Find the area of the shaded region under the standard normal curve. If​ convenient, use technology to find the area. z -2.13 0 A normal curve is over a horizontal z-axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.13 and 0. The area under the curve between negative 2.13 and 0 is shaded. The area of the shaded region is nothing.​(Round to four decimal places as​ needed.)

Answers

Answer 1

Answer:

The area of the shaded region under the standard normal curve is 0.4834.

Step-by-step explanation:

A random variable X is said to have a normal distribution with mean, µ and variance σ².

Then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).

The distribution of these z-variates is known as the standard normal distribution.

Compute the area under the curve between -2.13 and 0 as follows:

[tex]P(-2.13<Z<0)=P(Z<0)-P(Z<-2.13)[/tex]

                           [tex]=0.50-0.01659\\=0.48341\\\approx 0.4834[/tex]

Thus, the area of the shaded region under the standard normal curve is 0.4834.

Answer 2

Using the normal distribution, it is found that the area of the shaded region is of 0.4833.

In a normal distribution, our test statistic is the z-score, which measures how many standard deviations a measure is from the mean. Each z-score has an associated p-value,  which is given at the z-table, and represents the percentile of a measure or or the z-score, which is the area to the left under the normal curve.The area between two z-scores is the subtraction of their p-values.

In this problem, we want the area between Z = -2.13 and Z = 0.

Z = 0 has a p-value of 0.5.Z = -2.13 has a p-value of 0.0166.

0.5 - 0.0166 = 0.4833

The area of the shaded region is of 0.4833.

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Related Questions

If the bathtub holds a total of 46.2 gallons, how many minutes would it take to fill the entire tub? Write an equation in one variable to help you solve the problem. The variable represents the unknown time in minutes.

Answers

Answer:

46.2÷m=x

Step-by-step explanation:

u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).

16.5/min

time = m

gallons / minutes = rate

46.2  = 16.5 (m)

46.2 / 16.5 = 16.5 (m) / 16.5

2.8 = minutes

The deck for a card game contains 30 cards. 10 are red, 10 yellow, 5 blue, and 1 green, and 4 are wild cards. Each player is randomly dealt a five-card hand. a) What is the probability that a hand will contain exactly two wild cards? b) What is the probability that a hand will contain two wild cards, two red cards, and one blue cards?

Answers

Answer: a) 0.1095     b) 0.0095

Step-by-step explanation:

Given : The deck for a card game contains 30 cards.

10 are red, 10 yellow, 5 blue, and 1 green, and 4 are wild cards.

Each player is randomly dealt a five-card hand.

Number of ways to choose 5 cards out of 30 = [tex]C(30,5)=\dfrac{30!}{5!25!}=142506[/tex]

a)  Cards other than wild card = 30-4=26

Number of ways to choose exactly two wild cards = [tex]C(26,3)\timesC(4,2)[/tex]

[tex]=\dfrac{26!}{3!23!}\times\dfrac{4!}{2!2!}\\\\=15600[/tex]

Probability that a hand will contain exactly two wild cards = [tex]\dfrac{15600}{142506}=0.1095[/tex]

b) Number of ways to choose two wild cards, two red cards, and one blue cards = [tex]C(4,2)\times C(10,2)\times C(5,1)[/tex]

[tex]=\dfrac{4!}{2!2!}\times\dfrac{10!}{2!8!}\times5=1350[/tex]

Probability that a hand will contain two wild cards, two red cards, and one blue cards = [tex]\dfrac{1350}{142506}=0.0095[/tex]

A list of pulse rates is 70, 64, 80, 74,92. What is the median for this list?

Answers

Answer:

64 70 74 80 92

Answer = 74

Step-by-step explanation:

The median is when you have an order of numbers in ascending order (smallest to largest) then you find the middle number

Hope this helps :)

If anything is incorrect then please comment and I shall change the answer to the correct one

Median for the given data 70, 64, 80, 74,92 is equals to 74.

What is median?

"Median is defined as the central value of the given data after arranging them into ascending or descending order."

According to the question,

Given data for pulse rates = 70, 64, 80, 74,92

Arrange the data in ascending order we get,

64, 70 , 74, 80, 92

Number of pulse rate reading is 5 , which is an odd number.

Therefore, median is the central value.

Median for the given data = 74

Hence, median for the given data 70, 64, 80, 74,92 is equals to 74.

Learn more about median here

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2. 2(x+4) -5 = 3 + 3

Answers

Step-by-step explanation:

2x + 8 - 5 = 6

2x + 3 = 6

2x = 6 - 3

2x = 3

x = 3/2

Answer:

2 ( x+4) -5 = 3+3

=) 2x +8-5=6

=) 2x+3=6

=) 2x= 6-3

=)2x = 3

=) x =3/2= 1.5

What is the equivalent of 27/5 in decimal form?

Answers

5.4 is equivalent to 27/5.

Answer: 5.4

Step-by-step explanation: 27/5, so 5x5 makes 25 and 2 remaining so 5x0.4=2 so answer is 5+0.4 which equals to 5.4

-50 points- matrix system

Answers

Answer:

-20

-5

-18

Step-by-step explanation:

AX = B to find x

A^-1 AX = A^-1 B

X =  1 -4  -2          2

       -2  2 5    *      7

       2  -4  -2        -3

We multiply across  and down

-1 *2 + -4 *7 -2 *-3 = -20

-2 * 2 + 2 * 7 + 5 * -3 = -5

2 * 2  -4 * 7 -2 * -3 = -18

The matrix is

-20

-5

-18

Answer:

The value of X will be the following :

[tex]\begin{bmatrix}-20\\ -5\\ -18\end{bmatrix}[/tex]

Step-by-step explanation:

So as you can tell, through substitution the equation for this problem will be as follows,

[tex]\begin{bmatrix}1&-4&-2\\ \:-2&2&5\\ \:\:\:\:\:2&-4&-2\end{bmatrix}^{^{^{^{-1}}}}\cdot \:X\:=\:\begin{bmatrix}2\\ \:\:7\\ \:-3\end{bmatrix}[/tex]

Therefore to isolate X, we have to multiply the inverse of the inverse of the co - efficient of X on either side, such that X = A [tex]*[/tex] B,

[tex]X = A * B = \begin{bmatrix}1&-4&-2\\ \:\:-2&2&5\\ \:\:\:2&-4&-2\end{bmatrix}^{\:}\begin{bmatrix}2\\ 7\\ \:-3\end{bmatrix}[/tex]

To solve for X we can multiply the rows of the first matrix by the respective columns of the second matrix,

[tex]\begin{bmatrix}1&-4&-2\\ -2&2&5\\ 2&-4&-2\end{bmatrix}\begin{bmatrix}2\\ 7\\ -3\end{bmatrix} = \begin{bmatrix}1\cdot \:2+\left(-4\right)\cdot \:7+\left(-2\right)\left(-3\right)\\ \left(-2\right)\cdot \:2+2\cdot \:7+5\left(-3\right)\\ 2\cdot \:2+\left(-4\right)\cdot \:7+\left(-2\right)\left(-3\right)\end{bmatrix} = \begin{bmatrix}-20\\ -5\\ -18\end{bmatrix}[/tex]

[tex]X = \begin{bmatrix}-20\\ -5\\ -18\end{bmatrix}[/tex] - if this matrix is matrix 1, matrix 1 will be our solution

The time required for workers to produce each unit of a product decreases as the workers become more familiar with the production procedure. It is determined that the function for the learning process is T(x) = 2 + 0.3 1 x , where T(x) is the time, in hours, required to produce the xth unit. Find the time required for a new worker to produce units 10 through 19.

Answers

Answer: 2.79 hours.

Step-by-step explanation:

Given that the function for the learning process is T(x) = 2 + 0.3 1 x , where T(x) is the time, in hours, required to produce the xth unit

To calculate the time for the new worker to produce 10 units, substitute 10 for x in the equation above.

T(x) = 2 + 0.31 (10)

T(x) = 2 + 3.1

T(x) = 5.1 hours

To calculate the time for the new worker to produce 19 units, substitute 19 for x in the equation above.

T(x) = 2 + 0.31(19)

T(x) = 2 + 5.89

T(x) = 7.89 hours

The time required for a new worker to produce units 10 through 19 will be

7.89 - 5.1 = 2.79 hours

Help me PLS. Does anyone know the correct solution?

Answers

Answer:

Coefficient of Correlation

Step-by-step explanation:

Coefficient of Correlation is a value that ranges between -1 to 1, which is used to denote the closeness or linear relationship between two variables.

The closer the value of the coefficient is to -1 or 1, the stringer the relationship that exists between two variables.

A negative value suggests a negative relationship. Which means, as one variable decreases, the other variable increases.

A positive coefficient of correlation shows a positive relationship between two variables. Which means, as one variable increases, the other also increases.

If the Correlation coefficient is 0, it means there's no relationship between the variables.

When a number is doubled and the
result is decreased by 4 the answer
is 19. Find the number.

Answers

Answer:

7.5

Step-by-step explanation:

v divided by 5 is equal to 60.

Answers

Answer:

[tex]\boxed{v=300}[/tex]

Step-by-step explanation:

Hey there!

To find v we’ll set up the following,

v ÷ 5 = 60

To get v by itself we’ll do

5*60 = 300

v = 300

Hope this helps :)

What is seven to the fifth power equal to

Answers

multiply 7 five times and get

7x7x7x7x7 = 16807

Answer:

16,807

Step-by-step explanation:

Write it out: [tex]7^{5}[/tex]  [tex]7^{5}[/tex] = 7 × 7 × 7 × 7 × 77 × 7 = 4949 × 7 = 343343 × 7 = 24012401 × 7 = 16,807

Mr Gomez wants to put a ceramic Tile border along for all four sides of his kitchen wall mr. Gomez has measured and knows he needs enough tiles to make three rows with 63 tiles in each row on each of his for how many tiles is mr. Goma's need to make the border tiles are sold in boxes with 14 tiles in each box how many boxes of tile does mr. Gomez need to buy show all your mathematical thinking please explain step by step

Answers

Answer:

14 boxes

Step-by-step explanation:

We are given that he needs 3 rows with 63 tiles per row.

Hence total number of tiles needed:

= 3 rows x 63 tiles per row

= 189 tiles

we are also given that tiles come in boxes of 14 tiles.

Hence the number of boxes of tiles needed,

= 189 tiles ÷ 14 tiles per box

= 13.5 boxes

but because he cannot just buy 0.5 of a box (i.e he needs to buy whole boxes), we must round this number up to the next whole box

hence

13.5 boxes rounded up to next whole box = 14 boxes.

I drive 13 miles each way to work every day. It sometimes takes me 20 minutes to get to work, and sometimes it takes me 30 minutes. If Distance = Rate x Time, at what rate am I going if it takes me 20 minutes to get to work? At 30 minutes?

Answers

Answer:

39 mph

26 mph

Step-by-step explanation:

distance = rate * time

20 minutes:

13 miles = rate * 20 minutes

rate = (13 miles)/(20 minutes) * (60 minutes)/(hour)

rate = 39 mph

30 minutes:

13 miles = rate * 30 minutes

rate = (13 miles)/(30 minutes) * (60 minutes)/(hour)

rate = 26 mph

How many three-letter (unordered) sets are possible that use the letters q, u, a, k, e, s at most once each? (No Response) 20 sets

Answers

Answer:

20sets

Step-by-step explanation:

Since we are to select 3 unordered letters from the word q, u, a, k, e, s, we will apply the combination rule.

For example if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

Since the total number of letter in the word q, u, a, k, e, s is 6letters and we are to form 3 letters from it unordered, this can be done in 6C3 number of ways.

6C3 = 6!/(6-3)!3!

6C3 = 6!/3!3!

6C3 = 6×5×4×3×2×1/3×2×1×3×2×1

6C3 = 6×5×4/3×2

6C3 = 120/6

6C3 = 20

Hence 20sets of selection are possible

The function f(x) = (x - 4)(x - 2) is shown.
What is the range of the function?
o all real numbers less than or equal to 3
o all real numbers less than or equal to -1
O all real numbers greater than or equal to 3
O all real numbers greater than or equal to -1
2
61
-1028
-2​

Answers

Answer:

all real numbers greater than or equal to -1

Step-by-step explanation:

In order to solve this problem we need to know the vertex and the direction its pointing.

First we expand,

x^2-6x+8

To find the x value of the vertex we use this formula (-b/2a).

-(-6)/2(1) = 3

Now we plug 3 in the equation to get the y value,

(3)^2 - 6(3) + 8 = 9 - 18 + 8 = -1

The vertex is (3,-1)

We know the graph points up because x^2 is positive

The vertex is the lowest point, so we now know that -1 is the starting range and if the graph is pointing up, that means all values greater than -1.

This leads to our answer all real numbers greater than or equal to -1.

When csc(Theta)sin(Theta) is simplified, what is the result? StartFraction 1 Over cosecant squared EndFraction StartFraction 1 Over sine squared EndFraction 0 1

Answers

Step-by-step explanation:

csc θ sin θ

(1 / sin θ) sin θ

1

The simplified value of the given expression comes to be 1.

The given expression is:

[tex]cosec\theta.sin\theta[/tex]

What is the trigonometric ratio [tex]cosec\theta[/tex]?

The trigonometric ratio [tex]cosec\theta[/tex] is the ratio of the hypotenuse to the opposite side. It is the inverse of [tex]sin\theta[/tex].

[tex]cosec\theta=\frac{1}{sin\theta}[/tex]

We know that [tex]cosec\theta=\frac{1}{sin\theta}[/tex]

So [tex]cosec\theta.sin\theta[/tex]

[tex]=\frac{1}{sin\theta} .sin\theta[/tex]

=1

So, the simplified value is 1.

Hence, the simplified value of the given expression comes to be 1.

To get more about trigonometric ratios visit:

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A homeowner wants to build a fence to enclose a 320 square yard rectangular area in his backyard. Along one side the fence is to be made of heavy-duty material costing $9 per yard, while the material along the remaining three sides costs $1 per yard. Determine the least cost to the homeowner.

Answers

Answer:

Determination of the least cost of fence enclosure:

= cost of heavy-duty one side of the length plus cost of remaining three sides of the fence

= $416 ($360 + $56)

= $416

Step-by-step explanation:

Rectangular Fence Area = 320 square yard

Since fence is rectangular, the two sides are length and width

Length of rectangular is always greater than the width

Length cannot be 20 yard with width as 16 yard

Therefore, length = 40 yard and width = 8 yard.

Proof: Area of a rectangular = 40 x 8 = 320 square yard

Since, parameter = 2 (Length + Width)

= 2 x (40 + 8)

= 96 yards

Therefore, along one side with heavy-duty material is one length side of the fence = 40 yard

Cost of the one length with heavy-duty material = 40 x $9 = $360

Remaining three sides = 96 - 40 = 56 yard

Cost of remaining three sides = 56 x $1 = $56

Total cost of fencing = $416 ($360 + $56)

Need help please will mark brainliest

Answers

Step-by-step explanation:

Maximum = 62

Median = (34+37+39+32+48+45+53+62+58+61+60+41)/12= 47.5≈48

quartile

In increasing order

32, 34, 37, 39, 41, 45, 48, 53, 58, 60, 61, 62

Upper quartile= (58+60)/2 = 59

Lower quartile= (37+39)/2 = 38

Minimum= 32

the function y= -16t^2 + 248, models the hight y in feet of a stone t seconds after it dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground?

Answers

Answer:

[tex]t \: = 3.92 \: sec[/tex]

Step-by-step explanation:

When (t =0)

Height of cliff = 248 feet = 75.5m

Using Newton's equations of motion:

[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]

75.5 = 0 * t + 4.9 * t^2

Solving further :

[tex]t \: = 3.92 \: sec[/tex]

Solve this problem (-25) +(-12)+(-34)=show me the steps

Answers

So basically they are all negatives... positive and negative make negative you add them and put a negative in front.... -25-12-34 add them -37-34 = -71

Answer:

(-25)+(-12)+(-34) = -71

so when you add negative numbers you simply add them such as -2+-2 -4

so same conditions

so it will be -25+-12+-34 and it will simply be 25+12+34 so -71

A number is chosen at random from 1 to 50. Find
the probability of selecting multiples of 10.
Step by step.

Answers

Answer:

  1/10

Step-by-step explanation:

There are 5 numbers in the range that are multiples of 10: 10, 20, 30, 40, 50. The probability of choosing one of those at random from the set of 50 numbers is ...

  5/50 = 1/10

Black Diamond Ski Resort charges $50 for ski rental and $15 an hour to ski. Bunny Hill Ski Resort charges $75 for ski rental and $10 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same. 15x − 75 = 10x − 50 15x − 50 = 10x − 75 15x + 50 = 10x + 75 15x + 75 = 10x + 50

Answers

Answer:

The cost of 5 hours of skiing would be the same ($125) after 5 hours.

Step-by-step explanation:

Black Diamond:  ChargeBD(h) = $50 + ($15/hr)h, where h is the number of hours spent skiing.

Bunny Hill:  ChargeBH(h) = $75 + ($10/hr)h

We equate these two formulas to determine when the cost of using the ski slopes is the same:

ChargeBD(h) = $50 + ($15/hr)h = ChargeBH(h) = $75 + ($10/hr)h

We must now solve for h, the number of hours spent skiing:

50 + 15h = 75 + 10h

Grouping like terms, we obtain:

5h = 25, and so h = 5 hours.

The cost of 5 hours of skiing would be the same ($125) after 5 hours.

When conducting a hypothesis test concerning the population mean, and the population standard deviation is unknown, the value of the test statistic is calculated as __________.

Answers

Answer:

the value of the test statistic is calculated as "T - distribution" with the formula;

t = (x-bar - μ)/(s/√n)

Step-by-step explanation:

We are told that the standard deviation is unknown. But normally, we use a z-distribution if the standard deviation is known.

However, in a hypothesis test for a population mean where the population standard deviation is unknown is still conducted in the same way like we do when we know the population standard deviation. The only difference in this case is that we will use the t-distribution rather than the standard normal z-distribution.

The t-distribution formula used is;

t = (x-bar - μ)/(s/√n)

Sam have worked these hours during the week: 4.5, 8.75, 9.5, 10, and 4.25 hours. How many hours did Sam work?

Answers

Answer:

37 hours

Step-by-step explanation:

4.5 + 8.75 + 9.5 + 10 + 4.25 = 37 hours

Answer:

37 hours

Step-by-step explanation:

4.5 hours = 4 hrs and 30 mins

8.75 hrs = 8 hrs and 45 mins

9.5 hrs = 9 hrs and 30 mins

10 hrs = 10 hrs and 0 min

4.25 hrs = 4 hrs and 15 mins

(30 + 45 + 30 + 15) mins = 2 hrs

Therefore, total hours Sam worked = (4 + 8 + 9 + 10 + 4 + 2) hrs = 37 hours

What is the value of s?​

Answers

Answer:

s = 8

Step-by-step explanation:

2s = s + 8

2s - s = 8

s = 8

What is the answer, what are the steps to solve this, and what do the parts of the equation represent?

Answers

Step-by-step explanation:

Just sub 4 into where n is

Mr Osei has a rectangular field measured 85m long and 25m wide. How long is the distance around the field?

Answers

Answer:

220m

Step-by-step explanation:

l=85m

b=25m

perimeter=2(l+b)

2(85+25)

2(110)

=220m

perimeter is 220m

Answer:

Distance around the field is 220m

Step-by-step explanation:

The distance around the field means the perimeter of the field

Since the field is rectangular

Perimeter of a rectangle = 2l + 2w

where l is the length

w is the width

From the question

l = 85m

w = 25m

Perimeter = 2(85) + 2(25)

Perimeter = 170 + 50

The final answer is

Perimeter = 220m

Hope this helps you

Zamba has found a little black dress on sale for 50% off the original price of $239.99. She also has a coupon offering free shipping and an additional 10% off of her entire online purchase. If she buys the dress and a pair of shoes costing $34.70, how much will she pay for her ensemble?

$108.00
$104.70
$94.23
$139.23

Answers

Answer:

$139.23

Step-by-step explanation:

50% off the original price of $239.99

= $239.99-(0.5*239.99)

= 239.99-119.995

= $119.995

She purchase a pair of shoes also worth $34.70

Total cost now= $119.995 + $34.70

Total cost now= $154.695

But she has a coupon that gives her 10% off her total sales

Now she wants pay

= $154.695 - 0.1(154.695)

= $154.695-15.4695

= $139.2255

Approximately $139.23

Sin tita= 0.6892.find the value Of tita correct to two decimal places

Answers

Answer:

[tex]\theta \approx 6.28n + 2.38, \quad n \in \mathbb{Z}[/tex]

or

[tex]\theta \approx 6.28n + 0.76, \quad n \in \mathbb{Z}[/tex]

Considering [tex]\theta \in (0, 2\pi][/tex]

[tex]\theta \approx 2.38[/tex]

or

[tex]\theta \approx 0.76[/tex]

Step-by-step explanation:

[tex]\sin(\theta)=0.6892[/tex]

We have:

[tex]\sin (x)=a \Longrightarrow x=\arcsin (a)+2\pi n \text{ or } x=\pi -\arcsin (a)+2\pi n \text{ as } n\in \mathbb{Z}[/tex]

Therefore,

[tex]\theta= \arcsin (0.6892)+2\pi n, \quad n \in \mathbb{Z}[/tex]

or

[tex]\theta = \pi -\arcsin (0.6892)+2\pi n, \quad n\in \mathbb{Z}[/tex]

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

[tex]\theta \approx 6.28n + 2.38, \quad n \in \mathbb{Z}[/tex]

or

[tex]\theta \approx 6.28n + 0.76, \quad n \in \mathbb{Z}[/tex]

Question
Consider this expression.
4/2² - 6²
Type the correct answer in the box. Use numerals instead of words. For help, see this worked example e.
When a =
-5 and b = 3, the value of the expression is
Submit

Answers

Answer:

16

Step-by-step explanation:

4 * sqrt( a^2 - b^2)

Let a = -5 and b =3

4 * sqrt( (-5)^2 - 3^2)

Do the squaring first

4 * sqrt( 25 - 9)

Subtract inside the square root

4 * sqrt( 16)

Take the square root

4 * 4

Multiply 16

Answer:

[tex]\Large \boxed{16}[/tex]

Step-by-step explanation:

[tex]4\sqrt{a^2-b^2 }[/tex]

[tex]\sf Plug \ in \ the \ values \ for \ a \ and \ b.[/tex]

[tex]4\sqrt{-5^2-3^2 }[/tex]

[tex]4\sqrt{25-9 }[/tex]

[tex]4\sqrt{16}[/tex]

[tex]4 \times 4=16[/tex]

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