The city of Austin is erecting a radio tower to boost cell phone coverage. They must install guy wires to support the tower in the wind. The guy-wires must attach to the tower at a point 56 feet above the base of the tower, and must form a 50° angle with the ground. Assuming that the tower is on level ground, how far from the base of the tower will the guy-wires be secured to the ground?

Answer:

No, because the reflection of ABC is not congruent to A’B’C’.

Step-by-step explanation:

we know that

The rule of the reflection across the line y=x is equal to

(x,y) -------> (y,x)

so

A(-6,6) -------> A'(6,-6) ----> is ok

B(-3,3) ------> B'(3,-3) ----> is ok

C(-8,2) ------> C'(8,-2) ----> is not ok ( is not a reflection acros the line y=x)

therefore

The triangles are no t congruent, because the reflection of ABC is not congruent to A’B’C’

Answer:

  loss of $12,481.38

Step-by-step explanation:

It is usually a good idea to follow directions. (See attached.)

The sum of the three profit values is -$12,481.38, indicating a loss in the 3-year period.

Answer: Second Option

68%

Step-by-step explanation:

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

[tex]\mu=27[/tex]

The standard deviation is:

[tex]\sigma=3[/tex]

The z-score formula is:

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

For x=24 the Z-score is:

[tex]Z_{24}=\frac{24-27}{3}=-1[/tex]

For x=30 the Z-score is:

[tex]Z_{30}=\frac{30-27}{3}=1[/tex]

Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of pizzas are delivered between 24 and 30 minutes

Answer:

  see below

Step-by-step explanation:

The applicable rules of logarithms are ...

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

___

The expression can be rewritten as ...

[tex]\log{\dfrac{\sqrt[3]{2-x}}{3x}}=\log{\sqrt[3]{2-x}}-\log{3x}=\dfrac{1}{3}\log{(2-x)}-\log{(3x)}[/tex]

The expression can be written as a sum or difference as:

[tex]$$\boxed{\frac{1}{3} \log(2-x) - \log(3x)}$$[/tex]

To write the expression [tex]$\log(\frac{\sqrt[3]{2-x}}{3x})$[/tex] as a sum or difference, we can use the following logarithmic identities:

[tex]$\log(a/b) = \log(a) - \log(b)$[/tex]

[tex]$\log(a^n) = n \log(a)$[/tex]

First, we can use the first identity to split the logarithm of the fraction into two logarithms:

[tex]$$\log(\frac{\sqrt[3]{2-x}}{3x}) = \log(\sqrt[3]{2-x}) - \log(3x)$$[/tex]

Next, we can use the second identity to expand the logarithm of the cube root:

[tex]$$\log(\sqrt[3]{2-x}) = \log((2-x)^{1/3}) = \frac{1}{3} \log(2-x)$$[/tex]

Substituting this back into the first expression, we get:

[tex]$$\log(\frac{\sqrt[3]{2-x}}{3x}) = \frac{1}{3} \log(2-x) - \log(3x)$$[/tex]

Therefore, the expression can be written as a sum or difference as:

[tex]$$\boxed{\frac{1}{3} \log(2-x) - \log(3x)}$$[/tex]

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I hate rounding.

Let's call the diagonal x.  It's the hypotenuse of the right triangle whose legs are the rectangle sides.

According to the problem we have a length x-4 and a width x-5 and an area

82 = (x-4)(x-5)

82 = x^2 - 9x + 20

0 = x^2 - 9x - 62

That one doesn't seem to factor so we go to the quadratic formula

[tex]x = \frac 1 2(9 \pm \sqrt{9^2-4(62)}) = \frac 1 2(9 \pm \sqrt{329})[/tex]

Only the positive value makes any sense for this problem, so we conclude

[tex]x = \frac 1 2(9 \pm \sqrt{329})[/tex]

That's the exact answer.  Did I mention I hate rounding?  That's about

x = 13.6 meters

Answer: 13.6

----------

It's not clear to me this problem is consistent.  By the Pythagorean Theorem the diagonal satisfies

[tex]x^2 = (x-4)^2 + (x-5)^2[/tex]

which works out to

[tex]x=9 \pm 2\sqrt{10}[/tex]

That's not consistent with the first answer; this problem really has no solution.  Tell your teacher to get better material.

To find the length of the diagonal, we can use the formula for the area of a rectangle and quadratic equation. By substituting the given values and solving for D, we can find the length of the diagonal.

To solve this problem, we can use the formula for the area of a rectangle: length * width = area. Let's represent the length of the rectangle as L, the width as W, and the diagonal as D. According to the problem, L = D - 4 and W = D - 5, and the area is given as 82 m2. We can substitute these values into the formula and solve for D.

L * W = area

(D - 4) * (D - 5) = 82

Expanding and rearranging the equation, we get:

D2 - 9D - 82 = 0

Next, we can solve this quadratic equation either by factoring or by using the quadratic formula. After finding the value of D, we can round it to the nearest tenth to obtain the length of the diagonal.

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Answer:

  c.  Look at the first 7 digits in the table. Let digits from 0 to 3 ...

Step-by-step explanation:

The digits in a random number table are intended to be uniformly distributed, so that each digit has a probability of 0.1. By using combinations of digits you can fairly easily define an outcome that has a probability that is a multiple of 0.1.

Here, you want a probability of 40% = 0.4 = 4×0.1. By defining your outcome as any of 4 digit values, (0 to 3, for example), that outcome will have a probability of 0.4 = 40% when a digit is randomly chosen.

To choose the correct answer here, you only need to understand the above, then choose the answer choice that has an outcome that is defined as 4 of the digits.

___

By looking at 7 digits, you effectively run a simulation in which you do the trial 7 times. Here, you're buying 7 boxes of cereal, so you're interested in 7 trials, each with a probability of success of 40%. This further confirms that the answer choice should include the wording "look at the first 7 digits."

___

More explanation

If the first digit is a number 0-3, it means you got a toy in the first box of cereal.

If the second digit is a number 0-3, it means you got a toy in the second box of cereal.

...

If the 7th digit is a number 0-3, it means you got a toy in the 7th box of cereal.

By counting the number of digits of the first 7 digits that are in the range 0-3, you are effectively counting the number of toys you got in those 7 boxes of cereal.

For example, if the first 7 digits of the table are 9656369*, there is only 1 digit in the range 0-3. That means this purchase of 7 boxes of cereal resulted in 1 toy.

_____

In order to answer Lydia's question, many groups of 7 digits would need to be evaluated, and the ratio of 2-toy purchases to total purchases computed from those results. A trial involving 7000 digits resulted in 268 purchases out of 1000 that had exactly 2 toys, for an experimental probability of 26.8%. Using the binomial distribution, the theoretical probability is about 26.1%--a fairly good match.

___

* this number was generated by random [dot] org

Answer:

Probability = 0.2381

Step-by-step explanation:

A security alarm requires a four digit code by using 0 - 9 and the digits cannot be repeated.

First we calculate how many codes can be made.

Combination = [tex]^{n}p_{r}[/tex]

Where n = 10 and r = 4

[tex]^{n}p_{r}[/tex] = [tex]\frac{10!}{(10-4)!}[/tex]

         = [tex]\frac{10!}{6!}[/tex]

         = 10 × 9 × 8 × 7

        = 5,040 combinations.

Now we have to find the probability that the code contains only odd numbers. So in 0-9 the odd numbers are = 1, 3, 5, 7, 9

There are 5 odd numbers and we have to make a code of 4 numbers.

Therefore, On first place there are 5 options and in second place 4 options, in third place there are 3 options and in fourth place we have only 2 options.

5 × 4 × 3 × 2  = 120 combinations.

Total combinations of odd numbers are 120.

Then the probability that the code contains only odd numbers is

[tex]p=\frac{120}{5040}[/tex] = 0.0238095 ≈  0.02381

Probability = 0.2381

The approximate probability that the code contains only odd numbers is 0.0238.

The probability of the code containing only odd numbers can be found by determining the number of possible combinations of four odd digits out of the total number of possible combinations of four digits.

To calculate this, we first count the number of odd digits from 0 to 9, which is 5. Then, we determine the number of combinations of 4 digits that can be formed from the 5 odd digits, which is 5C4 or 5.

The total number of possible combinations of four digits without repetition is 10C4 or 210. Therefore, the probability of the code containing only odd numbers is 5/210 or approximately 0.0238.

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Answer:

[tex]2^53^5[/tex]

Step-by-step explanation:

So if we compare [tex]2^5 \cdot 3^7[/tex] to [tex]2^7 \cdot 3^5[/tex], we should see the most amount of factors of 2 that they have in common is 5 and the most amount of factors of 3 that they have in common is 5.

If you aren't sure on the number of factors of 2 and 3 they have in common you could write it all out:

[tex]2^53^7=(2)(2)(2)(2)(2)\cdot\text{ }(3)(3)(3)(3)(3)(3)(3[/tex]

[tex]2^73^5=(2)(2)(2)(2)(2)(2)(2)\text{ }(3)(3)(3)(3)(3)[/tex]

So if I were able to circle each pair of 2's they had in common I would circle 5 pairs.

If were able to circle each pair of 3's they had in common I would circle 5 pairs.

Answer: The following statement is true about indexes and scales: They rank-order the units of analysis in terms of specific variables.

Indexes provides with a way to make a complex measure that iterate consequence for multiple rank-ordered related questions or statements.  

Scale is a type of complex measurement that is combined of several items that have a empirical structure among them.

Let x = amount of 16% alloy, and y = amount of 30% alloy he should use.

Mixing the alloys will result in a compound weighing x + y = 100 grams.

For each gram of the 16% alloy used, 0.16 gram of titanium is contributed; similarly, for each gram of the 30% alloy used, there's a contribution of 0.3 gram. He wants to end up with an alloy of 23% titanium, or 23 grams (23% of 100), so that 0.16x + 0.3y = 23.

Solve the system:

[tex]x+y=100\implies y=100-x[/tex]

[tex]0.16x+0.3y=23\implies 0.16x+0.3(100-x)=23\implies7=0.14x[/tex]

[tex]\implies\boxed{x=50}\implies\boxed{y=50}[/tex]

A line graph would be the best type of chart to display the growth of Mike's hybrid tomato plant over a three-month period.

The type of chart that would best display the growth of Mike's hybrid tomato plant over a three-month period is a line graph. A line graph is suitable for showing the changes in a variable over time, making it ideal for displaying the growth of the tomato plant.

Answer: y = -1/4x - 4

Step-by-step explanation:

y = (-1/4)x + 2 (This is the first linear function.)

(4,3) has slope of (-1/4)x  or (1/-4)x

4(y2) - 4(y1= the new y  -1(x2) -3(x1) = new x which leads to (0,-4) so y-intercept = -4

so all in all, y = (-1/4)x -4 is the answer

Hopefully, you're able to understand this. It's difficult to explain through typed words rather than visually and through a written example.

Same y intercept as x+4y=8 through (4,3)

Y intercept is when x=0, so 4y=8, so y=2 and the y intercept is (0,2)

Answer for y intercept:  (0,2)

So we need the line through (0,2) and (4,3).  Point-point form says the line through (a,b) and (c,d) is

(c-a)(y-b) = (d-b)(x-a)

(4 - 0)(y - 2) = (3 - 2)(x - 0)

4y - 8 = x

Answer for the line:  x - 4y = -8

Check:

(0,2) is on the line: 0-4(2)  = -8 check

(4,3) is on the line 4 - 4(3) = -8 check

Answer:

Find the explicit from for the sequence [tex]t_n=t_{n-1}+4,t=6[/tex]:

[tex]a_n=4n+2[/tex]

This next question I edited a bit.  Your question just says find the four terms.  I'm assuming they meant the first four. I also changed the c to an [tex]a[/tex].

Find the first four terms of the sequence given by: [tex]a_n=n a_{n-1}-3,a_1=2[/tex]:

a) 2,1,0.-3

You might want to read that second question again because there is errors in the question or things that don't really make sense.  I made my own interpretation of the problem based on my own mathematical experience.

Step-by-step explanation:

So your first question actually says that you can find a term by taking that term's previous term and adding 4.

So more terms of the sequence starting at first term 6 is:

6,10,14,18,....

This is an arithmetic sequence.  When thinking of arithmetic sequences you should just really by thinking about equations of lines.

Let's say we have this table for (x,y):

x  |   y

----------

1      6

2    10

3     14

4     18

So we already know the slope which is the common difference of an arithmetic sequence.

We also know point slope form of a line is [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point on the line.  You can use any point on the line. I'm going to use the first point (1,6) with my slope=4.

[tex]y-6=4(x-1)[/tex]

[tex]y=6+4(x-1)[/tex]    :I added 6 on both sides here.

[tex]y=6+4x-4[/tex]     :I distribute here.

[tex]y=4x+2[/tex]        :This is what I get after combining like terms.

So [tex]a_n=y[/tex] and [tex]x=n[/tex] so you have:

[tex]a_n=4n+2[/tex]

---------------------------------------------------------------------------------------

The first four terms of this sequence will be given by:

[tex]a_1,a_2,a_3,a_4[/tex]

[tex]a_1=2[/tex] so it is between choice a, c, and d.

[tex]a_n=na_{n-1}-3[/tex]

To find [tex]a_2[/tex] replace n with 2:

[tex]a_2=2a_{1}-3[/tex]

[tex]a_2=2(2)-3[/tex]

[tex]a_2=4-3[/tex]

[tex]a_2=1[/tex]

So we have to go another further the only one that has first two terms 2,1 is choice a.

Answer:

4

(We didn't even need to use (9,6) )

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

We are given the line we are looking for has the same y-intercept as x+2y=8.

So if we put x+2y=8 into y=mx+b form we can actually easily determine the value for b.

So we are solving x+2y=8 for y:

x+2y=8

Subtract x on both sides:

  2y=-x+8

Divide both sides by 2:

   y=(-x+8)/2

Separate the fraction:

  y=(-x/2)+(8/2)

Reduce the fractions (if there are any to reduce):

y=(-x/2)+4

Comparing this to y=mx+b we see that b is 4.

So the y-intercept is 4.

Again since we know that the line we are looking for has the same y-intercept, then the answer is 4 since the question is what is the y-intercept.

4

Answer:

[tex]cosZ=\frac{3}{5}[/tex]

Step-by-step explanation:

Cos of an angle by definition of its ratio is side adjacent/hypotenuse.  The side adjacent to angle Z cannot be the hypotenuse, so it has to be 6.  The hypotenuse is 10.  Therefore,

[tex]cosZ=\frac{6}{10}=\frac{3}{5}[/tex]

Answer:

Karen spent $10, Maggie spent $30 and Jasmine spent $20

Step-by-step explanation:

let's call Karen's money spent 'x'

Maggie therefore is 3x

And Jasmine is 2x

6x=$60

x=$10

Now we substitute this back in

so Karen spent $10

Maggie spent $30

And Jasmine spent $20

Answer:

  n = 11

Step-by-step explanation:

100 mod 11 = 1, which is the remainder from division by 11 for each of the terms of the sum. 11 terms of the sum are needed in order to make the remainders add up to a number divisible by 11.

Answer: 25%

Step-by-step explanation:

Given : A rectangular dartboard has an area of 648 square centimeters.

The triangular part of the dartboard has an area of 162 square centimeters.

If we assume that the dart lands in the rectangle, then the probability that it lands inside the triangle will be :-

[tex]\dfrac{\text{Area of triangular part}}{\text{Area of rectangular dart board}}\\\\=\dfrac{162}{648}=0.25[/tex]

In percent, [tex]0.25\times100=25\%[/tex]

Hence, the required probability = 25%

[tex]|\Omega|={_{20}C_3}=\dfrac{20!}{3!17!}=\dfrac{18\cdot19\cdot20}{2\cdot3}=1140\\|A|=1\\\\P(A)=\dfrac{1}{1140}\approx0.09\%[/tex]

Answer:

0.014%

Step-by-step explanation:

To calculate the probability that she chooses that exact songs for the piano recital, you just first calculate the probability of her choosing one of them:

[tex]Probability of 1=\frac{1}{20}=.05[/tex]

This is 5%, now you multipy this with the probability of the second song after this one, since there is one less song, the total number of outcomes should be reduced to 19:

[tex]Probability of 2nd=(.05)(\frac{1}{19}[/tex]

[tex]Probability of 2nd=(0.05)(0.052}[/tex]

[tex]Probability of 2nd=0.002[/tex]

This would be .26%

To calculate the probability of the third song being chosen after the first two, we have 2 less outcomes possibles, so the total number of possibilities now is reduced to 18.

[tex]Probability of 3rd=(.0026)(\frac{1}{18}[/tex]

[tex]Probability of 3rd=(.0026)(0.055)[/tex]

[tex]Probability of 3rd=0.00014[/tex]

The probability of Noam choosing the three songs would be: 0.014%

Answer: 4x^2 -13x + 14

Step-by-step explanation:

(x^2 - 8x + 5)-(-3x^2 + 5x-9)

Subtract -3x^2 from x^2

(4x^2 - 8x + 5)-(5x-9)

Subtract 5x from -8x

(4x^2 -13x + 5)-(-9)

Subtract 9 from 5

4x^2 -13x + 14

Answer:

true

Step-by-step explanation:

yes, that is true.  Parallel lines have equal slopes and perpendicular lines have negative reciprocal slopes (or opposite reciprocals, the "opposite" being the sign).

The statement "If two lines are perpendicular, their slopes are negative reciprocals." is: True

The general form for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

We know that when two lines are parallel, that their slopes are the same. However, when two lines are perpendicular, then their slopes are  negative reciprocals of each other.

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Answer:

  11, 7, 44

Step-by-step explanation:

Let x represent the first number. Then the second is (x-4) and the third is (4x). Their sum is ...

  x +(x -4) +(4x) = 62

  6x = 66 . . . . . . . . . . . . add 4, collect terms

  x = 11 . . . . . . . . . divide by 6

  x -4 = 7 . . . . . . . find the second number

  4x = 44 . . . . . . . find the third number

The three numbers are 11, 7, and 44.

Answer:

The correct answer is option B.  

m<3 = m<6

Step-by-step explanation:

From the figure we an see that, a and b are parallel lines and line t is the traversal on the lines.

To find the correct option

From the given figure we get

Corresponding angles are,

<1 & <5,  <2&<6, <2&<7 and <4 &<8

Alternate interior angles are,

<3 & <6  and <4 &<5

Alternate interior angles are equal.

m<3 = m<6

Therefore the correct answer is optionB

Answer:

No they will not have to install a rest platform.

The ramp will be 29.88 feet long so they will not have to install a rest platform.

Step-by-step explanation:

Answer:

y-7 = 1/2x point slope form

y = 1/2x+7  slope intercept form

Step-by-step explanation:

y=-2x+9

This equation is in the form y= mx +b so the slope is -2

We want a line perpendicular

Take the negative reciprocal

m perpendicular is - (-1/2)

m perpendicular = 1/2

We have a slope of 1/2 and a point.  We can use point slope form

y-y1 = m(x-x1)

y-7 = 1/2(x-0)  point slope form

y-7 = 1/2x

Adding 7 to each side

y-7+7 =1/2x +7

y = 1/2x+7  slope intercept form

Answer: $80

Step-by-step explanation:

Given : Interest amount : [tex]T=\$40[/tex]

The rate of interest : [tex]r=10\%=0.1[/tex]

Time period : [tex]t=5[/tex] years

The simple interest formula is

[tex]l=prt[/tex], where l represents simple interest on an amount p for t years at a rate of r where r is expressed as a decimal.

Substitute all the values in the  formula , we get

[tex]40=p(0.1)(5)\\\\\Rightarrow\ p=\dfrac{40}{0.1\times5}=80[/tex]

Hence, the amount of money p that will generate $40 in interest at a 10% interest rate over 5 years= $80

The amount of money (p) required to generate $40 in interest at a 10% interest rate over 5 years is $80.

Given the parameters:

Simple interest l = $40

Interest rate r = 10% = 10/100 = 0.10

Time t = 5 years

To determine the amount of money (p) that will generate $40 in interest at a 10% interest rate over 5 years, we use the simple interest formula:

I = P × r × t

Solve for p:
P = I / rt

Plug in the values

P = $40 / ( 0.10 × 5 )

P = $40 / 0.5

P = $80

Therefore, the value of the principal is $80.

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Answer:

Each part is solved and working is shown  

Step-by-step explanation:

1)

[tex]-6\displaystyle\frac{4}{9}-3\displaystyle\frac{2}{9}-8\displaystyle\frac{2}{9}\\\\= -\displaystyle\frac{58}{9}-\displaystyle\frac{29}{9}-\displaystyle\frac{74}{9}\\\\= -\displaystyle\frac{161}{9}\\=-17\displaystyle\frac{8}{9}[/tex]

2)

[tex]-12.48-(-2.99) -5.62\\=-12.48 + 2.99 -5.62 \\=-15.11[/tex]

3)

[tex]-19\displaystyle\frac{2}{9}-4\displaystyle\frac{1}{9}+3\displaystyle\frac{4}{9}\\\\= -\displaystyle\frac{173}{9}-\displaystyle\frac{37}{9}+\displaystyle\frac{31}{9}\\\\= -\displaystyle\frac{179}{9}\\=-19\displaystyle\frac{8}{9}[/tex]

4)

[tex]-353.92 - (-283.56) - 131.29\\= -353.92 + 283.56 - 131.29\\= -201.65[/tex]

5)

[tex]83\displaystyle\frac{1}{5}-108\displaystyle\frac{2}{5} + 99\displaystyle\frac{1}{5}\\\\= \displaystyle\frac{416}{5}-\displaystyle\frac{542}{5}+\displaystyle\frac{496}{5}\\\\= -\displaystyle\frac{370}{5}\\= 74[/tex]

Answer:

Step-by-step explanation:

Answer:

2.

Step-by-step explanation:

is a geometric progression with common ratio of 1/4.

there, multiple 150 by 1/4 in 3 places. (4th, 5th and 6th day)

150 ÷ (4*4*4) = 150/64 = 2.3 ≈ 2

Using the formula for the n-th term of a geometric sequence, the number of mosquitoes killed on the sixth day is found to be approximately 2 when rounded to the nearest whole number.

The sequence representing the number of mosquitoes killed after spraying insecticide appears to decrease by a factor of 4 each day.

This pattern can be described as a geometric sequence. To find the number of mosquitoes killed on the sixth day, we will use the formula for the n-th term of a geometric sequence, which is an = a₁ × rⁿ⁻¹, where a1 is the first term, r is the common ratio, and n is the term number.

Day 1 (first term, a1): 2400 mosquitoes

Day 2: 2400 / 4 = 600 mosquitoes

Day 3: 600 / 4 = 150 mosquitoes

From this pattern, we identify the common ratio r as 1/4. To find the number of mosquitoes killed on the sixth day:

Let n = 6 for the sixth day.

Substitute a1 = 2400 and r = 1/4 into the formula: a6 = 2400 × (1/4)⁶⁻¹ = 2400 × (1/4)⁵.

Calculate the value: a6 = 2400 × (1/1024) ≈ 2.34, which rounds to 2 mosquitoes when rounded to the nearest whole number.

Therefore, approximately 2 mosquitoes were killed on the sixth day after the spraying.

Answer:

68% of the pizzas are delivered between 24 and 30 minutes

Step-by-step explanation:

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

[tex]\mu=27[/tex]

The standard deviation is:

[tex]\sigma=3[/tex]

The Z-score formula is:

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

For [tex]x=24[/tex] the Z-score is:

[tex]Z_{24}=\frac{24-27}{3}=-1[/tex]

For [tex]x=30[/tex] the Z-score is:

[tex]Z_{30}=\frac{30-27}{3}=1[/tex]

Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of the pizzas are delivered between 24 and 30 minutes

Using the empirical rule, approximately 68% of pizzas are delivered between 24 and 30 minutes, as this range falls within one standard deviation of the mean delivery time, which is normal distribution practice.

The question is about the percentage of pizzas delivered within a certain time frame, assuming a normal distribution of delivery times. The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

In this case, the mean delivery time is 27 minutes and the standard deviation is 3 minutes. Thus, using the empirical rule, about 68% of pizzas should be delivered between 24 minutes (27 - 3) and 30 minutes (27 + 3).