A raffle prize of 14x^2/15dollars is to be divided among 7x people. Write an expression for the amount of money that each person will receive. Show Work!

The scale is simply the ratio between the distances in the plan and the actual distances. So, first of all, let's convert all lengths to the same unit measure:

[tex]18\text{ ft} = 216\text{ in}[/tex]

So, the scale is

[tex]\dfrac{216}{6.4} = 33.75[/tex]

which means that one inch in the plan is the same as 33.75 inches in the real world.

Answer:

1 : 33.75

Step-by-step explanation:

6.4 inches ⇒ 18 feet

6.4 inches ⇒ 18 x 12 = 216 inches

scale used

= 6.4 : 216

= 1 : 216 ÷ 6.4

= 1 : 33.75

Answer:

My guess is

Mary:7

Ed:5

Step-by-step explanation:

Mary present age is 7 years while Ed present age is 5 years.

An equation is an expression that shows the relationship between two or more variables and number.

Let x represent Mary present age and y represent Ed present age, hence:

x = y + 2   (1)

And:

x - 3 = 2(y - 3)    (2)

x = 7, y = 5

Mary present age is 7 years while Ed present age is 5 years.

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Answer:

d+e =6       d=5 and e=1

d-e=4

Step-by-step explanation:

5+1=6

5-1=4

simple math you have to think hard to get it right might look easy but it is not

Answer:

the solution is (1, 5)

Step-by-step explanation:

If d - e = 4, then d = e + 4.  Substitute e + 4 for d in the first equation:

d + e = 6 →  e + 4 + e = 6.  Then 2e = 2, and e = 1.

Subbing 1 for e in the second equation, we get d + e = 6, or d + 1 = 6.

Thus, d = 5, and the solution is (1, 5)

Answer:

Total surface area = 154 in²

Step-by-step explanation:

The prism has a total of 6 surfaces:  top and bottom, 2 sides, and 2 ends.

We have to find the area of each top, side, end, and then add these together, and then multiply the result by 2 to finish the job.

Area of top:  (5 in)(3.5 in) = 17.5 in²

Area of side:  (5 in)(7 in) = 35 in²

Area of end:  (3.5 in)(7 in) = 24.5 in²

Now add these three results together and multiply the sum by 2:

2( 17.5 in² + 35 in² + 24.5 in²) = total surface area = 154 in²

To answer the other part of this question:  find the volume of this prism:

V = length · width · ht = (5 in)(3.5 in)(7 in) = 122 in³.  

Yes, this box can definitely hold 22 in³ of packing peanuts.

Eli's box has a surface area of 154 square inches, and this is the total area he will need to paint. The box has a volume of 122.5 cubic inches, thus it is large enough to hold 22 cubic inches of packing peanuts.

To calculate the total area Eli will paint on his wooden box, we need to find the surface area of the rectangular prism. The box has a length (L) of 5 inches, width (W) of 3.5 inches, and height (H) of 7 inches. The surface area (SA) of a rectangular prism is given by the formula:

SA = 2(LW + LH + WH)

Plugging in the dimensions, we get:

SA = 2(5 × 3.5 + 5 × 7 + 3.5 × 7) = 2(17.5 + 35 + 24.5) = 2(77) = 154 square inches

So, the total area Eli will paint is 154 square inches.

The volume of the box is calculated using:

Volume = L × W × H

Volume = 5 × 3.5 × 7 = 122.5 cubic inches

Since 122.5 cubic inches is greater than 22 cubic inches, the box can indeed hold 22 cubic inches of packing peanuts.

Answer:

5-7=-2

Step-by-step explanation:

positive integers: 5 and 7

Subtraction 5-7 is equal to a negative answer: -2

If two positive integers are 5 and 3. Then the subtraction of the positive integers will be negative 2.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

The subtraction problem that involves two positive integers and has a negative value

Let x and y be the two integers.  ​And y is greater than x.

Then we have

Then the difference between x and y should be negative

Then subtract y from x.

x - y = negative value

Let y be 5 and x be 3. Then we have

x - y = 3 - 5

x - y = -2

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$275*.15(15%)=41.25 (this is the amount of the discount)

$275-$41.25=$233.75 (cost of jacket after discount)

$233.75* .0725=$16.946(round to $16.95, this is the amount of the sales tax).

If you want to know the total cost after tax just add $16.95 to the discounted price of $233.75. The price you pay for the jacket is $250.70.

Answer:

$16.95

Step-by-step explanation:

A department store is having a 15% off sale on all winter coats.

The cost of the winter coat that you purchased = $275

The price after discount of 15% = 275 -(15% × 275)

                                                    = 275 - (0.15 × 275)

                                                    = 275 - 41.25

                                                    = $233.75

Sales tax rate on that location = 7.25%

Sales tax which you would pay = 7.25% × 233.75

                                                    = 0.0725 × 233.75

                                                    = $16.9468 ≈ $16.95

You have to pay $16.95 sales tax.

Answer:

(x + 2)² + (y - 5)² = 7²

Step-by-step explanation:

Incomplete question.  I believe you meant, "write the equation of the circle with center at (-2, 5) and radius 7.

That would be:

(x + 2)² + (y - 5)² = 7²

The equation of the circle with center (-2,5) and radius 7 is (x+2)² + (y-5)² = 49.

The question is asking for the equation of a circle with center at (-2,5) and radius 7. The general equation for a circle is (x-h)² + (y-k)² = r², with (h,k) as the center and r as the radius. In this case, h = -2, k = 5, and r = 7, so substituting these into the equation gives us the solution:

(x-(-2))² + (y-5)² = 7², which simplifies to (x+2)² + (y-5)² = 49.

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Answer:

OPTION A

Step-by-step explanation:

The exponential growth functions has the following form:

[tex]y=a(b)^x[/tex]

Where "a" is the principal coefficient and  "b" is the base greater than 1.

To know which of the functions shown has exponential growth, identify which one has a base greater than 1.

[tex]\frac{4}{3}=1.33>1[/tex]

Therefore, the exponential growth function is the function shown in the option A.

The answer is:

The correct answer is:

A) [tex]y=(\frac{4}{3})^{x}[/tex]

To identify which of the given functions is an exponential growth function, we need to remember the form of the exponenial growth or decay functions.

We can define the exponential growth or decay function by the following way:

[tex]P(x)=y=StartValue*(rate)^{x}[/tex]

Where,

P(x) or y, is the function

Start value is the starting amount or value

Rate, is the growth or decay rate

x, is the variable (time)

Now, we can identify if the function is a exponential growth or decay function by the following way:

If [tex]rate>1[/tex] the function is an exponential growth function.

If [tex]rate<1[/tex] the function is an exponential decay function.

Now, we are given the function first function, A)

[tex]y=(\frac{4}{3})^{x}[/tex]

Where,

[tex]rate=\frac{4}{3}=1.33[/tex]

and we have that:

[tex]rate>1\\1.33>1[/tex]

So, the function is an exponential growth function.

Hence, the correct answer is:

A) [tex]y=(\frac{4}{3})^{x}[/tex]

Have a nice day!

The probability that a student doesn't have lice, given that the student tested negative is 99.40%.

Correct option is (D).

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

As per the given diagram:

The probabilities of different events is given in the diagram.

Probability that a student doesn't have lice, given that the student tested negative P(B):

[tex]\frac{P(Test \: shows \: negative) \times P(Student \:has\: no\: lice)}{P(Test\: shows \:negative) \times P(Student\: has\: no\: lice) + P(Test\: shows\: positive) \times P(Student\: has\: no\: lice)}[/tex]

= [tex]\frac{0.94 \times 0.72}{0.94 \times 0.72 + 0.06 \times 0.72}[/tex]

= 0.994

Which is equal to 99.40%

Hence, the probability that a student doesn't have lice, given that the student tested negative is 99.40%.

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Answer: y= -6

Step-by-step explanation:

because you know the slope is 0, you simply plug in from there

y=mx+b

y=0x (no slope) -6 (where it intersects the y axis)

y= -6

The answer is:   " y = - 6 " .

_________________________________________________

Step-by-step explanation:

_________________________________________________

To start, We find the equation of the given line ;  (in "blue" ; within the "image attached");

in the slope-intercept form:  

  " y = mx + b " ;

in which:

   "m = the slope = 0 " ; since there is no "slope";

   "b" = the "y-intercept" ;  or more precise, the value of the "y-coordinate" of the [point of the "y-intercept" — that is; the point at which the graph crosses the "y-axis" .].

    Note:  From the graph shown (Refer to image attached);  the "y-intercept" is:  " (0, 4) " ;  

    As such:  " b = 4 " .

_____________________________

So,  the equation;  in "slope intercept format" ; that is:  " y = mx + b " for the original line;  is:   "y = 0x + 4 " .

Let us simplify this equation:

    " y = 0x + 4 " ;    Note:  " 0x = 0 " ;

      {since:  "0" ; multiplied by "any value" ;  results in:  "0" .}.

_____________________________

We are are left with " y = 4 " ;  

_____________________________

Now, we are asked to find the equation of the line that is "parallel" to this line and that passes through the point:  " (-4, 6) ".

If such a line is "parallel" to the original line, the slope would be the same, which is "0" .

So, " y = 0x + b" ;

_____________________________

Also, note the formula:

 y - y₁  = m(x - x₁) ;

in which we consider the point:  " (- 4, - 6) " ;

 in which:  " y₁ = -6 " ;  and:  " x₁ = -4 " ;

→  y - (-6) = m (x - (-4)) ;

→  y + 6  = m (x + 4) ;

Note:  " m = 0" ;

  So;  " m(x + 4) " =  (0)* (x + 4) = "0" ;  

      {since:  "0" ; multiplied by "any value" ;  results in:  "0" .}.

→  We have:

    y + 6 = 0 ;  

→ Let us subtract "6" from each side of the equation;

          to isolate "y" on one side of the equation;

          & to write the equation for the 'perpendicular line' ; as follows:

→   y + 6 - 6 = 0 - 6 ;

to get:  

→   y  =  - 6  ;

____________________________________________

The answer is:   " y = - 6 " .

____________________________________________

Hope this helps!

    Wishing you the best in your academic endeavors

             — and within the "Brainly" community!

____________________________________________

Answer:

If the function is [tex]y=\sqrt{x+6} -7[/tex] , the domain are all values of x  greater than or equal to -6

If the function is [tex]y=\sqrt{x+6-7}[/tex] , the domain are all values of x  greater than or equal to 1

Step-by-step explanation:

First case

we have

[tex]y=\sqrt{x+6} -7[/tex]

we know that

The radicand  of the function must be greater than or equal to zero

so

[tex]x+6 \geq 0[/tex]

[tex]x\geq-6[/tex]

the solution is the interval---------> [-6,∞)

therefore

The domain are all values of x  greater than or equal to -6

Second case

we have

[tex]y=\sqrt{x+6-7}[/tex]

so

[tex]y=\sqrt{x-1}[/tex]

we know that

The radicand  of the function must be greater than or equal to zero

so

[tex]x-1 \geq 0[/tex]

[tex]x\geq 1[/tex]

the solution is the interval---------> [1,∞)

therefore

The domain are all values of x  greater than or equal 1

356,000 would be the answer I believe

Answers:

4668.

Step-by-step explanation:

355790

3 +1 5 +1 5 +1 7+1 00

466800

=4668

well, do a payments table of values, just like before for each mont hmm let's see

1st month.......................3500 + p(1)

2nd month....................3500 + p(2)

3rd month.....................3500 + p(3)

4th month.....................3500 + p(4)

5th month.....................3500 + p(5)

36th month..................3500 + p(36)

[tex]\bf \stackrel{\textit{total value}}{17900}=\stackrel{\textit{down payment}}{3500}+\stackrel{\stackrel{\textit{payments for}}{\textit{36 months}}}{36p} \\\\\\ 14400=36p\implies \cfrac{14400}{36}=p\implies 400=p[/tex]

Answer:

6

Step-by-step explanation:

Q1 is 3, Q2 is 5, Q3 is 6, which is the upper quartile.

Answer:

√(A/4π) = r

Step-by-step explanation:

A = 4πr²

r² = A/4π

r = √(A/4π)

Answer:

r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

Step-by-step explanation:

Given

A = 4πr² ( isolate r² by dividing both sides by 4π )

r² = [tex]\frac{A}{4\pi }[/tex]

Take the square root of both sides

r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

Answer:

The probability is  0.977

Step-by-step explanation:

We know that the average [tex]\mu[/tex] is:

[tex]\mu=500[/tex]

The standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=100[/tex]

The Z-score is:

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

We seek to find

[tex]P(x>300)[/tex]

The Z-score is:

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

[tex]Z=\frac{300-500}{100}[/tex]

[tex]Z=-2[/tex]

The score of Z = -2 means that 300 is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 1 deviations from the mean has percentage of  2.35% for Z<-2

So

[tex]P(z>-2)=1-P(Z<-2)[/tex]

[tex]P(z>-2)=1-0.0235[/tex]

[tex]P(z>-2)=0.9765[/tex]

Final answer:

The probability of a randomly chosen exam score being above 300, given a normal distribution with a mean of 500 and a standard deviation of 100, is approximately 97.5%.

Explanation:

To find the probability that a randomly chosen exam score is above 300 on a college entrance exam with a mean score of 500 and a standard deviation of 100, we first calculate the z-score. A z-score is a measure of how many standard deviations an element is from the mean. Using the formula z = (X - \\(mu\\))/\\(sigma), where X is the score, \\(mu\\) is the mean, and \\(sigma\\) is the standard deviation, we get:

z = (300 - 500) / 100 = -2.

The z-score of -2 means the score is 2 standard deviations below the mean. The symmetry of the normal curve and the empirical rule tell us that approximately 95% of the scores lie within 2 standard deviations of the mean, or between 300 and 700 in this case. Given that 95% of the scores are between 300 and 700, and the curve is symmetrical, we find that roughly 2.5% of the scores are below 300. Therefore, the probability of a score being above 300 is 100% - 2.5% = 97.5%.

Answer: -0.52

Step-by-step explanation:

From the given scatter plot, it can be seen that there is a moderate negative correlation between the variables as variable X increases variable Y decreases.

i.e. the value of correlation coefficient must be negative.

Also, the value of weak correlation coefficient r, lies between the absolute value of 0.40 to 0.59.

From all the given options -0.52  is the value which is contained in interval  0.40 to 0.59 .

Therefore, the best estimate of the correlation coefficient for the variables in the scatter plot = -0.52

You would need to add 0.25 from t to get the number of hours ( this would be the total number of hours she has raced) and then multiply that by her speed.

The equation would be d = 35(t+0.25)

Answer:

Step-by-step explanation:

Givens

Formula

V = (a * b)/2  * h

Solution

V = (10 * 11)/2   * 10

V = 110/2  * 10

V = 55 * 10

V = 550

For this case we have that by definition, the volume of the prism shown is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

[tex]A_ {b} = \frac {b * h} {2}[/tex]

Where:

b: It is the base of the triangle

h: It's the height of the triangle

Substituting the values:

[tex]A_ {b} = \frac {10 * 11} {2}\\A_ {b} = 55 \ cm ^ 2[/tex]

Then, the volume is:

[tex]V = 55 * 10\\V = 550 \ cm ^ 3[/tex]

ANswer:

550

Answer:

49b^2 -36 = (7b -6)(7b +6)

so because there you missed some signs in these wrote choices  

hope helped  

Step-by-step explanation:

Answer:

[tex](b+1)^2(b+6)[/tex]

Step-by-step explanation:

The given rational expression is:

[tex]\frac{b}{b^2+2b+1}-\frac{6}{b^2+7b+6}[/tex]

We factor the denominators to get:

[tex]\frac{b}{(b+1)^2}-\frac{6}{(b+1)(b+6)}[/tex]

The least common denominator is the product of the highest powers of the common factors of the denominators.

Therefore the least common denominator is:

[tex](b+1)^2(b+6)[/tex]

b and c is the answer .

Number 7 - Second answer

Number 8 - Third answer

Answer:

2x < 600 or x < 300

Step-by-step explanation:

x = Johnny's current amount of records.

Answer:

Hence final answer is [tex]x \leq -3[/tex] or [tex]2 \leq x<7[/tex]

correct choice is A because both ends are open circles.

Step-by-step explanation:

Given inequality is [tex]\frac{x^2+x-6}{x-7}\leq 0[/tex]

Setting both numerator and denominator =0 gives:

[tex]x^2+x-6=0[/tex],  x-7=0

or  [tex](x+3)(x-2)=0[/tex],  x-7=0

or x+3=0, x-2=0,  x-7=0

or x=-3, x=2,  x=7

Using these critical points, we can divide number line into four sets:

[tex](-\infty,-3)[/tex], (-3,2), (2,7), [tex](7,\infty)[/tex]

We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.

Test for [tex](-\infty,-3)[/tex].

Clearly x=-4 belongs to [tex](-\infty,-3)[/tex] interval then plug x=-4 into [tex]\frac{x^2+x-6}{x-7}\leq 0[/tex]

[tex]\frac{(-4)^2+(-4)-6}{(-4)-7}\leq 0[/tex]

[tex]\frac{6}{-11}\leq 0[/tex]

Which is TRUE.

Hence [tex](-\infty,-3)[/tex] belongs to the answer.

Similarly testing other intervals, we get that only [tex](-\infty,-3)[/tex] and [tex](2,7)[/tex] satisfies the original inequality.

Hence final answer is [tex]x \leq -3[/tex] or [tex]2 \leq x<7[/tex]

correct choice is A because both ends are open circles.

The surface area of the smaller solid will be 144 m².

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The volumes of two similar solids are 1,331 m² and 216 m². The surface area of the larger solid is 484 m².

The sides length  will be

a³ = 1331

 a = 11 m

Then the surface area will be

SA = 4(11²)

SA = 484 m²

Then the surface area of the smaller solid will be

Let x be the surface area of the smaller solid. Then we have

b³ = 216

 b = 6 m

Then the surface area will be

x = 4 (6²)

x = 144 m²

Thus, the correct option is C.

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Answer:

The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2

Step-by-step explanation:

In the real world, length and width only make sense when they are positive. For that to be the case, the width must be greater than 2. There is nothing in the description that restricts the values to integers.

Answer:

C) the mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2

Step-by-step explanation:

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{8.4\times 8.4}{70.56}\\ h\approx& 8.6 \end{cases}\implies V=\cfrac{1}{3}(70.56)(8.6) \\\\\\ V=202.272\implies \stackrel{\textit{rounded up}}{V=202.3}[/tex]

Answer:

The value of P( A and B ) is 0.08.

Step-by-step explanation:

When two events are independent then the probability of both occurring is equal to the product of probabilities of both events individually,

That is, If X and Y are independent events,

Then, P(X∩Y) = P(X) × P(Y),

or P(X and Y) = P(X) × P(Y),

Here, P(A) = 0.40 and P(B) = 0.20,

Hence, P(A∩B) = P(A) × P(B)

= 0.40 × 0.20

= 0.08

The value of [tex]\( P(A \text{ and } B) \)[/tex] is 0.08. So option(a) is correct.

To determine[tex]\( P(A \text{ and } B) \)[/tex] for two independent events ( A ) and ( B ) with given probabilities ( P(A) = 0.40 ) and ( P(B) = 0.20 ), follow these steps:

Step 1: Understand the Concept of Independence

For independent events, the probability of both events occurring together (the intersection of A and B, denoted as [tex]\( P(A \cap B) \))[/tex] is the product of their individual probabilities.

Step 2: Apply the Independent Event Formula

Since (A ) and (B ) are self-contained,

[tex]P(A) \times P(B) = P(A \cap B)[/tex]

Step 3: Substitute the Given Probabilities

Insert the given probabilities [tex]\( P(A) = 0.40 \)[/tex] and [tex]\( P(B) = 0.20 \)[/tex] into the formula:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 \][/tex]

Step 4: Perform the Multiplication

Calculate the product of 0.40 and 0.20:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 = 0.08 \][/tex]

Step 5: Interpret the Result

The probability that both events ( A ) and ( B ) occur is 0.08.

Therefore, the correct answer is (a) 0.08.

Complete Question:

A and B are independent events. P(A)=0.40 and P(B)=0.20 . What is P(A and B) ?

A. 0.08

B. 0.60

C. 0

D. 0.80

ANSWER

y=x+5

EXPLANATION

We can observe the following pattern among the x and y-values.

9=4+5

12=7+5

18=13+5

22=17+5

24=19+5

Hence, in general, the function rule is

y=x +5

Answer: Third option.

Step-by-step explanation:

You need to substitute a value of "x" (input value) provided in the table into each function and observe in the value of "y" obtained (output value) matches with the coorresponding output value shown in the table.

For [tex]x=4[/tex]

First option:

[tex]y = 5x\\y = 5(4)\\y=20[/tex]

Second option:

 [tex]y = x + 3\\y = 4 + 3\\y=7[/tex]

Third option:

 [tex]y = x + 5\\y = 4 + 5\\y=9[/tex]

(This one matches with the function table)

Fourth option:

 [tex]y = 3x\\y = (3)(4)\\y=12[/tex]

Then the answer is: [tex]y = x + 5[/tex]

ANSWER

B. 4

EXPLANATION

The numbers on the first die are;

{1,2,3,4,5,6}

The numbers on the second die are;

{1,2,3,4,5,6}

The events of getting a sum of 5 are

2+3

3+2

1+4

4+1

There are four events.

The correct choice is B .