Assume z is a standard normal random variable. Then P(–1.20 ≤ z ≤ 1.50) equals

Answers

Answer 1

When is a standard normal random variable, the probability of P(–1.20 ≤ z ≤ 1.50) is 0.8181.

What is the probability?

The probability illustrates the likelihood of events.

From the information, it's important to note that P(–1.20 ≤ z ≤ 1.50) will be:

= P(Z ≤ 1.50) - P(Z ≤ -1.20)

= P(Z ≤ 1.50) - [1 - P(Z ≤ -1.20)]

It should be noted that by using the normal z table, the probability of the corresponding z score will be 0.9332 and 0.8849.

This will be:

= 0.9332 - (1 - 0.8849)

= 0.8181

Therefore, the probability is 0.8181.

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Related Questions

PLEASE HURRY I WANT TO FIISH MY TEST PLEASE ASAP!!!
Determine which integers in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false.

Answers

The integer in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false is 32

What is an inequality?

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, based on the information we will replace m with 32. This will be illustrated thus:

1/4(32 - 4) ≤ 1/8 (32 - 16)

= 1/4(28) ≤ 1/8(16)

= 7 ≤ 2

In this case, 7 isn't less than or equal to 2. Therefore, 32 is the correct integer.

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Can you help me solve this problem?

Answers

The probability that the sample proportion surviving for at least 3 years will be less than 67% is of:

0.1131 = 11.31%.

Normal Probability Distribution

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:

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

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

The proportion and the sample size are given as follows:

p = 0.73, n = 80.

Hence the mean and the standard error are given as follows:

[tex]\mu = 0.73[/tex].[tex]s = \sqrt{\frac{0.73(0.27)}{80}} = 0.0496[/tex]

The probability that the sample proportion surviving for at least 3 years will be less than 67% is the p-value of Z when X = 0.67, hence:

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

Z = (0.67 - 0.73)/0.0496

Z = -1.21

Z = -1.21 has a p-value of 0.1131.

Hence the probability is:

0.1131 = 11.31%.

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There was 3/5 of a gallon of paint in the bucket. Dr. Wu used 2/5 of that. How much paint was left?

Answers

Answer:

1/5

Step-by-step explanation:

equation: 3/5-2/5=x

we can multiply the whole equation by 5 so that we can easily subtract the numbers

3-2=1

now we divide it by 5 so that we get our number in a fraction

after we divide we get 1/5

A plant manufactures part whose lengths are normally distributed with a mean of 16.3 centimeters and a standard deviation of 2.5 centimeters.

Question:

If one part is randomly selected, find the probability that the part is between 10.8 and 12.8 centimeters.

Answers

The probability that the plant manufactures a part between 10.8 and 12.8 centimeters 13%

How to find the probability that the part is between 10.8 and 12.8 centimeters

The probability is solved z scores, this measures the amount of standard deviation sample X is from mean. the formula is below

z = (X - μ) / σ

Definition of variables

mean, μ = 16.3 centimeters

standard deviation, σ = 2.5 centimeters

X = 10.8 and 12.8 centimeters

z score, z

substituting into the formula

for X = 12.8 centimeters

=  (X - μ) / σ

= (12.8 - 16.3) / 2.5

= -1.4

the p value for z of -1.4 = 0.161513

for X = 10.8 centimeters

=  (X - μ) / σ

= (10.8 - 16.3) / 2.5

= -2.2

the p value for z of -2.2 = 0.027807

the probability is calculated as below

0.161513 - 0.027807= 0.133706

= 0.13

=13%

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Juan is playing a game in which he can win $100 with probability 0.2, $300 with probability 0.3, and $500 with probability 0.5. What is the expected value of Juan's winnings?

Answers

Juan's winnings has an expected value of $360

How to determine the expected value of Juan's winnings?

The given parameters in the question are:

$100 with probability 0.2,

$300 with probability 0.3,

$500 with probability 0.5.

The expected value is then calculated as

E(x) = Sum of (amount * probability)

Substitute the known values in the above equation, so, we have the following representation

E(x) = 100 * 0.2 + 300 * 0.3 + 500 * 0.5

Evaluate

E(x) = 360

Hence, the expected value  is $360

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A plant manufactures parts whose links are normally distributed with a mean of 16.3 cm and a standard deviation of 2.5 cm if one part is randomly selected find the probability that the part is between 10.8 and 12.8 cm

Answers

The probability that the part is between 10.8 and 12.8 cm is 0.0669.

What is a normal distribution?

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is symmetric around the mean.

Here, we have

Mean = 16.3cm

Standard deviation = 2.5cm

We have to find the probability that the part is between 10.8 and 12.8 cm

Now,

we know that z = (x−μ)/σ

putting values in the normal distribution formula, we get

P( 10.8 < x < 12.8) = P( (10.8 - 16.3)/2.5 < z < (12.8 - 16.3)/2.5)

                            = P ( -2.2 < z < -1.4)

P( 10.8 < x < 12.8) = 0.0669, by normal distribution table

Hence, the probability that the part is between 10.8 and 12.8 cm is 0.0669.

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Given the inequality 4x ≤ 28, determine the value of x.

Answers

Step-by-step explanation:

Given the inequality 4x ≤ 28, determine the value of x.

4x ≤ 28

divide both sides by 4:

4x/4 ≤ 28/4

x ≤ 7

set builder notation: (-∞, 7]

answer:

The value of x is 7.

Step-by-step explanation:

4x ≤ 28 | divide both sides by 4

4x / 4 = x  and 28 / 4 = 7

therefore, x ≤ 7

What is the solution to the equation 1/3x + 2/9x =10

Answers

The solution to x in the  equation is 1/3x + 2/9x =10 is 18

To solve for x we follow the step;

Step 1: Combine the equation multiple into single fraction

1/3x + 2/9x =10

[tex]\frac{x}{3}[/tex] +[tex]\frac{2x}{9}[/tex] =10

Step 2: Find the common denominator

[tex]\frac{3x}{9}[/tex] + [tex]\frac{2x}{9}[/tex] =10

Step 3: Add the fraction with common denominator

[tex]\frac{3x +2x}{9}[/tex]= 10

[tex]\frac{5x}{9}[/tex] =10

Step 4: Cross multiply

5x = 9(10)

5x = 90

Step 4: Divide both 5

[tex]\frac{5x}{5}[/tex] =[tex]\frac{90}{5}[/tex]

x= 18

Therefore, the solution for x in the equation is 18

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The blood types of 200 people are collected at a doctor’s office. The table shows the breakdown of patients by blood type.

If a person from this group is selected at random, what is the probability that this person has type AB blood? Express your answer as a fraction

Blood Type Survey Results
Blood Type Number of Patients
A 45
B 65
O 75
AB 15

Answers

When a person from this group is selected at random, the probability that this person has type AB blood is 3/40

What is probability?

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

It should be noted that in this case, the number of people with AB blood is 15 and there are 200 people. The probability will be:

= Number of AB blood type / Total number of people

= 15 / 200

= 3/40

The probability is 3/40.

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hole me out on this thanks

Answers

Answer: [tex]5^{2} + 4[/tex]

Step-by-step explanation:

[tex]2 + 3^3[/tex] =?

2 + 27 = 29

10 * 2 - 9 = 20 - 9 = 11

[tex]5^2 + 4[/tex] = 25 + 4 = 29

[tex]5^3\\[/tex] = 5 * 5*5 = 125

3+ 4 * 3 = 3 + 12 = 15

Assessment Practice
5. A science teacher has $225 to spend on lab equipment.
He buys 4 posters with a guide to classifying rocks, for
$19 each. Student rock collections cost $9 each. How
many rock collections can he buy? Explain how you solve.
Use one or more equations and bar diagrams in your
explanation. Tell what your variables represent. 4.AR.1.1.4.AR.2.2

Answers

Answer:

Assessment Practice 5. A science teacher has $225 to spend on lab equipment. He buys 4 posters with a guide to classifying rocks, for $19 each. Student rock collections cost $9 each. How many rock collections can he buy? Explain how you solve

Let

x -----> number of rock collections that he can buy

so

the algebraic expression that represents this situation is

Solve the inequality for x

subtract 76 both sides

Divide both sides by 9

therefore

The maximum number of rock collections that he can buy is 16

Step-by-step explanation:

The equation is 9x+76=225 and the number of rock collections he can buy is 17.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a science teacher has $225 to spend on lab equipment.

Let the number of rocks collected be x.

He buys 4 posters with a guide to classifying rocks, for $19 each.

That is 19×4=76

Student rock collections cost $9 each.

Now, 9×x=9x

So, the equation is 9x+76=225

Subtract 76 on both the sides of equation, we get

9x=149

Divide 9 on both the sides of equation, we get

x=16.5

x≈17

Therefore, the number of rock collections he can buy is 17.

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Select the correct answer.
Which set of absolute values is compared correctly?
A. -71 <181<|9|<1-10|

B.1-41 <1-3/<13<|4|

C. 1211-51> |-7|>1-81

D. 1-41>19> |-31 >|-10|

Answers

In actuality, "absolute value" refers to thinking of all numbers as positive and removing all negative signs from front of them (or zero). Symbol for absolute value. -71<181<|9|<1-10| set of absolute values

Explain about the absolute values?

Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0.

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.

The exact distance of an integer or number from zero on a number line is its absolute value. As a result, the absolute value is never negative and is always positive.

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The formula for finding the surface area of a cube is 6s2, where s is the length of each side of the square. Evaluate for s=10 to find the number of square centimeters (cm2) for the surface area of a cube with a side length of 10 cm. i need helpp

Answers

The surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].

Given:

The formula for finding the surface area of a cube is 6s2.

side length s = 10 cm.

Surface area of a cube =  6[tex]s^{2}[/tex] = 6*s*s

= 6 * 10 * 10

= 60 * 10

= 600 [tex]cm^{2}[/tex].

Therefore the surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].

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Find the dimensions of the rectangle with the largest area; it has two vertices on the x-axis and two vertices above the x-axis on the graph of
y = 5 − x^2.

Answers

Answer:

  (2/3)√15 wide by 10/3 tall, approx 2.582 by 3.333

Step-by-step explanation:

You want the dimensions of the largest rectangle that fits under the graph of y = 5 -x² above the x-axis.

Dimensions

The graph of y=5-x² is symmetrical about the y-axis, so the width of it will be x -(-x) = 2x and the height will be 5-x².

Area

The area will be the product of the width and height:

  A = WH

  A = (2x)(5 -x²) = 10x -2x³

Maximum area

The area will be a maximum where the derivative of the area function is zero.

  dA/dx = 10 -6x² = 0

  x² = 10/6

  x = (√15)/3

The corresponding rectangle dimensions are ...

  width = 2x = (2/3)√15

  height = 5 -x² = 5 -5/3 = 10/3

The rectangle with largest area is (2/3)√15 wide by 10/3 tall.

Katyhas$100,000inasavingsaccount.Theinterestrateis8%peryearandisnotcompounded.Howmuchwillshehaveintotalin2years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $

Answers

The amount that Katy would have saved in her savings account in 2 years is $16, 000

How to find the amount saved?

Given that the interest on the savings account is not compounded, the amount that Katy would have saved in 2 years can be found by the formula:
= Principal x Interest Rate x Time

Principal = $100, 000

Interest rate = 8%

Time = 2 years

The amount that Katy would have saved is:

= Principal x Interest Rate x Time

= 100, 000 x 8% x 2

= $16, 000

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1. Given segment AB with A(-3, 2) and B (5, -4). If point P lies on segment AB such that the ratio of
AP to PB is 2:6. Find the coordinates of p

Answers

The coordinates of P is ( -1 , 0.5) .

What is section formula ?

  We can get a point's coordinates using the section formula when it divides a line segment externally or internally in a certain ratio. It is a useful tool for determining the coordinates of the point that divides the line segment in a particular ratio. The midpoint of a line segment can be found using this section formula, and it can also be used to derive the midpoint formula.

Here Using the section formula, if a point P(x,y) divides the line joining the points A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex]  in the ratio of m:n then,

=>  (x,y) = [tex](\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n} )[/tex]

Here A[tex](x_1,y_1)[/tex] =( -3,2) and  B[tex](x_2,y_2)[/tex]  = (5,-4)  and m:n = 2:6

Then,

=> ( x,y ) = [tex](\frac{2(5)+6(-3)}{2+6} ,\frac{2(-4)+6(2)}{2+6})[/tex]

=> (x,y) = [tex](\frac{10-18}{8},\frac{-8+12}{8} )[/tex]

=> (x,y) = [tex](\frac{-8}{8} ,\frac{4}{8})[/tex]

=> (x,y) = (-1,0.5)

Hence the coordinates of P is (-1 , 0.5) .

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v+8w=4v,for v

-m+5n=-2, for n

Answers

Answer:

v = 8w/3,n = (m - 2)/5.

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

Given equationsv + 8w = 4v and - m + 5n = - 2

Solve the first equation for vv + 8w = 4v4v - v = 8w3v = 8wv = 8w/3

Solve the second equation for n- m + 5n = - 25n = m - 2n = (m - 2)/5

Answer:

Value of v = (8w)/3Value of n = (m - 2)/5

Step-by-step explanation:

1) v + 8w = 4v, for v?

→ v + 8w = 4v

→ 8w = 4v - v

→ 8w = 3v

→ [ v = (8w)/3 ]

Thus, value is (8w)/3.

2) -m + 5n = -2, for n?

→ -m + 5n = -2

→ 5n = -2 + m

→ 5n = m - 2

→ [ n = (m - 2)/5 ]

Thus, value is (m - 2)/5.

The first section of a newspaper has 16 pages. Advertisements take up 3 and 3/8 of the pages. How many pages are not advertisements?

Answers

A total of 12 5/8 pages is not meant for advertisement

How to determine the number of pages that are not for adverts?

From the question, we have the following parameters

First section = 16 pages

Pages for advertisement = 3 and 3/8 pages

Rewrite the above parameters as

First section = 16 pages

Pages for advertisement = 3 3/8 pages

The number of pages that are not for adverts is then calculated as

Pages not for adverts = First section - Pages for advertisement

Substitute the known values in the above equation

So, we have the following equation

Pages not for adverts = 16 - 3 3/8

Evaluate the difference

Pages not for adverts = 12 5/8

Hence, the number of pages that are not for adverts is 12 5/8 pages

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Marvin is helping his teachers plan a field trip. There are 136 people going on the field trip and each school bus holds 51 people. What is the minimum number of school buses they will need to reserve for the trip?

Answers

Answer: 3 busses

Step-by-step explanation:

FIRST ANSWER GETS FIVE STARS AND BRAINLIEST!

Pine Street, Rector Street, and Taylor Street intersect to form a triangular-shaped park as shown.

(picture below)

​What is the correct order of the lengths of the streets from longest to shortest?

Answers

Answer:

Rector, Pine, Taylor

Step-by-step explanation:

The opposite side of each angle's lengths depend on how large the angle is. The larger the angle is, the longer the side. Because the angle opposite to Rector is the greatest, then it is the longest. Thus, then follows Pine and Taylor. Hope this helps!

student enrollment at a local school is concerning because the number of student has dropped to 504, which is 20% decrease from the previous year. what was the student enrollment the previous year?

Answers

The student enrollment the previous year is 630 students.

How to calculate the number of students?

Sine the percentage given is 10% decrease, us implies that the percentage for the previous year will be x

Based on the information given, this will be illustrated as:

x - (20% × x) = 504

x - 0.2x = 504

0.8x = 504.

Divide.

x = 504 / 0.8

x = 630

There were 630 students.

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(x-2x³-29x² - 43x+8)÷(x-7)

Answers

Answer:

-2x^2  - 43x - 343 - 2393/x-7

3.) Johannes sold an order of 3 Strawberry pies
for $12.50 each. She paid her assistant
$1.10 for each Strawberrye pie sold. How much
money did Johannesearn from the pies sold?

Answers

Answer:

$34.20

Step-by-step explanation:

Since each pie is $12.50 but the assistant gets $1.10 for each pie, Johannes will get $11.40 for each pie sold.

We know that there were 3 pies sold so you must solve the equation below

11.40*3

The answer is $34.20

Does anyone know the answer to this problem?

Answers

It is a scalene triangle .

What is a scalene triangle?A triangle called a Scalene Triangle in geometry is one with equally spaced-apart sides. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.The sides and angles of the triangles are used to define them. A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional plane object having three sides and three angles. There are three edges and three vertices.

acc to our quesion-

all the sides of triangle are unequal

if all sides are unequal ,it is called scalene triangle.

hence,It is a scalene triangle .

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The sum of two odd consecutive integers is 88. Find the integers.

Answers

Answer:

43, 45 are the numbers

Step-by-step explanation:

work out the size of angle x 24

Answers

Answer:

  78°

Step-by-step explanation:

You want the measure of base angle x in an isosceles triangle with a.pex angle 24°.

Base angle

The two base angles of an isosceles triangle are congruent. The sum of all angles is 180°, so we have ...

  24° +2x = 180°

  12° +x = 90° . . . . . . divide by 2

  x = 78° . . . . . . . subtract 12°

The measure of angle x is 78°.

Kyle buys $50,000 of company XYZ's shares, at a share price of
$100. A year later, XYZ's share price is $110, and Kyle sells all his
shares. How many dollars did Kyle's investment gain?

Answers

The share Kyle sells worth $55000 and Kyle's gain amount is $5000

Given,

The share bought by Kyle of company XYZ = $50,000

The share price = $100

The  share price after an year = $110

We have to find the gain amount by Kyle when Kyle sells all his shares.

Here,

We can apply Unitary method;

100 ⇒ 110

50000 ⇒ x

Compute;

100x = 110 x 50000

x = (110 x 50000) / 100

x = 110 x 500

x = $55000

Now,

Kyle gains,

55000 - 50000 = $5000

That is,

The share Kyle sells worth $55000 and Kyle's gain amount is $5000

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Which algebraic expression represents the amsplit the cost of a $20.00 gift?
A. f + 20
B. 20f
C. 20 ÷ f
D. f ÷ 20

Answers

Answer:

The answer is C: 20 ÷ f

Step-by-step explanation:

find zeros f(x)=x^4-6x^3-21x^2=150x-100 given k=5

Answers

The zeros of the polynomial x⁴ - 6x³ - 21x² - 150x - 100  are 0.6511 and 8.262 respectively

Zeros of a Polynomial

Zeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively.

The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.

To find the zeros of this polynomial function, we have to write the function appropriately.

x⁴ - 6x³ - 21x² = 150x - 100

x⁴ - 6x³ - 21x² - 150x - 100 = 0

The roots of this function is 0.6511 and 8.262 respectively

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i need some help on these, can anybody help me?

Answers

A: m< Y = 60
All the ángles inside have to equal 180 º
Other Questions
create a CLAIM to answer the supporting question, Why were African Americans conflicted in their support during the Revolution? Your claim should be at least two sentences, a Select "Correct" if the sentence is punctuated correctly and "Run-on" if it is not.The museum bought the painting by Goya it was displayed in the West Gallery.A) CorrectB) Run-on Graph the line that represents a proportional relationship between d and t with the property that an increase of 5 units in t corresponds to an increase of 8 units in d.What is the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will correspond to a change of how many units in d?)The unit rate is ?Graph the relationship. George runs cross country. He runs 3 miles in 24 minutes. If he keeps the same pace how long will it take him to run 7 miles? The equalizing temperature changes in response to changes in external forces of the boundary conditions of climate. What is this about?. Solve for x.2/x^24 1/x+2 = 3/x2 Which of the following was identified as a problem by highest percentage of international corporations when two pipes fill a pool together, they can finish in 4 hours. if one pipe fills half of the pool and then the other takes over and finishes filling the pool, the pool will fill in 9 hours. how long would it take each pipe to fill the pool if it were working alone? A triangle has interior angles of 50, 55, and 75 with side lengths of 3.1 m, 3.2 m, and 4.0 m. A secondtriangle has side lengths of 10.3 m, 10.5 m, and 12.0 m. What must the interior angles of the second trianglebe for the two shapes to be similar? a company is planning to have a booth at a job fair to recruit for landscapers. in order to help potential applicants decide whether they are a good fit for the job, the company should: 1-Choose the correct interrogative for the following questions: y=2/3x-18 rate of change Laura and Kirk are comparing how much they have been running. Laura has alreadyrun 36 miles and Kirk has run 64. Laura begins running 21 miles per week and Kirk runs 17 milesper week. How many additional weeks, w, will it take for their total distance run to be equal? PLEASE HELP!!!! I WILL GIVE YOU BRAINLIST!! PLEASE ASAP :)Which graph shows the image of ABC after a rotation about the origin? A story focused on events that really happened with characters who are real-life people is probably a: Which of these is produced during photosynthesis? A. chemical energy B. water C. carbon dioxide bill wrote all the numbers from 1 to 1000. how many digits did he write down? Select the answer that best describes the relationship between photosynthesis and cellular respiration. Question 5 options:Cellular respiration and photosynthesis have a linear relationship where cellular respiration creates energy for photosynthesis to occur. Photosynthesis uses light eneregy to create the carbon dioxide needed for cellular respiration to occur while cellular respiration also creates carbon dioxide that is released into the atomosphere. This creates a positive feedback loop of carbon dioxide production. Photosynthesis uses light energy to convert carbon dioxide and water into glucose and oxygen which is needed for cellular respiration to occur. Cellular respiration takes the glucose and oxgyen and produces water and carbon dioxide that is needed for photosynthesis while also producing energy. Celluar respiration uses the energy from the sun to create ATP which is used in the process of photosynthesis to produce oxygen and water which are essential to life on this planet. Explain how the hawley-smoot tariff was intended to combat the depression but instead made the depression worse. The ______________ is the original component of personality and is located completely in the ______________ region of the mind.