graph.

(ii) To find the maximum number of rabbits the farmer can buy, we need to find the coordinates of the vertex of the feasible region.

The coordinates of the vertex of the feasible region is (x,y) the point where the line 2x+3y=30 and x-2y=-10 intersects.

We can substitute the x-2y=-10 into the 2x+3y=30 equation

2x+3y=30

2x+3y+2y=-10

2x+5y=-10

x=-5y+10

substituting this into one of the equation we have

2(-5y+10)+3y=30

-10y+20+3y=30

-7y=10

y= -10/7

substituting this into x = -5y+10 we have

x = -5(-10/7)+10 = 15

the maximum number of rabbits the farmer can buy is 15

Step-by-step explanation:

In the given word problem, Mr. Garcia total paid $259.75 for his journey.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, Mr. Garcia rents a car at a rate of $29.95 per day. There is an additional mileage charge of $20.00 per 100 miles or fractions of 100, and Mr. Garcia drives 550 miles in 5 days,

Since, cost of 100 mile = $20

Therefore, cost for 1 mile = $0.2

Since, Mr. Garcia travelled for 550 miles,

Therefore, cost of 550 miles = $0.2 × 550 = $110

Since, cost for one day = $29.95

Therefore, cost for 5 days = $29.95 × 5 = $149.75

Now,

Mr. Garcia used the car for 5 days and travelled for 550,

Therefore, total cost he paid = $110 + $149.75

= $259.75

Hence, Mr. Garcia total paid $259.75 for his journey.

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Answer:

$8,600 - $31,100

Step-by-step explanation:

Hope this helps :)

The smallest equivalent fraction of the number is considered to be its simplest form.The answer is  7/3 : 21/5 = 5 : 9.

Values should now be entire numbers.By removing the denominators, convert fractions to integers.

Since the denominators of our two fractions are different, we must identify the least common denominator and rewrite our fractions using the common denominator as necessary.

LCD(7/3, 21/5) = 15

Now we have:

7/3 : 21/5 = 35/15 : 63/15

Now that the denominators of our two fractions are similar, we may multiply them both by 15 to get rid of the denominators.

Then, we have:

7/3 : 21/5 = 35 : 63

With the highest common factor, attempt to further reduce the ratio (GCF).

GCF is 7 for 35 and 63.

Divide both terms by GCF 7, then:

35 ÷ 7 = 5

63 ÷ 7 = 9

By multiplying both components by the GCF = 7, it is possible to reduce the ratio 35: 63 to its simplest terms.

35 : 63 = 5 : 9

Therefore:

7/3 : 21/5 = 5 : 9

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If a new I phone costs $799 and is estimated to lose 25% of its value every six months after its purchase ,then the value of phone after 2 years is $253  .

The cost of new i phone is = $799 ;

the percent loss in the value after every 6 month is = 25% = 0.25  ;

in 2 years , there are 4 period of six months , so , n = 4  ;

The depreciated value of i phone can be calculated by formula ;

⇒ Value = Cost × (1 - 0.25)ⁿ ;

Substituting value of n =4 and cost = $799 ;

⇒ Value = 799 × (1 - 0.25)⁴ ;

⇒ Value = 799 × (0.75)⁴ ;

⇒ Value = 799 × (0.75)⁴ ;

⇒ Value = 799 × 0.31640625 = 252.8085 ≈ 253 .

Therefore , the value of the phone after 2  years is $253  .

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In dollars and cents, the total projected cost of gas and oil for two years would be $ 756.00

First we will calculate per year how much is spent.

First year, we have :-

= 13000 * 0.028 = 364.00

Second year, we have:-

12000 * 0.028 = 336.00

The total cost in the two years is the sum of both:

= first year + second year

= 364.00 + 336.00 = 700.00

In dollars and cents, the total projected cost of gas and oil for two years would be $ 700.00.

Total cost

Total cost refers to the overall cost of production, which includes both fixed and variable components of the cost.

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complete question is :-

Compute the requested operating costs as indicated, based on the preceding table and the following information.

Choose the correct answer.

Car = 6 cylinder compact

Years driven = second and third

Miles driven = 13,000 miles in year two and 12,000 in year three

In dollars and cents, the total projected depreciation cost for these two years would be $?

After the increment in the function the value of x is -2.25

In math the term function is denoted as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here we know that the function g(x)=6cos(7x+22), x increase by for 7x+22 to increase by 2π.

In order to calculate the value of x in the function, we have to equate the value of function with 2π.

Then we get,

=> 7x + 22 = 2π

When we solve the equation for x then we get,

=> 7x = 2π - 22

=> x = (2π - 22)/7

When we simplify this one then we get the value of x as,

=> x = 0.285π - 3.14

=> x = 0.89 - 3.14

=> x = -2.25

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Question 1:

[tex]\frac{2}{3} n-16=-\frac{5}{6}n+2[/tex], solve for n.

[tex]\frac{2}{3} n-16=-\frac{5}{6}n+2[/tex]

=> [tex]\frac{2}{3} n=-\frac{5}{6}n+18[/tex]

=> [tex]\frac{2}{3} n+\frac{5}{6}n=18[/tex] =>[tex]\frac{4}{6} n+\frac{5}{6}n=18[/tex]

=> [tex]\frac{9}{6} n=18[/tex] => [tex]\frac{3}{2} n=18[/tex]

=> [tex]n=18(\frac{2}{3})[/tex]

=> [tex]n=6(2)[/tex]

Sol: n=12

Question 2:

[tex]5-\frac{1}{3}p=\frac{4}{9}p+12[/tex], solve for p.

[tex]5-\frac{1}{3}p=\frac{4}{9}p+12[/tex]

=>[tex]5=\frac{4}{9}p+\frac{1}{3}p+12[/tex]

=> [tex]5=\frac{4}{9}p+\frac{3}{9}p+12[/tex]

=>[tex]5=\frac{7}{9}p+12[/tex]

=> [tex]-7=\frac{7}{9}p[/tex]

=> [tex]-7(\frac{9}{7}) =p[/tex]

=> [tex]-(9)=p[/tex]

Sol: p=-9

Question 3:

The relationship between ∠2 and ∠7 is that they are alternate interior angles.

Question 4:

The relationship between ∠1 and ∠3 is that they are corresponding angles.

Question 5:

The relationship between ∠4 and ∠5 is that they are alternate exterior angles.

Answer:

c)12:16​

Step-by-step explanation:

We know

The ratio is 6:8; we times 2 and get the ratio of 12:16

So, the answer is C

The value of the function f(0) + f(-4) is -12

From the question, we have the following equation that can be used to solve the question

f(x) = 3 - |2x - 5|

Also, we have the function values to be

f(0) and f(-4)

When these values are calculated, we have

f(0) = 3 - |2(0) - 5| = -2

f(-4) = 3 - |2(-4) - 5| = -10

substitute the known values in the above equation, so, we have the following representation

f(0) + f(-4) = -2 - 10

Evaluate

f(0) + f(-4) = -12

Hence, the solution is -12

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Liquid with density 0.135 grams over milliliter and volume 182.8 milliliter has weight equal to 24.68 grams.

Let 'm' represents the weight in grams of a liquid

Volume 'V' of the container to fill a liquid is = 182.8milliliter

Density 'ρ'  of the given liquid is 0.135 grams over milliliter

Density =  mass / Volume

Substitute the values we get,

⇒ 0.135 = m / 182.8 ×

⇒ m = 0.135  grams over milliliter ×  182.8milliliter

⇒ m = 24.678 grams

⇒ m = 24.68 grams

Therefore, the weight of a liquid for the given density and the volume is equal to 24.68 grams.

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The number 868 represents the final balance of the acount, then we conclude that the correct option is C.

"The value 868 represents the final balance in the account, which means the account ended with $868."

Weknow that the equation 868 = 700(1 + 0.04t) represents the amount of money earned on a savings acount.

We want to see what does 868 represent in this situation.

Where the form of the equation is:

money earned = function that depends on t.

So the value at the left, 868, just represents the final balance of the account, this is the amount of money that there is in the account at the end.

Thus, the correct option is C.

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The time in years for which the values are the same is given as follows:

7.25 years.

A decaying exponential model is given as follows:

y = a(1 - r)^t.

For which:

The parameters for this problem are given as follows:

a = 56000, r = 0.12.

Hence the exponential model is given as follows:

y = 56000(0.88)^x.

The linear model is given as follows:

y = b - mx.

In which:

The parameter values for this problem are given as follows:

b = 56000, m = 56000/12 = 4666.67.

Hence the linear model is:

y = 56000 - 4666.67.

The point of intersection of the two graphs is at a time of 7.25 years.

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Answer:

3

Step-by-step explanation:

Take the x-intercept (1,0) and y-intercept (0,-3) to find the slope/gradient:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-3)}{1-0}=3[/tex]