In a random sample of ​people, the mean driving distance to work was miles and the standard deviation was miles. Assume the population is normally distributed and use the​ t-distribution to find the margin of error and construct a ​% confidence interval for the population mean . Interpret the results. Identify the margin of error.

Answer:

The removed number is 11.

Step-by-step explanation:

Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :

[tex]let \: x = total \: values[/tex]

[tex] \frac{x}{5} = 7[/tex]

[tex]x = 7 \times 5[/tex]

[tex]x = 35[/tex]

Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :

[tex]let \: y = removed \: number[/tex]

[tex] \frac{35 - y}{4} = 6[/tex]

[tex]35 - y = 6 \times 4[/tex]

[tex]35 - y = 24[/tex]

[tex]35 - 24 = y[/tex]

[tex]y = 11[/tex]

Okay, let's slightly generalize this

Average of [tex]n[/tex] numbers is [tex]a[/tex]

and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.

Solution:

If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]

Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]

For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .

so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]

or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]

Simplify the equation, and solve for [tex]x[/tex] to get,

[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]

Hope you understand it :)

Answer:

3:45 pm

Step-by-step explanation:

Every 90 degree = 15 minutes

270 degrees = 15 x 3 = 45 minutes

3:00 + 0:45 = 3:45 pm

Hope this helps!

Answer:

3:45 pm

Step-by-step explanation:

∆T = (270/360)° × 60 minutes

=45 mins

Time = 3hrs + 45 mins

3:45 pm

Answer:

Yes, the constant of proportionality is the same for the three rows.

The relationship between amount of water (W) in terms of time (t) can be written as:

W = 16.5 t

Step-by-step explanation:

To find the constant of proportionality, find the number of gallons per minute for each row:

First row: 16.5 gal in 1 minute means: 16.5 Gal/min

Second row: 24.75 gallons in 1.5 minutes means 24.75/1.5 = 16.6 Gal/min (same proportionality as above)

Third row: 33 gallons in 2 minutes means: 33/2 = 16.5 Gal/min (again same proportionality)

Then: Yes, the constant of proportionality is the same for the three rows.

Therefore the amount (W) of water in gallons per time (t) in minutes can be written as the product of 16.5 times time (t):

W = 16.5 t

Answer:

The numbers prove that there is a proportional relationship between the gallons of water and the time in minutes. The bathtub fills at a constant rate.

Step-by-step explanation:

Answer:

Median: 4.44

Mean: 4.11

On edge

Step-by-step explanation:

The mean and median of the data is

Mean ≈ 4.1 pounds

Median = 4.44

The ratio of the total number of observations to the sum of the observations is known as the mean.

The median is a value for an ordered data collection that has the same amount of observations on its left and right (in either ascending or descending order).

We have the following data:

3.25, 3.25, 3.66, 3.83, 4.57, 4.52, 4.74, 4.69, 4.44

So, Mean of the data is

= sum/number of observations

= (3.25 + 3.25 + 3.66 + 3.83 + 4.57 + 4.52 + 4.74 + 4.69 + 4.44) / 9

= 36.95 / 9

= 4.10555

Now, Arranging the data in ascending order gives

3.25, 3.25, 3.66, 3.83, 4.44, 4.52, 4.57, 4.69, 4.74

Here mid value is the 5th value from both end.

Thus, median of the data set = 4.44

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Answer:

[tex]k = 2.6[/tex]

Step-by-step explanation:

Given

[tex]5k + 3.8 = 3k + 9[/tex]

Required

Solve

[tex]5k + 3.8 = 3k + 9[/tex]

Collect like terms

[tex]5k -3k+ 3.8 = 3k -3k + 9[/tex]

[tex]2k+ 3.8 = 9[/tex]

Subtract 3.8 from both sides

[tex]2k+ 3.8 - 3.8= 9 - 3.8[/tex]

[tex]2k= 9 - 3.8[/tex]

[tex]2k = 5.2[/tex]

Divide through by 2

[tex]k = 5.2/2[/tex]

[tex]k = 2.6[/tex]

Answer:

x ≥-10

Step-by-step explanation:

–2.5x ≤ 25

Divide each side by -2.5, remembering to flip the inequality

–2.5x/-2.5 ≥ 25 /-2.5

x ≥-10

Answer:

[tex]x\leq -10[/tex]

Step-by-step explanation:

[tex]-2.5x\leq 25[/tex]-----> Multiply by -1:

[tex]2.5x\geq -25[/tex]-----> Divide by 2.5:

[tex]x\geq -10[/tex]

Hope this helps!

Answer:

21

Step-by-step explanation:

√1500 = 38.7

Round to nearest whole number

≈39

39²-1500

= 1521 - 1500

= 21

Answer:

8,8,-8,-8,8, ... is neither arithmetic nor geometric

Step-by-step explanation:

8,8,-8,-8,8, ...

This sequence is neither arithmetic nor geometric

We could also write

8,8,8,8,8, ... this is geometric since we multiply by 1 each time

Answer:

The probability that at least, one of the four children the couple has is a boy is 0.8.

Step-by-step explanation:

Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..

Note that it is possible to have the following for 4 children:

1. 4 boys, 0 girls

2. 3 boys, 1 girl

3. 2 boys, 2 girls

4. 1 boy, 3 girls

5. 0 boys, 4 girls.

To have at least, one boy, out of the 5 options, only 4 is possible.

1. 4 boys, 0 girls.........YES

2. 3 boys, 1 girl ...........YES

3. 2 boys, 2 girls.........YES

4. 1 boy, 3 girls.............YES

5. 0 boys, 4 girls..........NO

The probability is therefore,

(Probability of event = 4) ÷ (Total possible outcome = 5)

P = 4/5 = 0.8

Answer:

12.1%

Step-by-step explanation:

Given that:

Mean (μ) = 20.2 grams and standard deviation (σ) = 0.18 grams.

The z score is a score used to determine the number of standard deviations by which the raw score is above or below the mean. A positive z score means  that the raw score is above the mean and a negative z score means that the raw score is below the mean. It is given by:

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

a) For x < 19.99 g:

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{19.99-20.2}{0.18} \\\\z=-1.17[/tex]

From the normal distribution table, P(x < 19.99) = P(z < -1.17) = 0.1210 = 12.1%

The probability that a randomly chosen mouse has a mass of less than 19.99 grams is 12.1%

The value of x using complete sentences is 40 degrees.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees. A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

We are given that;

The measure of angles 75,50 and 85

Now,

In triangle 1

50+75+y=180

y=180-125

y=55

In triangle 2

55+85+x=180

140+x=180

x=40

Therefore, by angle sum properties of triangle answer will be 40 degrees.

Learn more about the triangles;

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Answer:

BC = 13.4

Step-by-step explanation:

its a law of cosines S-A-S

a² = b² + c² - 2bc cosA

a² = 12.6² + 4.6² - ( 2 * 12.6 * 4.6 * cos 90 )

a² = 179.92

a = sqrt (179.92)

a = 13.4

Answer:

e. HS

Step-by-step explanation:

The argument:

[(P ≡ T) • (H • N)] ⊃ (T ⊃ ~S)

(T ⊃ ~S) ⊃ [(H ∨ E) ∨ R]

[(P ≡ T) • (H • N)] ⊃ [(H ∨ E) ∨ R]

is an instance of one of hypothetical syllogism (HS).

Hypothetical syllogism contains conditional statements for its premises.

Let

p = [(P ≡ T) • (H • N)]

q = (T ⊃ ~S)

r = [(H ∨ E) ∨ R]

The this can be interpreted as:

p ⊃ q

q ⊃ r

p ⊃ r

This interprets that:

If p then q

but if q then r

therefore if p then r

Thus, in logic HS is a valid argument form:

p → q

q → r

∴ p → r

Note that ⊃ symbol is used to symbolize implication relationships. This is used in conditional statements which are represented in the if...then... form.  For example p ⊃ q means: if p then q. So the type of Hypothetical syllogism used in this is conditional syllogism.

There are three parts of syllogism:

major premise

minor premise

conclusion

An example is:

If ABC is hardworking, then ABC will go to a good college.  

Major premise: ABC is hardworking.

Minor premise: Because ABC is hardworking , ABC will score well.

Conclusion: ABC will go to a good college.

Example of Hypothetical syllogism:

If AB is a CD, then EF is a GH

if WX is a YZ, then AB is a CD

therefore if WX is a YZ, then EF is a GH

This can be understood with the help of an example:

If you study the topic, then you will understand the topic.  

If you understand the topic, then you will pass the quiz.

Therefore, if you study the topic, then you will pass the quiz.

Answer:

x = 3

Step-by-step explanation:

To answer for x first distribute the 4 in the parenthesis

4x + 1 - 5x = 2x +4x - 20

Next add or subtract the x's

-x + 1 = 6x - 20

Now subtract 6x and 1 on both sides to get x on the left and the rest on the right

-7x = -21

Lastly, divide -7 on both sides

x = 3

Answer:

The two numbers are: 8 and 16.

Step-by-step explanation:

Let the two unknown numbers be a and b.

The sum of the two number is 24. In other words:

[tex]a+b=24[/tex]

The second number is equal to twice the first number. In other words:

[tex]a=2b[/tex]

This is a system of equations. Solve by substitution:

[tex]a+b=24\\a=2b\\\\2b+b=24\\3b=24\\b=8\\a=2b\\a=2(8)=16[/tex]

Answer: 60%

Step-by-step explanation:

Given, AP$ of Brisket = $4.72

Weight of each brisket on purchase : 10.4 lbs

Weight of each brisket after smoking : 6.24 lbs

Yield % of the briskets after Carol is done smoking them=[tex]\dfrac{\text{Weight after smoking}}{\text{Weight on purchase}}[/tex]

[tex]\dfrac{6.24}{10.4}\times100\\\\=60\%[/tex]

Hence, the yield % of the briskets after Carol is done smoking them = 60%

Answer:

z -score = 0.0459

Step-by-step explanation:

Given that:

the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12.

The objective is to find the z- score , but before we can do that , we need to determine the mean and the standard deviation of the sample.

Mean = sum of the sample/ total number of the sample

Mean = (3+9+ 5+ 5+ 14+ 10+ 5+ 11+ 9+ 6+ 1+ 8+ 10+ 7+ 9+13+ 18+ 9+ 8+11+ 9+ 7+ 6+ 14+ 12)/25

Mean = 219/25

Mean = 8.76

Standard deviation = [tex]\sqrt{\dfrac {\sum (x_i - \mu)^2}{N}}[/tex]

Mean (in order )= 1, 3,5,5,5,6,6,7,7,8,8,9,9,9,9,9,10,10,11,11,12,13,14,14,18)

Standard deviation = [tex]\sqrt{\dfrac { (8.76 - 1)^2}{25} + \dfrac { (8.76 - 3)^2}{25} +\dfrac { (8.76 - 5)^2}{25} +...+ \dfrac { (8.76 - 18)^2}{25} }[/tex]

Standard deviation = 5.2174

The standard z score formula is:

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

where X = median (13th observation ) = 9

[tex]z = \dfrac{9- 8.76}{5.2174}[/tex]

[tex]z = \dfrac{0.24}{5.2174}[/tex]

z -score = 0.0459

Answer:

[tex]\large \boxed{6(2n-3)}[/tex]

Step-by-step explanation:

[tex]12n-18[/tex]

Factor out 6 from each term.

[tex]6(2n)+6(-3)[/tex]

Take 6 as a common factor.

[tex]6(2n-3)[/tex]

Answer:

Step-by-step explanation:

[tex] \mathsf{12n - 18}[/tex]

In such expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor

Factor out 3 from the expression

[tex] \mathsf{ = 3(4n - 6)}[/tex]

Hope I helped!

Best regards!

Answer:

y = -9x - 82

Step-by-step explanation:

Line with slope m=-9 passing through A(x1, y1) =A(-9,-1)

y-y1 = m(x-x1)

Substitute values

y-(-1) = -9(x-(-9)

y+1 = -9x -81

y = -9x - 82

Answer:

60%

Step-by-step explanation:

9/20 is 45%

Answer:

60 %

Step-by-step explanation: If you divide 9/20, it equals to 0.45, makes it 45% and the number 45 in general is smaller than 60. Thus, 60% is greater than 9/20. I hope this helps.

Answer:If Rachel texted 221 text messages, then Deshaun texted 231 text messages, and Trey texted 924 text messages.

Step-by-step explanation:

221+10=231, 321 times 4 equal 924

Answer:

6 pounds 10 ounces

Step-by-step explanation:

I take this to mean "a baseball weighs approximately 3 pounds and a golf ball three pounds ten ounces."

Adding these two weights together, we get 6 pounds 10 ounces.

Answer:

-7/6

Step-by-step explanation:

-2/3 x 7/4 = -14/12 = -7/6

Answer: -7/6

Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).

Remember that dividing by a fraction is the same thing

as multiplying by the reciprocal of the fraction.

Before multiplying however, notice that we

can cross-cancel the 2 and 4 to 1 and 2.

So multiplying across the numerators and denominator and

remembering our negative in the first fraction, we have -7/6.

Answer:

x=7

Step-by-step explanation:

If P is the midpoint of XY, then XP = PY:

Answer:

f(x)=1/2x+2

Step-by-step explanation:

Using formula y=mx+b.

m is 0.5 or 1/2 as stated above

f(x)= 1/2x+b

If it were y=1/2x, it would intersect at 0,0 and we want 0,2

so b should be 2

therefore

Y=1/2x+2

or

f(x)=1/2x+2

Answer:

D

Step-by-step explanation:

Answer:

-19

Step-by-step explanation:

By looking at the 2 numbers provided, -10 and -4, you can work out that there is a gap of 6 numbers as(-4) - (-10) = 6

There are 2 intervals between -10 and -4, so each interval is

6/2 = 3

a gap of 3

This means the number to the left of -4 is -7, then -10 which works.

From there, you count how many intervals there is between -10 and the ?

There are 3 intervals, so you have to decrease -10 by -3x3 or -9

Therefore the ? is -19

Another way is to just count it directly

The number directly left of -10 is going to be -13, then -16 and finally -19

Option a) -10

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

put $x=-1$

$f(-1)=-|(-1)^2-5(-1)+4|$

$\implies f(-1)=-|1+5+4|=-|10|=10$

Answer:

option a

Step-by-step explanation:

Option a) -10

put $x=-1$

$f(-1)=-|(-1)^2-5(-1)+4|$

$\implies f(-1)=-|1+5+4|=-|10|=10$

Answer:

Not a solution

Step-by-step explanation:

We want to check and see if 5 is a solution to the inequality. Therefore, we must substitute 5 into the inequality.

[tex]10+7g < 44[/tex]

Plug 5 in for g.

[tex]g=5[/tex]

[tex]10+7(5) < 44\\[/tex]

First, multiply 5 and 7.

[tex]10 + (7*5) < 44[/tex]

[tex]10 + 35 < 44[/tex]

Next, add 10 and 35.

[tex](10+35) < 44[/tex]

[tex]45 < 44[/tex]

This statement is not true. 45 is not less than 44. Therefore, 5 is not a solution.

Answer:

it is not a solution

Step-by-step explanation:

By replacing the letter g with a 5 the answer would be 45<44 which is not true

Answer:

10/1 +54/-6

Step-by-step explanation:

Is this the answer?