A clinical psychologist is administering the Hamilton Rating Scale for Depression (Hamilton, 1967). The scale ranges from 0 to 52. Scoring is based on the 17-item scale and scores of 0–7 are considered as being normal, 8–16 suggest mild depression, 17–23 moderate depression and scores over 24 are indicative of severe depression (Zimmerman, Martinez, Young, Chelminski, & Dalrymple, 2013).

We have some evidence about the mean score for the Hamilton Rating Scale for Depression among the population of adolescents: μ = 6 with a standard deviation of σ =1.5. The clinical psychologist’s patient, a 14-year old girl, scores a 10 on the scale. How would you describe her score relative to the population of adolescents? (Please use your knowledge of z-scores to answer this question.)

Answer:

I think YZ 'cause the triangle is iscoceles triangle. As the two sides XY and XZ are equal the longest side is YZ.

Answer:

[tex]1)\text{ Friday}\\2)\text{ }7:00\\3a)\text{ }0\\3b)\text{ }4\\3c)\text{ }0\\4a)\text{ }6\\4b)\text{ }4\\4c)\text{ }2[/tex]

The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is [tex](x,y) \longrightarrow (x+2, y+2)[/tex]

The time for the ball to pass the top of the building is determined as 4 s.

The time for the ball to pass the top of the building is obtained when the velocity of the ball is zero.

h = -16t² + 128t + 144

v = dh/dt

v = -32t + 128

at maximum height, v = 0

0 = -32t + 128

32t = 128

t = 128/32

t = 4 s

Thus, the time for the ball to pass the top of the building is determined as 4 s.

Learn more about time of motion here: https://brainly.com/question/2364404

#SPJ1

After 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have:

An object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second.

When the ball pass the top of the building, h = 144 foot

Plug h = 144 foot in h= -16t² + 128t + 144

144 = -16t² + 128t + 144

[tex]\rm -16t^2+128t=0[/tex]

t = 0 or t = 8 seconds

At t = 0, initially, the ball was thrown upward.

At t = 8 seconds, the ball passes the top of the building

Thus, after 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second.

Learn more about quadratic equations here:

brainly.com/question/2263981

#SPJ1

Answer:

(1, 1)  (1, 2)  (1, 3) (1,4)

(1,5)  (2,1)   (2,2) (2,3)

(2,4)  (3,1)  (3,2)   (3,3)

(4,1)   (4,2) (5,1)

Step-by-step explanation:

An event is a specified set of results of a random experiment in probability theory. The number of possible outcomes that Event E has is 21.

An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.

Let E be the event where the sum of two rolled dice is greater than or equal to 7. Therefore, the outcomes in E are represented in red in the given table below.

(1, 6)

(2, 6)

(3, 6)

(4, 6)

(5, 6)

(6, 6)

(2, 5)

(3, 5)

(4, 5)

(5, 5)

(6, 5)

(3, 4)

(4, 4)

(5, 4)

(6, 4)

(4, 3)

(5, 3)

(6, 3)

(5, 2)

(6, 2)

(6, 1)

Hence, the number of possible outcomes that Event E has is 21.

Learn more about the Event:

https://brainly.com/question/12961938

#SPJ2

Answer:

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

Given polynomial

Factorize it as below:

4ab + 6bn - 2a - 3n​ =    

(4ab - 2a) + (6bn - 3n) =         Regroup        

2a(2b - 1) + 3n(2b - 1) =           Factorize each group using common factors

(2b - 1)(2a + 3n)                       Factorize using common factor

Answer:

[tex](2b-1)(2a+3n)[/tex]

Step-by-step explanation:

Given expression:

[tex]4ab+6bn-2a-3n[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 2b(2a+3n)-1(2a+3n)[/tex]

Factor out the common term (2a + 3n):

[tex]\implies (2b-1)(2a+3n)[/tex]

Answer:

5:11:9

Step-by-step explanation:

Change the decimal to fractions

45/10:99/10:81/10

Multiply through by the Lowest Common Factor 10

10×45/10:10×99/10:10×81/10

Which makes it

45:99:81

They have a common factor which is 9, so divide through by 9

45/9:99/9:81/9

Your answer is

5:11:9

Hope it helps

Answer:

20

Step-by-step explanation:

Answer:

20$ For the Roses

Step-by-step explanation:

Think about it like this. For each daisy (1$), the price is double for roses (2$).

Brad has a limit of 33$. And he bought 3 more daisies than roses.

If each daisy is 1$, and he bought 3+ over roses, take away 3$ to get 30$. If he bought 10 (excluding 3+) Daisies, He must have bought 10 roses.

(10 Daisies = 10$) + (10 Roses = 20$) = 30$

30$ + (3 Daisies = 3$) = 33$

The simplified expressions are

1.  990√2

2.  80 √3

3. 30- √35 / √42

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

(11 √40) (9 √5)

= 11*9* √40*√5

= 99*√200

= 99* 10√2

= 990√2

(2 √6) (10 √8)

= 2*10 *  √6 * √8

=20*  √48

= 20* 4 √3

= 80 √3

5 √6 ÷ √7 - √5 ÷ √6

=30- √35 / √42

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ1

Answer:

○ Length = 20 centimeters and Width = 5 centimeters

Step-by-step explanation:

Let the length = L

Then the width is L - 15

A = lw

100 = L(L - 15)

L² - 15L - 100 = 0

(L - 20)(L + 5) = 0

L - 20 = 0  or  L + 5 = 0

L = 20  or  L = -5

Since a length of a rectangle cannot be negative, we discard the solution L = -5 and keep the solution L = 20.

L = 20

width = L - 15 = 20 - 15 = 5

Answer:  ○ Length = 20 centimeters and Width = 5 centimeters

It's the sum of a geometric sequence.

Let's rewrite it a bit:

[tex]\displaystyle\\\sum_{n=1}^{10}8\left(\dfrac{1}{4}\right)^{n-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot \left(\dfrac{1}{4}\right)^{-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot 4=32\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]

And now let's calculate this sum [tex]\displaystyle \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\a=\dfrac{1}{4}\\n=10\\r=\dfrac{1}{4}\\\\S_{10}=\dfrac{\dfrac{1}{4}\cdot\left(1-\left(\dfrac{1}{4}\right)^{10}\right)}{1-\dfrac{1}{4}}=\dfrac{\dfrac{1}{4}\cdot\left(1-\dfrac{1}{1048576}\right)}{\dfrac{3}{4}}=\dfrac{\dfrac{1048575}{1048576}}{3}=\dfrac{1048575}{3145728}=\\=\dfrac{349525}{1048576}[/tex]

Now let's calculate the initial sum:

[tex]\displaystyle 32\cdot \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n=32\cdot \dfrac{349525}{1048576}=\dfrac{349525}{32768}\approx10.67[/tex]

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer:

53 hours and 45 minutes

Step-by-step explanation:

since they open for 10 hours and 45 minutes a day.

10*5=50 hours, 45*5=225 minutes

add the minutes and hours together and it is 53 hours and 45 minutes

The equation of the circle is [tex](x-8)^2 + (y-6)^2 = 25[/tex].

A pattern is a recurring arrangement of numbers, forms, colours, and so on.

In mathematics, a pattern is a recurring arrangement of numbers, forms, colours, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.

As per the pattern, Each figure has 3 more squares than the one before it.

Hence, the correct option is C.

Learn more about Pattern:

https://brainly.com/question/14720576

#SPJ1

Answer:

there is no answer

Step-by-step explanation:

If you multiply 15^x by 15^y, the answer is 15^(x+y) so 2 plus -7 is negitive 5.

but there is no answer equal to this.

The equivalent expression will be;

⇒ 15⁻⁵

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ (15²) × (15⁻⁷)

Now,

Since, The expression is,

⇒ (15²) × (15⁻⁷)

Hence, We solve as;

⇒ (15²) × (15⁻⁷)

⇒  15²⁻⁷

⇒ 15⁻⁵

⇒ 1 / 15⁵

Thus, The equivalent expression is,

⇒ 15⁻⁵

⇒ 1 / 15⁵

Learn more about the subtraction visit;

https://brainly.com/question/17301989

#SPJ2

Answer: 20

Step-by-step explanation:

Let [tex]f(y)=x[/tex]

[tex]x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}[/tex]

The Gross pay which Derek gets is 690 dollars.

Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages. The amount remaining after all withholdings are accounted for is net pay or take-home pay.

Here, Total hours worked by Derek = 43 hours

Rate of pay = $15 per hour

Rate of pay beyond 40 hours = $30 per hour

Now,

Rate of pay for the first 40 hours = 40 X 15 = $ 600

Since the pay rate doubles after 40 hours,

Rate of pay for the remaining 3 hours = 3 X 30 = $ 90

Gross Pay = 600 + 90 = $ 690

Thus, the Gross pay which Derek gets is 690 dollars.

Learn more about Gross Pay from:

https://brainly.com/question/13143081

#SPJ1

Answer:

−135z

2

−2z
The 2 is representing Square

Step-by-step explanation:

(3z)
2

−4z+11−(12z)
2

+2z−11

Expand (3z)

2

.

3

2

z

2

−4z+11−(12z)

2

+2z−11

Calculate 3 to the power of 2 and get 9.

9z

2

−4z+11−(12z)

2

+2z−11

Expand (12z)

2

.

9z

2

−4z+11−12

2

z

2

+2z−11

Calculate 12 to the power of 2 and get 144.

9z

2

−4z+11−144z

2

+2z−11

Combine 9z

2

 and −144z

2

 to get −135z

2

.

−135z

2

−4z+11+2z−11

Combine −4z and 2z to get −2z.

−135z

2

−2z+11−11

Subtract 11 from 11 to get 0.

−135z

2

−2z

Answer:

x f(x)

0 0

-2 -4

4 -2

You need to draw y = 2 f (x-1)

So you need to choose x so that x-1 = 0, -2, 4 then you can use the above values

New function

x-1 = 0, x = 1, y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0

x-1 = -2 x = -1 y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8

x-1 = 4 x = 5 y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4

So 3 points on the new graph are (1, 0) (-1, -8) and (5, -4)

Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move) y = f(x) a units to the right.

y = f(x) to y = 2 f(x), you dilate f(x) with center (0,0) factor 2, so (a,b) > (2a, 2b)

So basically here you are doing both things.

So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b)

Our graph for A was the same, but my B was a bit different. I hope this helps regardless. :)

Answer: [tex]\frac{\sqrt{113}}{7}[/tex]

Step-by-step explanation:

As X is an acute angle, all 6 trigonometric functions with an argument of X are positive.

Using the identity [tex]1+\tan^{2} X=\sec^{2} X[/tex],

[tex]1+\left(\frac{8}{7} \right)^{2}=\sec^{2} X\\\\\sec^{2} X=\frac{113}{49}\\\\\therefore \sec X=\boxed{\frac{\sqrt{113}}{7}}[/tex]

Answer: x-1

Step-by-step explanation:

Answer:

E = [1,2,3,4,5,6,7,8,9,10,11,12]

S = [4,9]

E = [2,4,6,8,10,12]

The number that satisfies both conditions S and E is [4]

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

The numbers in the Venn diagram are given,

S          S∩E         E

1,9          4          2, 6, 8, 10, 12

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

S = square numbers

This means,

1² = 1

2² = 4

3² = 9

S = {1, 4, 9}

E = even numbers

This means,

E = {2, 4, 6, 8, 10, 12}

Now,

S ∩ E = Numbers that are even and square.

S ∩ E = {4}

Thus,

The numbers in the Venn diagram are given,

S          S∩E         E

1,9          4          2, 6, 8, 10, 12

Learn more about Venn diagram here:

https://brainly.com/question/1605100

#SPJ2

Answer:

See below

Step-by-step explanation:

She combined 3x and - 9x   incorrectly

  she should have gotten  - 6 x       not  - 12 x

Answer:

≈ 14.6%

Step-by-step explanation:

percentage increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase = 2.75 - 2.40 = 0.35 , then

percentage increase = [tex]\frac{0.35}{2.40}[/tex] × 100% ≈ 14.6% ( to the nearest tenth )

The mean and the standard deviation are 233 and 208.95 respectively.

The mean of a distribution is its average, while the standard deviation is the summary of how far each data in the dataset, is to the mean.

First, we calculate the class midpoint (x) from the given intervals.

The class midpoint is the average of the intervals. So, we have:

X1 = (0+199)/2 = 99.5

X2 = (200+399)/2 = 299.5

X3 = (400+599)/2 = 499.5

X4 = (600+799)/2 = 699.5

X5 = (800+999)/2 = 899.5

X6 = (1000+1199)/2 = 1099.5

X7 = (1200+1399)/2 = 1299.5

So, the table becomes:

X values Frequency (f)

99.5 345

299.5 97

499.5 52

699.5 21

899.5 9

1099.5 8

1299.5 3

The mean of the distribution is:

This gives:

Mean = (99.5*345)+(299.5*97)+(499.5*52)+(699.5*21)+(899.5*9)+(1099.5*8)+(1299.5*3)/(345+97+52+21+9+8+3)

Mean = 124832.5/535 = 233

Therefore, Mean = 233

The standard deviation is calculated as follows:

So, we have:

Б =

√(99.5*(345-233)²+((299.5-233)² * 97)+((499.5-233)² * 52)+((699.5-233)² * 21)+((899.5-233)² * 9)+((1099.5-233)² * 8)+((1299.5- 233)² * 3)/ (345+97+52+21+9+8+3)

Standard Deviation = √(23357155.5)/535

        = √43658.23

        = 208.95

Б = 208.95

Hence, the mean and the standard deviation are 233 and 208.95 respectively.

Read more about mean and standard deviation at: https://brainly.com/question/14451674

#SPJ10

Answer:

Yes, k = 1/3 and y = 1/3x

Step-by-step explanation:

[tex]\text{The given line passes through the origin, hence it has equation of the form:}\\y=kx[/tex]

[tex]\text{Therefore y varies directly as x.}The line passes through the point (3,1)}[/tex]

[tex]\text{This implies that,}[/tex]

[tex]1=k(3)\\k=\frac{1}{3}[/tex][tex]\text{Hence the constant of variation is}[/tex] ⇒ [tex]\frac{1}{3}[/tex]

The equation would be ⇒ [tex]y=\frac{1}{3} x[/tex]