The table shows the annual profits (in thousands of dollars) of a county fair from 2013 to 2016. What must the 2017 profit be (in hundreds of dollars) to break even over the five-year period?

Answer:

-14

Step-by-step explanation:

Observe first that $x=0$ is not a solution to the equation since it makes the denominator of $\frac{1}{2x}$ equal to 0. For $x\neq 0$, we may multiply both sides by both denominators and move all the resulting terms to the left-hand side to get $2x^2-2rx+7=0$. Observe that there are two ways the original equation could have exactly one solution. Either $2x^2-2rx+7=0$ has two solutions and one of them is 0, or else $2x^2-2rx+7=0$ has exactly one nonzero solution. By trying $x=0$, we rule out the first possibility.

Considering the expression $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ for the solutions of $ax^2+bx+c=0$, we find that there is exactly one solution if and only if the discriminant $b^2-4ac$ is zero. Setting $(-2r)^2-4(2)(7)$ equal to 0 gives $4r^2-4(14) = 0$. Add 4(14) and divide by 4 to find $r^2=14$. The two solutions of this equation are $\sqrt{14}$ and $-\sqrt{14}$, and their product is $\boxed{-14}$.

The value of r from the given equation is r=(2x²+7)/2x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is [tex]\frac{1}{2x}=\frac{r-x}{7}[/tex].

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

By cross multiplication, we get

7=2x(r-x)

7=2rx-2x²

2rx=7+2x²

r=(2x²+7)/2x

Therefore, the value of r from the given equation is r=(2x²+7)/2x.

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Answer:

128

Step-by-step explanation:

3a² - 4b

plug in values

3(-6)² - 4(-5)

use PEMDAS and simplify (-6)² first

3(36) -4(-5)

multiply

108 + 20

add

128

hope this helps :)

Answer:

b=13

Step-by-step explanation:

2|208

2|104

2|52

2|26

 |13

208=2^4×13=16×13

now (16,13)=1

as a is an even number so a=16

b=13

∵g.c.d of 16 and 13=1

or (16,13)=1

Answer:

a)45min

b)900min

Step-by-step explanation:

We were told that it takes Matt 3 minutes to read one page in a book.

It implies that 3minutes = 1page of the book

Then he continues to read at the same pace, he can read 15 similar pages in minutes.

a)Then, he can read 15 similar pages in

15x3 minutes.which is 45minutes.

b)Then if the book has 300 pages, it will take him. 300×3 minutes to read it.which is 900mins

Answer: has anyone seen my dad?

Answer:

(I) 17.25 miles

(ii) 1hr56mins20seconds

(III) 4hrs47mins38seconds

Step-by-step explanation:

(I) read from the lowest distance given

(ii) read from the longest time given

(III) added all times together to get total cycling time

Step-by-step explanation:

here,

shortest distance is 17.25 miles

the longest time is 1:56:20 hrs:mins:secs

total time is 4:47:38

Complete Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

Answer:

The  95%  confidence interval is  [tex]0.2392 < p < 0.3108[/tex]

No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25%

Step-by-step explanation:

From the question we are told that

  The total sample size is  [tex]n = 432 + 164 =596[/tex]

   The  number of  offspring that is yellow peas is [tex]y = 432[/tex]

   The  number of  offspring that is green peas   is [tex]g = 164[/tex]

The sample proportion for offspring that are yellow peas is mathematically evaluated as

        [tex]\r p = \frac{ 164 }{596}[/tex]

        [tex]\r p = 0.275[/tex]

Given the the  confidence level is  95% then the level of significance is mathematically represented as

       [tex]\alpha = (100 - 95)\%[/tex]

      [tex]\alpha = 5\% = 0.0 5[/tex]

The  critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

      [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p )}{n} }[/tex]

=>      [tex]E = 1.96 * \sqrt{\frac{0.275 (1- 0.275 )}{596} }[/tex]

=>      [tex]E = 0.0358[/tex]

The  95%  confidence interval is mathematically represented as

      [tex]\r p - E < p < \r p + E[/tex]

=>   [tex]0.275 - 0.0358 < p < 0.275 + 0.0358[/tex]

=>   [tex]0.2392 < p < 0.3108[/tex]

Answer:

(90/60)*36 = 54 km

Step-by-step explanation:

Answer:

sqrt(30)+sqrt(50) = 12.5482933869171364     which is between   m and n    12 and 13

Answer:

  (a)  (x -3)^2 = -6(y +5.5)

Step-by-step explanation:

The equation of a parabola can be written as ...

  (x -h)^2 = 4p(y -k)

where (h, k) is the vertex, and p is the distance from the focus to the vertex.

The vertex is half-way between the focus and directrix, so is ...

  (h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)

The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...

  -7 -(-5.5) = -1.5

Then the equation for the parabola is ...

  (x -3)^2 = 4(-1.5)(y -(-5.5))

  (x -3)^2 = -6(y +5.5) . . . . matches the first choice

Answer:

Malcom's maximum speed = 200 km/h

Ravi's maximum speed = 320 km/h

Step-by-step explanation:

Let m = Malcom's maximum speed

Let r = Ravi's maximum speed

Average of their maximum speed would be represented as [tex] \frac{m + r}{2} = 260 [/tex]

[tex] m + r = 520 [/tex].

Make m the subject of the formula by subtracting r from both sides:

[tex] m = 520 - r [/tex]. Let this be equation 1.

Given that Malcom's speed (m), when doubled is 80 km/h more than that of Ravi (r). This can be expressed as: [tex] 2m = r + 80 [/tex]. This is equation 2.

Plug in (520 - r) into equation 2 to replace m:

[tex] 2(520 - r) = r + 80 [/tex]

[tex] 1040 - 2r = r + 80 [/tex]

Solve for r. Subtract 1040 from both sides:

[tex] 1040 - 2r - 1040 = r + 80 - 1040 [/tex]

[tex] - 2r = r - 960 [/tex]

Subtract r from both sides

[tex] - 2r - r = r - 960 - r [/tex]

[tex] - 3r = - 960 [/tex]

Divide both sides by -3

[tex] \frac{-3r}{-3} = \frac{-960}{-3} [/tex]

[tex] r = 320 [/tex]

To find m, plug in the value of r into equation 1.

[tex] m = 520 - r [/tex]. =>Equation 1

[tex] m = 520 - 320 [/tex]

[tex] m = 200 [/tex].

Malcom's maximum speed = m = 200 km/h

Ravi's maximum speed = r = 320 km/h

Answer:

the sign is positive

Step-by-step explanation:

to negatives make a positive.

and that last point you added is wrong two positives equals a positive.

different signs= negative

same signs=positive

Answer:

[tex] 9.3 + b = 14.5 [/tex]

Step-by-step explanation:

Longest side of ∆ = 2a = 6.2 cm

If the shortest side is, a, and we are told that the longest side is twice the shortest side, therefore, length of shortest side is

The sum of the 3 sides = perimeter = 14.5 cm

Thus,

[tex] a + 2a + b = 14.5 cm [/tex]

Plug in the values of a and b

[tex] 3.1 + 6.2 + b = 14.5 [/tex]

The equation that can be used to find the side lengths is [tex] 9.3 + b = 14.5 [/tex]

Answer:

Length = 3.2feets ; width = 6feets

Step-by-step explanation:

Given the following :

Actual dimension of Mural:

8feets by 15feets

Scale drawing ratio of Mural :

2feets : 5feets

This means :

2 Feets on paper equals 5 Feets of actual drawing:

Therefore, with actual dimension of Length = 8feets ;

Length of scale drawing = (2/5) * 8 = 3.2feets

Actual dimension of width 15feets ;

Width of scale drawing = (2/5) * 15 = 6 Feets

Answer:

Step-by-step explanation:

The standard from of equation of a line written in slope-intercept format is expressed as y = mx+c where c is the slope of the line and c is the y-intercept.

Given the equation of the line x+3y = 10, to get the slope of the line, we need write he equation in standard from first by making y the subject of the formula as shown;

[tex]x+3y = 10\\\\subtract\ x \ from \ both \ sides\\\\x+3y-x = 10 -x\\\\3y = -x+10\\\\Divide \ through\ by \ 3\\\\\frac{3y}{3} = -\frac{x}{3} +\frac{10}{3} \\\\[/tex]

[tex]y = -\frac{1}{3}(x) +\frac{10}{3} \\[/tex]

Comparing the resulting equation with y = mx+c, the slope 'm' of the equation is -1/3

The slope of the line is -1/3.

the correct option is D.

To find the slope of the line given by the equation x + 3y = 10, we need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope.

Let's rearrange the equation to solve for y:

x + 3y = 10

3y = -x + 10

y = (-1/3)x + 10/3

Comparing this equation to the slope-intercept form, we can see that the coefficient of x (-1/3) represents the slope.

Therefore, the slope of the line is -1/3.

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Answer:

Step-by-step explanation:

d is directly proportional to the square of a speed v

d = av²

5 = a•10²

5 = 100a

a = 0.05

d = 0.05v²

d = 0.05•70²

d = 0.05•4900

d = 245

Answer:

3 boxes with 4 sweets and 2 boxes with 5 sweets

Step-by-step explanation:

As per given, we have following equations:

x= 5- y as per the first equation, considering in second one:

Then:

So there 3 boxes with 4 sweets and 2 boxes with 5 sweets

Answer: 46.1 megabytes

Step-by-step explanation:

Answer:

x = -1.5

Step-by-step explanation:

16x - 5 = 18x -2

Subtract 16x from each side

16x-16x - 5 = 18x-16x -2

-5 = 2x-2

Add 2 to each side

-5+2 = 2x-2+2

-3 = 2x

Divide by 2

-3/2 = 2x/2

-3/2 =x

Answer:

-3/2

Step-by-step explanation:

To solve this problem, start by moving all of your x's on to one side, and all of your constants on to the other as such:

16x-5=18x-2

     +2       +2

16x-3=18x

-16x    -16x

-3=2x

-3/2 = x

P.S. please give me brainliest. Thank you! :)

Greetings from Brasil...

Here we will apply rule of 3...

This formula, A = πR²,  its for the whole circle, that is, 360° (2π)

We want the area of only a part, that is, a circular sector whose angle π/6

 sector           area            

    2π     -----    πR²

    π/6    -----     X

2πX = (π/6).πR²

2πX = π²R²/6

X = π²R²/12π

If Ronisha multiply the area by 1/12 she will get the area of sector with angle of π/6

Answer:

4.331507 x 10⁶

Step-by-step explanation:

you move the decimal place 6 times to the right, so 10⁶

Answer:

Step-by-step explanation:

4,331,507=4.331507×10^6

Answer:

25/4 laps or (6.25 laps)

Step-by-step explanation:

1 lap = 1 1/5 miles

kellyn plans to jog 7 1/2 miles

                                                      1  lap

number of laps = 7 1/2 miles x  --------------   = 25/4 laps or (6.25 laps)

                                                    1 1/5 miles

Answer:

Nina can run:

13 1/2 km in 1 hour

Step-by-step explanation:

4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2

proportions:

9/2 hours ⇔  1/3 hour

N hours ⇔ 1 hour

N = (9/2)*1 / (1/3)

N = (9/2) / (1/3)

N = (9*3) / (2*1)

N = 27/2

27/2 = 26/2 + 1/2 = 13 + 1/2 = 13 1/2

Nina can run:

13 1/2 km/h

13 1/2 km in 1 hour

Nina can run [tex]13\frac{1}{2}[/tex] km in an hour

The distance Nina can run in an hour can be determined by dividing the distance she can run in 1/3 of an hour by 1/3

Distance Nina can run in an hour = distance run ÷ [tex]\frac{1}{3}[/tex]

[tex]4\frac{1}{2}[/tex] ÷ [tex]\frac{1}{3}[/tex]

Convert the mixed fraction to an improper fraction [tex]\frac{9}{2}[/tex] × 3 = [tex]\frac{27}{2}[/tex]

Convert the improper fraction back to an mixed fraction = [tex]13\frac{1}{2}[/tex] km

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Answer:

A inch

Step-by-step explanation:

Answer:

once upon a time a dude went to a store. there was a dude jacket for 20% off.

Step-by-step explanation:

Now do the opposite. for exapmle, the price increased by 20 %.

Answer:

see below

Step-by-step explanation:

Multiplying the equation by 2x - 2 on both sides to cancel out the denominator gives us (x - 1)(x + 2)(x - 3)(x + 7)(x - 5) = 0. Using Zero Product Property and setting each factor to 0, we get:

x - 1 = 0 or x + 2 = 0 or x - 3 = 0 or x + 7 = 0 or x -  5 = 0

x = 1, x = -2, x = 3, x = -7, x = 5

Unfortunately, x cannot be 1 as the numerator would become 0 and then the expression on the left side would become undefined so the final answer is x = -2, x = 3, x = 7, x = 5.

Answer:

25000000

5000 X 10 is 50000

50000 X 10 is 500000

500000 X 50 is 25000000

Step-by-step explanation:

Answer:

25000000

Step-by-step explanation:

A way to tackle this is to split all the numbers up into a digit and a power of 10.

5000 = 5*1000, and 1000 can be written as 10^3

10 = 1*10, and obviously 10 is 10^1

50 = 5*10, where 10 is 10^1

Now we have (5*10^3) * (1 * 10) *(1 *10)*(5 *10)

Gathering all the digits, we have 5*1*1*5, giving us 25

Gathering all the powers of 10, we have 10^3*10*10*10 = 10^6

expanding and multiplying gives us the final answer of 25000000

By using PEDMAS rule, 7 + (5 – 9)2 + 3(16 ÷ 8) is  5.

PEDMAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, D- Division, M- Multiplication, A- Addition, and S- Subtraction.

Given

7 + (5 – 9)2 + 3(16 ÷ 8)

By using PEDMAS rule,

= 7 + (-4)2 + 3(2)

= 7 + (-8) + 6

= 7 - 8 + 6

= -1 + 6

= 5

By using PEDMAS rule, 7 + (5 – 9)2 + 3(16 ÷ 8) is  5.

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The solution of equation, 7 + (5 – 9)2 + 3(16 ÷ 8) is,

⇒ 29

Since, We knw that,

PEMDAS stands for P- Parentheses, E- Exponents, D- Division, M- Multiplication, A- Addition, and S- Subtraction.

We have to given that,

Expression is,

7 + (5 - 9)² + 3(16 ÷ 8)

Now, Simplify By using PEDMAS rule,

= 7 + (5 - 9)² + 3(16 ÷ 8)

= 7 + (-4)² + 3(2)

= 7 + 16 + 6

= 23 + 6

= 29

Thus, By using PEDMAS rule, 7 + (5 – 9)2 + 3(16 ÷ 8) is, 29

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Answer:

The answer is below

Step-by-step explanation:

The distance traveled the first day = Distance from San Jose to Santa Barbara = 320 mile.

The distance traveled the second day = Distance from Santa Barbara to Los Angeles.

But From San Jose to Los Angeles = 425 mile. Therefore:

Distance From San Jose to Los Angeles =  Distance from San Jose to Santa Barbara +  Distance from Santa Barbara to Los Angeles

425 = 320 +  Distance from Santa Barbara to Los Angeles.

Distance from Santa Barbara to Los Angeles = 425 - 320 = 105 mile

The distance traveled the second day = Distance from Santa Barbara to Los Angeles = 105 miles

The distance traveled the first day  + The distance traveled the second day = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles = 320 + 105 = 425 miles

The distance traveled the first day  + The distance traveled the second day = 425 miles

Answer:

2 teaspoons

Step-by-step explanation:

24 tsp/12 cups = x tsp /1 cup

Cross multiplying, we have:

12x = 24

x = 2

The solution is 2 teaspoons of cocoa

Number of teaspoons of cocoa is given by the equation A = 2 teaspoons

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of teaspoons of cocoa be represented as A

Now , the equation will be

A batch of hot chocolate is made with 24 teaspoons of cocoa and 12 cups of milk

So , for 12 cups of milk = 24 teaspoons of cocoa is required

And , for 1 cup of milk A = 24 teaspoons of cocoa is required / 12

Substituting the values in the equation , we get

Number of teaspoons of cocoa A = 24 teaspoons / 12

Number of teaspoons of cocoa A = 2 teaspoons

Therefore , the value of A is 2 teaspoons

Hence , the number of teaspoons is 2

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Answer:

  GH = 16; CH = 12

Step-by-step explanation:

First of all, you need to understand the meaning of "perpendicular bisector." It means that GH is divided into two equal parts by line AC, and that AC makes a right angle to GH.

The right angle is marked.

(a) The length of one of the halves of GH is marked as being 8 units long, so the other half will also be 8 units long. Of course, the length of GH is the sum of its two halves:

  GH = GB +BH = 8 + 8

  GH = 16

__

(b) Triangles CBG and CBH share side CB, so have that length in common. They have equal lengths BG and BH because BC bisects GH. They have a right-angle at B in common, so can be considered congruent by SAS, the fact that two congruent sides have a congruent angle between them.

Since triangles CBG and CBH are congruent, their corresponding sides CG and CH are also congruent. Side CG is marked 12 units long, so CH will be 12 units long, also.

  CH = 12

You could shortcut all of the congruent triangle logic by recognizing that an altitude (CB) is a perpendicular bisector of the base (GH) if and only if the triangle is isosceles. The sides of an isosceles triangle are always congruent, so CG = CH = 12.

__

In part (c), you're supposed to choose possible theorems for demonstrating the congruence of the triangles we described above.