Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives less than 159 miles in a day. Round your answer to four decimal places.

Answer:

=============================================================

Explanation:

The letter O looks very similar to the number zero, so I'm going to use other letters to avoid confusion. For the smaller circle on the left, it'll have center P. The circle on the right will have center Q. See the diagram below.

Based on that, we can say that PQ = 20 cm.

Let x = length of PK

PK + KQ = PQ

KQ = PQ - PK

KQ = 20 - x

We'll keep this in mind for later. I'll refer to this as "Fact 1" when it does come up later.

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

We're given this equation

3AK=2BK

Let's get the numbers to one side and the letters to the other side like so:

3AK=2BK

3AK/BK = 2

AK/BK = 2/3

We'll use this later as well.  I'll refer to this as "Fact 2" when it does come up later.

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

Next, draw a segment from P to A to form triangle PAK (also shown in the diagram below). Do the same for points Q and B to form triangle QBK.

The segments PA and PK are radii of the smaller circle, so PA = PK which leads to triangle PAK being isosceles. Triangle QBK is also isosceles for similar reasoning.

The angles AKP and QKB are vertical angles, so they are congruent.

The facts mentioned so far boil down to the two triangles being similar triangles (use the angle angle method to prove).

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

Now that we know the triangles are similar, we can use a proportion to solve for x.

PK/KQ = AK/KB

PK/KQ = 2/3  .... use fact 2

x/(20-x) = 2/3 .... use fact 1

3x = 2(20-x) .... cross multiply

3x = 40 - 2x

3x+2x = 40

5x = 40

x = 40/5

x = 8

So,

The radius of the smaller circle on the left is 8 cm.

The radius of the larger circle on the right is 12 cm.

Answer:

[tex] \implies{\sf{ \dfrac{p + 7}{p - 6} = \dfrac{1}{3}}}[/tex]

By cross multiplication :

[tex] \implies{\sf{ {3(p + 7)} = 1{(p - 6)} }}[/tex]

[tex]\implies{\sf{3p + 27 = p - 6 }}[/tex]

[tex]\implies{\sf{3p - p = - 6 - 21}}[/tex]

[tex]\implies{\sf{2p = - 27}}[/tex]

[tex]\implies{\sf{\underline{\underline{\red{p = \dfrac{ - 27}{2}}}}}}[/tex]

Hence, the value of p is -27/2

[tex]\begin{gathered}\end{gathered}[/tex]

[tex] \implies{\sf{ \dfrac{p + 7}{p - 6} = \dfrac{1}{3}}}[/tex]

Substituting the value of (p = -27/2)

[tex] \implies{\sf{ \dfrac{ \dfrac{ - 27}{2} + 7}{ \dfrac{ - 27}{2} - 6} = \dfrac{1}{3}}}[/tex]

[tex] \implies{\sf{ \dfrac{ \dfrac{ - 27 + 14}{2}}{ \dfrac{ - 27 - 12}{2} } = \dfrac{1}{3}}}[/tex]

[tex] \implies{\sf{ \dfrac{ \dfrac{ - 13}{2}}{ \dfrac{ - 39}{2} } = \dfrac{1}{3}}}[/tex]

[tex] \implies{\sf{ \dfrac{ - 13}{2} \times \dfrac{2}{ - 39} = \dfrac{1}{3}}}[/tex]

[tex] \implies{\sf{ \dfrac{ - 13}{\cancel{2}} \times \dfrac{\cancel{2}}{ - 39} = \dfrac{1}{3}}}[/tex]

[tex] \implies{\sf{ \dfrac{ - 13}{ - 39} = \dfrac{1}{3}}}[/tex]

[tex] \implies{\sf{ \cancel{\dfrac{ - 13}{ - 39}} = \dfrac{1}{3}}}[/tex]

[tex] \implies{\sf{ \dfrac{1}{3} = \dfrac{1}{3}}}[/tex]

[tex]\implies{\sf{\underline{\underline{\red{LHS = RHS}}}}}[/tex]

Hence Verified!

[tex]\underline{\rule{220pt}{3pt}}[/tex]

Answer:

It grows at a rate  

4/9 ft/second

Step-by-step explanation:

If tall is completely dominant over short, then the mother's genotype is either TT or Tt. The father is short so his genotype is tt.

Crossing TT with tt produces only heterzygous offspring with genotype Tt. Then the genotypic and phenotypic ratios are 0 TT : 1 Tt : 0 tt and 1 tall : 0 short, respectively. As percentages, these would

• geno:   0% TT : 100% Tt : 0% tt

• pheno:   100% tall : 0% short

Crossing Tt with tt on the other hand produces offspring with genotype either Tt or tt with equal probability, so that the geno and pheno ratios are 0 TT : 1 Tt : 1 tt and 1 tall : 1 short. As percentages,

• geno:    0% TT : 50% Tt : 50% tt

• pheno:   50% tall : 50% short

Answer:

hiiiiiiiiiiiiiiiiiiiiiiiiiii

First, let's find the area! The formula to find the area of a circle is πr²

πr²

3.14 · 4²

50.24 yds²

Now let's find the circumference. The formula for this is 2πr

2πr

2 · 3.14 · 4

25.12 yds

Hope this helps!

Answer:

6200

Step-by-step explanation:

first find how much she would make purely based on hours worked:

8x40 = 320 dollars

next subtract this from total on her paycheck so 692-320 is 372

we know that 372 is 6% of a number so...

[tex]\frac{6}{100}[/tex] x = 372

[tex]\frac{6x}{100}[/tex] = 372

6x= 37200(100)

x=6200 $ divide by 6

so she sold $6200 worth of merchandise to earn $372 of commission

Answer:

7.5lbs

Step-by-step explanation:

82/11 = 7.45454545lbs

Rounded to 7.4lbs

Hope that helps

Answer:

7 5/11

Step-by-step explanation:

you divide 82 and 11 and you get 7.45454545

Answer:

1386

Step-by-step explanation:

First multiply 8 and 77 to get 616

Then multiply 10 and 77 to get 770

Finally, add them all together to get 1386

Answer:

Answer:

2.8

Step-by-step explanation:

.4 × 7 =2.8

.4+.4+.4+.4+.4+.4+.4

Hope this helps!!:)

Answer:

2.8

Step-by-step explanation:

This is the same as:

[tex]0.4+0.4+0.4+0.4+0.4+0.4+0.4[/tex]

If we were to change the question to:

[tex]4+4+4+4+4+4+4=28[/tex]

That would be 10x this question's answer, Therefore you divide 28 by 10 to give you 2.8  

Answer:

n = 34/13

Step-by-step explanation:

13 x 4 = n x 26

=> 68 = 26n

=> n = 68/26

=> n = 34/13

Therefore, n = 34/13

Hoped this helped.

[tex]GeniusUser[/tex]

Step-by-step explanation:

remark : it is very unusual for a map to mix two measurement norms. they are normally either fully in the American or fully in the metric system.

but let's do the exercise.

the scale says 1/2 in = 10 km

but our measurement on the map brought us quarter inches.

so,

1/2 in = 2/4 in = 10 km

therefore

1/4 in = 10/2 = 5 km

now,

2 1/4 = 9/4 in

this is 9 times 1/4.

therefore, the distance between the 2 cities is

9 × 5 = 45 km.

Answer:

search-icon-header

Search for questions & chapters

search-icon-image

Class 11

>>Maths

>>Sets

>>Complement of Sets

>>If U = {1,2,3,4,5,6, 7, 8, 9 }, A = {2,

Question

Bookmark

If U={1,2,3,4,5,6,7,8,9},A={2,4,6,8} and B={2,3,5,7}. Verify that

(i) (A∪B)

′

=A

′

∩B

′

(ii) (A∩B)

′

=A

′

∪B

′

Medium

Solution

verified

Verified by Toppr

U={1,2,3,4,5,6,7,8,9}

A={2,4,6,8}

B={2,3,5,7}

(i) (A∪B)

′

={2,3,4,5,6,7,8}

′

={1,9}

A

′

∩B

′

={1,3,5,7,9}∩{1,4,6,8,9}={1,9}

∴(A∪B)

′

=A

′

∩B

′

(ii) (A∩B)

′

={2}

′

={1,3,4,5,6,7,8,9}

A

′

∪B

′

={1,3,5,7,9}∪{1,4,6,8,9}={1,3,4,5,6,7,8,9}

∴(A∩B)

′

=A

′

∪B

Answer:

shoe store $7.80/hour

telemarketer: $6.90/hour

Step-by-step explanation:

Let s = hourly salary at the shoe store.

Let t = hourly salary as a telemarketer.

14s + 19t = 240.3

19s + 22t = 300

Multiply both sides of the first equation by 19. Multiply both sides of the second equation by -14. Then add them.

         266s + 361t = 4565.7

(+)     -266s - 308t = -4200

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

                       53t = 365.7

t = 6.9

Substitute 6.9 for t in the first equation and solve for s.

14s + 19(6.9) = 240.3

14s + 131.1 = 240.3

14s = 109.2

s = 7.8

Answer:

shoe store $7.80/hour

telemarketer: $6.90/hour

Answer:

80% of 75 is 60

Step-by-step explanation:

0.80x=60

x=60/0.80

x=75

Answer:

A) Yes...ABC and GFC are similar using AA.

Step-by-step explanation:

Hi,

3(1/5x - 1/7)

= 3/5x - 3/7

B

✅(◠‿◕)

Answer:

Unknown

Step-by-step explanation:

What is the question? You have the information listed but you forgot to ask the question.

Answer:

Step-by-step explanation:

Question 1

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

Explanation:

The x coordinates of the points for the restrooms and fountain are -2 and 4 in that order. Add up those values and divide by 2

(-2+4)/2 = 2/2 = 1

The midpoint of -2 and 4 on the number line is the value 1. So if the restrooms and fountain were on the x axis and at -2 and 4 respectively, then the midway point is 1 on that same number line. Note: The value 1 is exactly 3 units away from -2 and 4.

We'll use this idea for the y coordinates as well. Add them up, then divide by 2.

Add: 4+(-5) = -1

Divide by two:  -1/2 = -0.5

The y coordinate of the midpoint is -0.5

Overall, the midpoint between the restrooms and fountain is the point (1, -0.5)

For more info, check out the midpoint formula.

====================================================

Question 2

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

Explanation:

We'll use the same idea as before. This time we focus on the locations of the swings and ball field only.

Add the x coordinates for each point: -5+5 = 0

Divide in half: 0/2 = 0

The x coordinate of the midpoint is 0

Repeat for the y coordinates.

Add: 5+(-4) = 1

Cut in half: 1/2 = 0.5

The y coordinate of the midpoint is 0.5

We get the midpoint (0, 0.5) which is where the two pets meet.

====================================================

Question 3

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

Explanation:

Apply the distance formula for the results of the previous two questions.

So we'll apply the midpoint formula for the points (1, -0.5) and (0, 0.5)

[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(1-0)^2+(-0.5-0.5)^2}\\\\d = \sqrt{(1)^2+(-1)^2}\\\\d = \sqrt{1+1}\\\\d = \sqrt{2}\\\\d \approx 1.414\\\\d \approx 1\\\\[/tex]

Answer:

59

Step-by-step explanation:

hope it helps brainliest pls

Answer:

[tex]5.5[/tex]

Step-by-step explanation:

Since 1pt = 2qt, 2.75pt = 5.5qt

Answer:

1 solar radiationnnnnmnnmnnnnn

Answer:

x = 8 - 4y

Step-by-step explanation:

16/2 = 8

8y/2 = 4y

The value of x of the expression is x = 8 - 4y.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x = (1/2)(16 - 8y)

Removing the parenthesis.

x = 16/2 - 8y/2

x = 8 - 4y

Thus,

The value of x is 8 - 4y.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

y=-1x-6

Step-by-step explanation:

According to the confidence interval given, the non-equivalent expression is:

A. [tex]161.7 \pm 13.9[/tex]

The interval given is:

[tex]161.7 \leq \mu \leq 189.5[/tex]

Which can also be written as: (161.7.189.5)

The point estimate is the halfway point of the interval, hence:

[tex]\overline{x} = \frac{161.7 + 189.5}{2} = 175.6[/tex]

The margin of error is half the difference of the bounds, hence:

[tex]M = \frac{189.5 - 161.7}{2} = 13.9[/tex]

According to the point estimate and to the margin of error, the interval can also be written as:

[tex]175.6 - 13.9 \leq \mu \leq 175.6 + 13.9[/tex]

[tex]175.6 \pm 13.9[/tex]

Hence, the only expression which is non-equivalent is:

A. [tex]161.7 \pm 13.9[/tex]

You can learn more about confidence intervals at https://brainly.com/question/25779324

Answer:

33.33

Step-by-step explanation:

(48-36):36*100

(48:36-1)*100

133.33333333333-100 = 33.33

=========================================================

Explanation:

Angle BFE is 117 degrees. The adjacent angle to this (angle BFA) is 180-117 = 63 degrees since the two angles form a straight line, and must add to 180.

Now because BD is parallel to AE, we know that the alternate interior angles BFA and FBD are the same measure. This makes angle FBD to be 63 degrees.

We're told that segment BF bisects angle ABD. That indicates the two smaller pieces (angles ABF and FBD) are the same measure. Both are 63 degrees in this case.

Let x be the measure of angle DBC. This angle will add to angles ABF and FBD to form a 180 degree straight angle

(angleABF) + (angleFBD) + (angleDBC) = 180

(63) + (63) + (x) = 180

x+126 = 180

x = 180-126

x = 54

Angle DBC is 54 degrees.

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

The last set of steps has us focus on triangle BCD. The three angles of any triangle always add to 180.

B+C+D = 180

54 + 85 + D = 180

139 + D = 180

D = 180-139

D = 41

Angle CDB is 41 degrees, and so is angle CEA as they are corresponding angles. Corresponding angles are congruent when we have parallel lines like this.

Therefore, angle E is 41 degrees.

The diagram is below showing all of the angles we found.

Answer:

  C.  90

Step-by-step explanation:

The numbers being multiplied are "factors." The result of multiplication is a "product." In this problem, the product is 90.