15. Ellen records the time it takes for her to commute to work on 100 consecutive mornings and finds that the times are approximately Normally distributed with a mean of 25 minutes and a standard deviation of 4.6 minutes. What percentage of the time does Ellen’s commute take less than 14 minutes?
(a) 0.8%
(b) 1.1%
(c) 1.6%
(d) 98.3%
(e) 99.2%
16. Ellen records the time it takes for her to commute to work on 100 consecutive mornings and finds that the times are approximately Normally distributed with a mean of 25 minutes and a standard deviation of 4.6 minutes. What percentage of the time does Ellen’s commute take between 14 and 36 minutes?
(a) 0.8%
(b) 1.1%
(c) 1.6%
(d) 98.3%
(e) 99.2%
17. Ellen records the time it takes for her to commute to work on 100 consecutive mornings and finds that the times are approximately Normally distributed with a mean of 25 minutes and a standard deviation of 4.6 minutes. What is the 80th percentile for Ellen’s driving times?
(a) -0.84
(b) 0.84
(c) 3.9
(d) 25.8
(e) 28.9
18. Ellen records the time it takes for her to commute to work on 100 consecutive mornings and finds that the times are approximately Normally distributed with a mean of 25 minutes and a standard deviation of 4.6 minutes. On Tuesday, it takes 19 minutes to get to work. What is the z-score for her commute that day?
(a) -6.0
(b) -1.30
(c) -0.77
(d) 0.77
(e) 1.30

Answer:

400

Step-by-step explanation:

because 380 + 20 is 400

Answer:

The key is to prove that the triangles are congruent, then their corresponding parts are congruent.

Step-by-step explanation:

#5)

It it given that:

Angle CBD is congruent to angle CDB.

Angle BAE is congruent to angle DEA.

Triangle CBD is isosceles because it's base angles are equal. Therefore, segment CB is congruent to segment CD.

Triangle CAE is isosceles because it's base angles are equal. Therefore, segment CA is congruent to segment CE.

CA-CB=BA

CE-CD=DE

segment BD is congruent to segment DB.

Angle ABD is supplementary to angle CBD (180-angle CBD= angle ABD).

Angle EDB is supplementary to angle CDB (1980-angle CDB=angle EDB).

therefore, angle ABD=angle EDB.

Triangles ABD and EDB are congruent because of the Side-angle-side theorem.

Triangles ABD and EDB are congruent, segment AD is congruent to segment EB because corresponding legs of congruent triangles are congruent.

#6)

It is given that:

Angle EBC is congruent to angle ECB

Segment AE is congruent to segment DE.

Triangle BEC is iscsceles because it's base angles are equal. Therefore, segment EB is congruent to segment EC.

AE+EC=AC

DE+EB=DB

segment BC is congruent to segment CB.

Triangle BAC is congruent to triangle CDB because of the side-angle-side theorem.

Segment AD is congruent to segment DC because corresponding legs of congruent triangles are congruent.

Answer:

Problem 5)

Step 1:  < CBD = <CDB Reason: given

Step 2: BC = CD  Reason: opposed sides in the isosceles triangle BCD

Step 3: < BAE = < DEA Reason: given

Step 4: AC = CE Reason: opposed sides in the isosceles triangle ACE

Step 5: triangle ACD  = triangle BCE Reason: angle <C is common, and equal sides shown above so use SAS theorem.

Step 6: AD =  BE Reason: third side in the equal triangles shown above.

Problem 6)

Step 1: < ECB = <EBC Reason: Given

Step 2> triangle BEC is isosceles Reason: has two equal angles

Step 3: BE = EC Reason: opposite sides in the isosceles triangle

Step 4: <DEC = < AED Reason: opposed by the vertex (vertical angles)

Step 5: AE = ED Reason: given

Step 6: triangle BAE = triangle EDC Reason SAS theorem

Step 7: side AB = side CD Reason: third side in the equal triangles

Answer:

The vertex of a parabola is (h,k)

Step-by-step explanation:

The vertex form of a parabola is y=a(x-h)^2+k where a is the stretch/compression factor and (h,k) is the vertex. So to find the vertex, you will need (h,k) which represents the horizontal and vertical shift of the parabola

Answer:

f(x)=-8x-6 : -6=y-8x

f(x)=x-9 : -9=y-x

Step-by-step explanation:

f(x)=-8x-6 : -6=y-8x

f(x)=x-9 : -9=y-x

Answer:

$23.20

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year,

then, solving our equation

I = 20 × 0.04 × 4 = 3.2

I = $ 3.20

The simple interest accumulated

on a principal of $ 20.00

at a rate of 4% per year

for 4 years is $ 3.20.

Based on the calculations, your balance after four (4) years is equal to $23.2.

Given the following data:

To determine the balance after four (4) years:

Mathematically, simple interest is given by this formula:

[tex]I = PRT[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]I=20 \times 0.04 \times 4[/tex]

Simple interest = $3.2.

Balance = [tex]3.2 +20[/tex] = $23.2.

Read more on simple interest here: https://brainly.com/question/24341207

Answer: 242.54

Step-by-step explanation: your welcome

Answer: 60.635

Step-by-step explanation:

Answer:

Step-by-step explanation:

p/s=5/16

x/4=5/16

x=4(5)/16

x=20/16

x=5/4

x=1.25 pints

Answer:

The equation of the circle is [tex](x + 1)^2 + y^2 = 25[/tex]

Step-by-step explanation:

Equation of a circle:

The equation of a circle of centre [tex](x_c,y_c)[/tex] has the following format:

[tex](x - x_c)^2 + (y - y_c)^2 = r^2[/tex]

In which r is the radius.

Center (-1,0)

This means that [tex]x_c = -1, y_c = 0[/tex]. So

[tex](x - x_c)^2 + (y - y_c)^2 = r^2[/tex]

[tex](x - (-1))^2 + (y - 0)^2 = r^2[/tex]

[tex](x + 1)^2 + y^2 = r^2[/tex]

Finding the radius:

Distance between the radius and the centre and a point of the circle. In this case, point (2,-4). Using the formula for the distance between two points:

[tex]r = \sqrt{(2-(-1))^2+(-4-0)^2} = \sqrt{3^2 + 4^2} = \sqrt{25} = 5[/tex]

So, the equation of the circle is:

[tex](x + 1)^2 + y^2 = 5^2[/tex]

[tex](x + 1)^2 + y^2 = 25[/tex]

Answer:

36

Step-by-step explanation:

Answer: 36

Step-by-step explanation: Good luck!!

50 - 2(6+1)

50 - 2(7)

50 - 14

36

Answer:

x=1.5

Step-by-step explanation:

No hablo espanol

Answer:

x = -6 and x = 1

Step-by-step explanation:

Move everything to the left side of the equation by subtracting (-10x + 12)

2x² = -10x + 12

2x² + 10x - 12 = 0

Divide each side by 2:

x² + 5x - 6

Find 2 factors of -6 that add up to 5. These factors are 6 and -1

x² + 5x - 6

(x + 6)(x - 1)

Set this equal to 0 and solve for x

(x + 6)(x - 1)

x + 6 = 0

x = -6

x - 1 = 0

x = 1

So, the solutions to the equation are x = -6 and x = 1

The solutions to the equation 2x² = -10x + 12 are x = -6 and x = 1.

To find the solutions to the quadratic equation 2x² = -10x + 12, we can rearrange the equation into standard quadratic form, which is ax² + bx + c = 0.

First, we move all the terms to one side of the equation:

2x² + 10x - 12 = 0

Next, we can solve this equation by factoring, completing the square, or using the quadratic formula. In this case, we'll use factoring.

Looking at the equation, we notice that all coefficients are even, so we can simplify the equation by dividing both sides by 2:

x² + 5x - 6 = 0

Now, we factor the quadratic expression:

(x + 6)(x - 1) = 0

By setting each factor equal to zero, we can find the solutions:

x + 6 = 0 --> x = -6

x - 1 = 0 --> x = 1

Therefore, the solutions to the equation 2x² = -10x + 12 are x = -6 and x = 1. These values make the equation true when substituted back into the original equation.

To learn more about the quadratic equation;

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#SPJ6

Answer:

Step-by-step explanation:

Here are your workings

4.87 x 7.23  simplify

Step 2

(4.87)(7.23)  Add brackets(Optional)

Then you multiply the two exponents to get 35.2101

Your answer would be 35.2101

Answer:

Step-by-step explanation:

Since there are 2 digits in 29, the very last digit is the "100th" decimal place. So we can just say that . 29 is the same as 29/10

Answer:

0.29 = 29/100

Explanation:

Answer:

Step-by-step explanation:

Question 3

The triangle is right isosceles (45°)

The legs have equal length

Question 4

The figure is a square

The angle between sides 24 and 24 is the right angle

Answer:

ooh I am Gryffindor

I love Harry potter

9

57+7=64 (no. of slices)

64 ÷ 7 = 9 R 1

Answer:

while installing a window in an older home, you find that the measurements are not square and will need to shim one side. you find a packet of shims that have 0.25 inch marked on the outside of the wrapper. What fraction of an inch is 0.25, reduce to its lowest terms 0.30

Step-by-step explanation:

Answer:

X intercepts (2/3, 0) and Y intercepts (0,2)

Slope of -3x+2: m= -3

Step-by-step explanation:

Answer:

x = 5/2 km/h

Step-by-step explanation:

Lets x be the speed of the current

The sea lion's speed with the current: 15 + x

The sea lion's speed against the current: 15 - x

Total distance in km with the current: 35

Total distance in km against the current: 25

Time with the current: 35/(15 + x)

Time against the current: 25/(15 - x)

So we do...

35/(15 + x) - 25/(15 - x) = 0

35(15 - x)/(15 + x) - 25(15 + x)/(15 - x): Having common denominators which is (15 + x)(15 - x)

525 - 35x - 375 - 25x = 0: Mutipling the (15 + x)(15 - x)to 0 getting 0

150 - 60x = 0

30(5 - 2x) = 0

x = 5/2

The speed of the current is 2.5 km/hr

From the given information

Lets x be the speed of the current

Also, we have that;

Total distance in km with the current to be 35 while the total distance in km against the current is 25

mathematically;

Time with the current = 35/(15 + x)

Time against the current =  25/(15 - x)

Equating both expression to get the value of "x

35/(15 + x) = 25/(15 - x) = 0

35/(15 + x) - 25/(15 - x) = 0

35(15 - x)/(15 + x) - 25(15 + x)/(15 - x)

Mutiplying the (15 + x)(15 - x)to have:

150 - 60x = 0

30(5 - 2x) = 0

x = 5/2

x = 2.5

Hence the speed of the current is 2.5 km/hr

Learn more on speed and distance here: https://brainly.com/question/4931057

Answer:

bet power of 7

Step-by-step explanation:

I'm help you 2 cubed plus b times 4

Answer:

1.  16

2.  12

3.  5

4.  15

5.  55

6.  8

7.  46

:)

Answer:

(44-8) ÷3=

Step-by-step explanation:

Answer:

Imao

Step-by-step explanation:

Answer:

60°

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

5 times 6 equals 30

That's how I did it.

Answer:

The answer should be 2

Step-by-step explanation:

16 pi    = 1/3  pi    r^2    ( 12)        Divide both sides by pi

16        = 1/3        r^2     (12)         1/3   * 12 = 4

16         = 4          r^2                     divide both sides by 4

4           =             r^2                     You should be able to take it from here !

For 0<x<4, the average rate of change will be -60

For 4<x<8 the the average rate of change will be -31

And for the sentence (on savass in order is)

Stay negative, -31, decrease but at a slower rate

In this exercise we have to use the knowledge of functions to describe the average rates of each one of them, so:

For 0<x<4 will be -60

For 4<x<8 will be -31

First, we have to remember what an average rate means, like:

So we can say that:

[tex]0

See more about functions at brainly.com/question/5245372

Answer:

2

Step-by-step explanation: