The heights of the adults in one town have a bell-shaped distribution with a mean of 67.5 inches and a standard deviation of 3.4 inches. Based on the empirical rule, what should you predict about the percentage of adults in the town whose heights are between 57.3 and 77.7 inches?

Answer:

  x = -5, x = -6

Step-by-step explanation:

After canceling common terms from numerator and denominator, there are two factors remaining in the denominator that can become zero. The vertical asymptotes are at those values of x.

[tex]\displaystyle F(x)=\frac{x\frac{2x}{2}}{x(x+5)(x+6)}=\frac{x}{(x+5)(x+6)}[/tex]

The denominator will be zero when ...

  x + 5 = 0 . . . . at x = -5

  x + 6 = 0 . . . . at x = -6

Answer:

14,740

Step-by-step explanation:

The mean of a set of data is another way of saying the average

To find the average you find the sum of all the numbers/amount of numbers

In this case it would be 221,100/15

Answer:

x = 2.4

Step-by-step explanation:

To find the value when f(x) = x, you just have to replace f(x) for x

[tex]f(x) =-\frac{1}{4}x +3 \\x = - \frac{1}{4}x +3 \\x +\frac{1}{4}x=3 \\\frac{5}{4} x= 3 \\ x = 3*\frac{4}{5} \\x = 2.4[/tex]

Answer:

The two clock will chime together in 75 minutes

Step-by-step explanation:

- Two clocks are turned on at the same time

- One clock chimes every 15 minutes

- The other clock chimes every 25 minutes

- We need to know in how many minutes they will chime together

- The two clock will chime together in the multiples of 15 and 25

- Lets find the first common multiple of 15 and 25

∵ 15 = 5 × 3

∴ The prime factors of 15 are 3 and 5

∵ 25 = 5 × 5

∴ The prime factor of 25 is 5

∴ The lowest common multiple of 15 and 25 = 5 × 3 × 5 = 75

∴ The two clocks will chime together every 75 minutes

The two clock will chime together in 75 minutes

Answer:

Step-by-step explanation:

Look at the picture.

The lines l and m are parallel, therefore alternate interior angles are congruent.

Therefore [tex]\beta=50^o[/tex]

Supplementary angles add up to 180°.

Therefore

[tex](5x-16)+\theta=180[/tex]          add 16 to both sides

[tex]5x+\theta=196[/tex]         subtract 5x from both sides

[tex]\theta=196-5x[/tex]

We know: the sum of the triangle angle measures is 180°.

Therefore we have the equation:

[tex]50+2x+196-5x=180\\\\-3x+246=180\qquad\text{subtract 246 from both sides}\\\\-3x=-66\qquad\text{divide both sides by (-3)}\\\\x=22[/tex]

Westbound boats speed = X

Southbound boats speed = X + 5

In 3 hours they are 27 miles apart:

3X + 3(x+5) = 27

Simplify:

3x + 3x +15 = 27

Combine like terms:

6x + 15 = 27

Subtract 15 from both sides:

6x = 12

Divide both sides by 6:

x = 12/6

x = 2

Westbound was 2 miles per hour

Southbound was 2 +5 = 7 miles per hour

Check:

2 miles per hour x 3 hours = 6 miles

7 miles per hour x 3 hours = 21 miles

21 + 6 = 27 miles

Answer:

The demand equation is: D=-4p+23

Step-by-step explanation:

To get started, we should keep in mind that the market price (p=3) occurs when supply equals demand ,therefore when p=3

S=2(3)+5=11

Thus, when p=3 D=11 and, according to the problem  when p=1 D=19.

We already know two points on the demand curve. Great!

The demand equation is linear, so it has form D=bp+c.

The variable b is the slope of  the demand linear equation . It can be computed through the formula

[tex]b=\frac{y2-y1}{x2-x1}[/tex].  equation 1

Substituting the two points (3,11) and (1,19) on equation 1.

[tex]b=\frac{19-11}{1-3} =\frac{8}{-2}[/tex]

b=-4

Now we can find the value of  intercept of the demand equation c trough point-slope form y-y1=b(x-x1).

We can use any of the points. Let's take (3,11) and write in point-slope :

y-11=-4(x-3)

y=-4x+11+12

y=-4x+23

Rewrite the linear equation according our variables D and p

D=-4P+23

Finally we found the demand equation !

Answer: [tex]\frac{3}{8}\ kg[/tex]

Step-by-step explanation:

The table attached is part of the exercise (Without the table the question was incomplete).

We know that the cost of 1 kilogram of Chihuahua cheese is 78 and the Chihuhua cheese bought the day before cost 195.

The first step is to calculate the amount of cheese bought with 195:

[tex]\frac{195}{78}=\frac{5}{2}\ kg[/tex]

Now, we need to add the fractions provided in the table (This table shows the amount of cheese that was used in that day). Then:

[tex]\frac{1}{2}\ kg+\frac{7}{8}\ kg+\frac{3}{4}\ kg=\frac{17}{8}\ kg[/tex]

Finally, in order to find what fraction of Chihuahua cheese is left, we must subtract [tex]\frac{5}{2}\ kg[/tex] and [tex]\frac{17}{8}\ kg[/tex]:

[tex]\frac{5}{2}\ kg-\frac{17}{8}\ kg=\frac{3}{8}\ kg[/tex]

Answer:

5/8 after subtraction :)

Step-by-step explanation:

Answer:  The answer is:  62.5 % (left over).

______________________________________________

Step-by-step explanation:

______________________________________________

[tex]\frac{1}{4} + \frac{1}{8} = ?[/tex]   ;  

Change "(1/4)" to: "(?/8)" ;

What is "(?)" ?  ;

→  (1/4) = (?/8) ;

notice the denominators;

(1/4) = (?/8) ;  In the first fraction, how does the "denominator", "4" ;  turn to "8" ?   Specifically, since we dealing with "fractions", what number do we multiply "4" by, to get:  "8" ??? ;

→  " 4  * ? = 8 " ?? ;

→  " 8 ÷ 4 = ? " ;

               = 2 ;

______________________________________________

so  " 1/4 = ?/8 " ;

Since we multiply the denominator, "4" ;  by "2" , to get:  

                     "8" (the denominator in the other fraction);  

we multiply the numerator, "1" ; by "2" ; to get:

                     "2" (the denominator in the other fraction):

______________________________________________

   →  " [tex]\frac{1}{4} = \frac{(1*2)}{(4*2)} = \frac{2}{8}[/tex] ;

______________________________________________

Now, the amount of the pizza that "you" ate is:  "(2/8)" ;

The amount of the pizza eaten by "your dog" is: "(1/8)" ;

Let's add up the amount of pizza eaten:

[tex]\frac{2}{8} + \frac{1}{8}  = \frac{(2+1)}{8} = \frac{3}{8}[/tex] .

The total amount of the pizza would be:  " [tex]\frac{8}{8}[/tex] " .

Note:  " [tex]\frac{8}{8}[/tex] = 8 ÷ 8 = 1 whole [pizza].

To find the amount left over,  subtract the amount eaten; "(3/8)" ; from the whole pizza; "(8/8)" ; as follows:

______________________________________________

   →  [tex]\frac{8}{8} - \frac{3}{8} = \frac{(8-3)}{8} = \frac{5}{8}[/tex] .

______________________________________________

Now, the question asks, what percent is left over? ;

So, we convert "(5/8)" into a percentage;

Change "(5/8)" to: "(?/100)" ;

  →  Notice the denominators;

(5/8) = (?/100) ;  In the first fraction, how does the "denominator", "8" ;  turn to "100" ?   Specifically, since we dealing with "fractions", what number do we multiply "8" by, to get:  "100" ??? ;

→  " 8  * ? = 100 " ?? ;

→  " 100 ÷ 8 = ? " ;

                  = 12.5 ;

______________________________________________

so  " 5/8 = ?/100 " ;

Since we multiply the denominator, "8" ;  by "12.5" , to get:  

                     "100" (the denominator in the other fraction);  

we multiply the numerator, "5" ; by "12.5" ; to get:

                     "2" (the denominator in the other fraction):

______________________________________________

   →  " [tex]\frac{5}{8} = \frac{(5*12.5)}{(100*12.5)} = \frac{62.5}{100}[/tex] ;

______________________________________________

   →  [tex]\frac{62.5}{100} = 62.5 % .

______________________________________________

Hope this helpful to you!

       Wishing you the best!

______________________________________________

Answer:

540 feet

Step-by-step explanation:

225x(8/5)

360 feet in 1 hour

6 feet in 1 minute

540 feet in 90 minutes

The equivalent expressions of the given expressions is 540 feet in 90 minutes.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

The expression of 225 divided by 5/8 as 225 x 8/5.

225 x (8/5)

So, the quotient says a sloth may move 360 feet in 1 hour.

360 feet in 1 hour

Then, 6 feet in 1 minute

90 minutes as 1 1/2 hour.

Multiply by 1 1/2 to get feet in 90 minutes.

540 feet in 90 minutes

The equivalent expressions of the given expressions is 540 feet in 90 minutes.

Learn more about expression here;

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Answer:

Step-by-step explanation:

There are 5 green marbles among the 10 in the bag, so the probability of drawing one at random is 5/10 = 0.50.

The odds in favor of drawing a green marble will be the ratio of the number of green marbles to the number that are not green: 5 : 5. Usually, the odds are expressed using integers with no common factors, so they would be written as 1 : 1.

Answer:

Step-by-step explanation:

SOH CAH TOA can remind you of the relationships between triangle measures. The distance east is the side of the right triangle that is opposite the angle, so is related to the hypotenuse (ship's travel distance) by the sine function.

  sin(43°) = (travel distance)/(distance east)

So, ...

  (distance east) = (travel distance)·sin(43°)

Likewise, the cosine function can be used to find the distance south.

Then we have ...

  east = (130 km)sin(43°) ≈ 95 km

  south = (130 km)cos(43°) ≈ 89 km

Answer:

20 months

Step-by-step explanation:

Let x be the number of months. The cost  equation for each dealer is the total of the down payment and the total monthly contribution. Thus,

Deal 1 cost = $2,350 + $175x

Dealer 2 cost =$2,850 + $150x

The number of months after which the costs from both dealers are equal is calculated by equating the costs for both dealers. Therefore,

$2,350 + $175x = $2,850 + $150x

$175x -$150x =$2,850 -$2,350

   $25x =$500

        x= $500/$25

         x = 20 months

Answer:

Step-by-step explanation:

independent quantity=60 m/h

dependent =time taken=t

60 t=325

t=325/60=65/12=5 5/12 hours

Answer:

  A = 7

  B = 2

Step-by-step explanation:

The question is asking for the simplified form of √(-98). You are expected to know that √-1 = i, and you are expected to be able to factor the number 98.

[tex]\sqrt{-98}=\sqrt{(-1)(7^2)(2)}=7i\sqrt{2}[/tex]

Matching parts of the simplified expression to the form you are given, you see that ...

  A = 7

  B = 2

Answer:

D

Step-by-step explanation:

((p^4*q)/p^8)^2.

p^4/p^8=p^(4-8)=p^-4=1/p^4

(q/p^4)^2=(q^2/p^8)

To simplify an algebraic expression, eliminate denominators, distribute factors, rearrange and combine like terms, and isolate the variable. Checking the reasonableness of the answer is also important after simplification.

To simplify an algebraic expression or equation involving variables, you should first look at what needs to be solved for and then work the problem out using only variables. This helps in minimizing calculation time and reducing the chance of errors. Here are some steps to simplify algebraic expressions:

Additionally, by variable rescaling and setting some limits for the error margin, you can further simplify the algebra by eliminating as many parameters as possible. Always check your final answer to ensure it's reasonable.

Answer:

We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489

Step-by-step explanation:

This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.

However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.

Observe that:

Line segment AB - b) AB with a line above it.

Ray AB - c) AB with a line above it going only left.

The length of line segment AB - a) AB

Line AB - d) AB with a line with both arrows on either side.

To match the given terms with the correct letter options, let's define each term and find its corresponding notation:

These notations are crucial in geometry to clearly communicate different types of lines and measurements.

Answer:

30%

Step-by-step explanation:

27 over 90 is equal to 0.3 in decimal form, turn that into percentage by multiplying by 100, and you get 30%

Answer: x-10

Since you're finding the difference of a number, x, and 10, you would do x-10.

Final answer:

The variable expression for "the difference between a number and 10" is represented by x − 10, which implies the subtraction of 10 from a variable x.

Explanation:

The phrase "the difference between a number and 10" as a variable expression is represented by x − 10. When we discuss 'the difference' in mathematical terms, we are referring to the result of subtracting one number from another. Here, whatever the unknown number (represented by the variable x) is, we are subtracting 10 from it.

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is:

(n-2)*180

where n = number of sides

Here you have :

(5 - 2)*180 = 540°

Answer:

Option c)  $78,250 unfavorable

Step-by-step explanation:

The given information in the question :

Standard cost = $810,000

Actual cost = $888,250

Cost variance can be calculated as using the following formula :

Cost variance = standard cost - actual cost

                       = 810,000 - 888,250

                       = ($78,250) unfavorable

Favorable indicates how much under budget the project.

unfavorable indicates how much over budget the project.

Therefore, Option c) 78,250 unfavorable is the answer.

Answer:

Step-by-step explanation:

(a) If we let k = f(m), we can solve for m to find f⁻¹(k).

  k = 1.609344m

  k/1.609344 = m = f⁻¹(k)

__

(b) Since k is the number of kilometers in m miles, m is the number of miles in k kilometers.

__

In summary ...

  (a) f⁻¹(k) = k/1.609344

  (b) f⁻¹(k) is the exact number of miles in k kilometers

Answer:

The length of the patio is 32 ft and the width is 13 ft

Step-by-step explanation:

see the attached figure to better understand the problem

Let

L ----> the length of his patio

W ---> the width of his patio

we know that

[tex]L+2W=58[/tex] ----> equation A

[tex]L=2W+6[/tex] ----> equation B

substitute equation B in equation A and solve for W

[tex]2W+6+2W=58[/tex]

[tex]4W+6=58[/tex]

[tex]4W=58-6[/tex]

[tex]4W=52[/tex]

[tex]W=13\ ft[/tex]

Find the value of L

[tex]L=2W+6[/tex]  ----> [tex]L=2(13)+6=32\ ft[/tex]

therefore

The length of the patio is 32 ft and the width is 13 ft

The required patio length(L) = 32 and width(w) = 13.

Given that,

Wayne is hanging a string of lights 58 feet long,

And the side along the house, is 6 feet long.

We have to find,

The length and width of the patio.

According to the question,

Let, the length of his patio be L and width w,

Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house.

L + 2W = 58

And The length of his patio, the side along the house, is 6 feet longer than twice its width.

L = 2W + 6

Solving the equation putting the of L from equation 2 in equation 1,

= 2W + 6 + 2W = 58

= 4W = 58 - 6

= 4W = 52

= W = [tex]\frac{52}{4}[/tex]

= W = 13

And L = 2(13) + 6 = 32

Patio length(L) = 32 And width(w) = 13.

Hence , The required patio length(L) = 32 And width(w) = 13.

For the more information about Measurement click the link given below.

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Answer:

y = 50 - 7.5x

Step-by-step explanation:

Given,

The original area for painting = 50 m²,

Let c meter per hour be the constant rate of painting,

So, after 2 hours, the area painted = 2c m²,

Thus, the area left to paint = 50 - 2c

According to the question,

50 - 2c = 35

2c = 15

⇒ c = 7.5

i.e. the constant rate of painting is 7.5 meters per hour,

Hence, the area left after x hours = 50 - 7.5x

If y represents the area left to paint after x hours,

Then,

y = 50 - 7.5x

Which is the required equation.

Two complementary angles equal 90 degrees.

If one is 20, the larger one would be 90 - 20 = 70 degrees.

Answer:

Step-by-step explanation:

An  way  to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer: all real numbers greater than it equal to negative one.

Step-by-step explanation: if you graph this equation you see that the vertex is at (3,-1). We know that Range is all possible Y values.so, By looking at their graph we can see that the lowest point it touches is at -1. The rest of the graph goes off into positive and negative infinity.

Range= Y is greater than it equal to -1.

Answer:

All real numbers greater than or equal to −1

Step-by-step explanation:

Here, the given parabola,

[tex]f(x) = (x-4)(x-2)[/tex]

[tex]f(x) = x^2-4x-2x + 8[/tex]

[tex]f(x) = x^2 - 6x+8[/tex]

∵ Leading term = positive

So, the parabola is upward.

We know that an upward parabola is minimum at its vertex

Or it gives minimum output value at its vertex.

for instance, If (h, k) is the vertex of an upward parabola,

then its range = { x  : x ≥ k, x ∈ R }

Note : Range = set of all possible output values

We have given,

Vertex = (3, -1)

Hence, Range = all real numbers greater than or equal to −1

LAST option is correct.

Answer: You only have 5 samples, always when you want to do statistics, you need a large sample size.

let's suppose you throw a dice 5 times, the results that it shows are 1,4,2,1,4. If you make statistics whit that numbers, you will think that the 1 and 4 have a bigger possibility than the other numbers, but that can't be, if you throw the dice enough times you will se that all numbers have the same possibility.

Answer:

Step-by-step explanation:

Since we know that the height is 0, we can figure out how long it took the ball to reach the ground by setting [tex]f(x) = 0[/tex] and solving for [tex]x[/tex]:

[tex]f(x) = 16(x^{2} - 6x - 7)[/tex]

[tex]0 = 16(x^{2} - 6x - 7)[/tex]

[tex]0 = x^{2} - 6x - 7[/tex]

[tex]0 = (x - 7)(x + 1)[/tex]

[tex]x = -1, 7[/tex]

Because time can only be positive, the answer is 7 seconds.

Answer:

7 seconds.

Step-by-step explanation:

height h = 16(x^2-6x-7) = 0

x^2 - 6x - 7 = 0

(x - 7)(x + 1) = 0

x = 7 seconds (we ignore the negative).