The results of a common standardized test used in psychology research is designed so that the population mean is 135 and the standard deviation is 30. A subject earns a score of 198. What is the z-score for this raw score?

z-score=

Answer:

( - [tex]\frac{1}{3}[/tex], [tex]\frac{3}{4}[/tex] )

Step-by-step explanation:

Given the 2 equations

9x + 8y = 3 → (1)

6x - 12y = - 11 → (2)

To eliminate the y- term multiply (1) by 1.5

13.5x + 12y = 4.5 → (3)

Add (2) and (3) term by term

(6x + 13.5x) + (- 12y + 12y) = (- 11 + 4.5)

19.5x = - 6.5 ( divide both sides by 19.5 )

x = [tex]\frac{-6.5}{19.5}[/tex] = - [tex]\frac{1}{3}[/tex]

Substitute this value into either of the 2 equations and solve for y

Using (1), then

- 3 + 8y = 3 ( add 3 to both sides )

8y = 6 ( divide both sides by 8 )

y = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]

Solution is (- [tex]\frac{1}{3}[/tex], [tex]\frac{3}{4}[/tex] )

Answer:

  Q

Step-by-step explanation:

Each line from a vertex to the midpoint of the opposite side is called a median. The point where the medians intersect, point Q, is the centroid.

The centroid of ΔABC is point Q.

Answer:

Q

Step-by-step explanation:

We are given that L,M and N are midpoints of sides AC,AB and BC of a triangle.

We have to find the centroid of triangle ABC.

Centroid of triangle : It is defined as the intersection point of medians of triangle.

Medians of triangle ABC are BL,CN and  AM.

Medians BL, CN and AM are intersect at point Q.

Therefore, centroid of triangle ABC is Q by definition of centroid of triangle.

Answer:Q

Answer:

The surface area is [tex]SA=384\ mm^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the cube is equal to

[tex]SA=6s^{2}[/tex]

we have

[tex]s=8\ mm[/tex]

substitute

[tex]SA=6(8)^{2}[/tex]

[tex]SA=384\ mm^{2}[/tex]

The answer is:

The correct option is A. 8.3.

To calculate the number of weeks that will pass, we need to use the given information.From the statement we know that we need to use the value of $600 substituting it as "y", and then, isolate "x", so, calculating we have:

[tex]log(y)=0.30x+0.296\\\\log(600)=0.30x+0.296\\\\2.78=0.30x+0.296\\\\2.78-0.296=0.30x\\\\x=\frac{2.78-0.296}{0.30}=8.28=8.3[/tex]

Hence, the correct option is A. 8.3.

Have a nice day!

Answer:

D=5/2

Step-by-step explanation:

Circumference of a circle = πD where D is the diameter of the circle.

In the question Circumference is =55/7 and π provided =22/7

55/7 = (22/7)D

We multiply both sides with the reciprocal f 22/7

D = (55/7) (7/22)

D = 5/2

Answer:

Domain is 2 and range is 4

Step-by-step explanation:

[tex]A=\{1,3,5,\ldots,99\}\\B=\{50,55,\ldots,150\}\\\\A\cap B=\{55,65,75,85,95\}[/tex]

Answer:

[tex]A\bigcap B=\left \{ 55,65,75,85,95 \right \}[/tex]

Step-by-step explanation:

Set A contains odd numbers between 0 and 100.

So, the elements in set A are as, Set A[tex]=\left \{ 1,3,5,7,9,11,13,15,...99 \right \}[/tex]

Set B contains the numbers between 50 and 150, that are evenly divisible by 5.

So, the elements in set B are are as, Set B

[tex]=\left \{ 55,60,65,70,75,80,85,90,... 145\right \}[/tex]

Now, we need to find [tex]A\bigcap B[/tex]

To find  [tex]A\bigcap B[/tex] , we need to find the common elements in Set A and Set B.

The common elements in Set A and Set B is [tex]\left \{  55,65,75,85,95 \right \}[/tex]

So, [tex]A\bigcap B=\left \{ 55,65,75,85,95 \right \}[/tex]

Answer:

  1

Step-by-step explanation:

The constant term in a perfect square trinomial with leading coefficient 1 is the square of half the coefficient of the linear term.

  (2/2)² = 1

The missing constant term is 1.

Answer:  The correct answer is:  " 1 " .

_____________________________________________________

                               →   "  x²  +  2x  +    1     =   (x + 1)²  " .

_____________________________________________________

_____________________________________________________

Step-by-step explanation:

_____________________________________________________

Let us assume that the question asks us to solve for the "missing constant term in the following equation:  

      →   " x² + 2x + b = 0 " ;  

      →  in which:  " b " is the "missing constant term" for which we shall solve.

_____________________________________________________

The form of an equation in the perfect square would be:

                →  (x + b) ² =  x² + 2bx + b²  ;

                →  In our case, "b" ; refer to the "missing constant term" for which we shall solve.

_____________________________________________________

      →   " x² + 2x + b = 0 " ;  

       Note that the term in the equation with the highest degree (highest exponent) is:  

            →  " x² " ;  with an "implied coefficient" of: " 1 " (one) ;

      →   {since "any value" , multiplied by " 1 " , results in that same initial value.}.

      →   Since the term with the highest degree has a "co-efficient" of " 1 " ;

  we can solve the problem;   i.e. "Solve for "b" ;  accordingly:

_____________________________________________________

      →   " x² + 2x + b = 0 " ;

Subtract "b" from each side of the equation:

      →   " x² + 2x + b - b = 0 - b " ;

      →  to get:

      →   x² + 2x  =  - b

Now we want to complete x² + 2x into a perfect square.

To do so, we take the:  "2" (from the:  "+2x" );  

     →  and we divide that value {in our case, "2"};  by "2" ;

to get:  "[2/2]" ;  and then we "square" that value;

     →  to get:  " [2/2]² " .

_____________________________________________________

Now, we add this "squared value" to:  " x² + 2x " ;  as follows:

     →  " x² + 2x + [2/2]² " ;  and simply:  " [2/2]² = [1]² = 1 ."

_____________________________________________________

     x² + 2x + (2/2)² = x² + 2x + 1 ;

                              =  (x + 1)² ;

_____________________________________________________

Now:  " x² + 2x = - b " ;

 We add "(2/2)² " ;  to each side of the equation;

 →  In our case,  " [2/2]² = [1]² = 1 " ;

 →  As such, we add:  " 1 " ;  to each side of the equation:

              →   x² + 2x + (2/2)² =  - b + (2/2)² ;

              →  Rewrite;  substituting " 1 " [for:  " (2/2)² "] :

              →   x² + 2x + 1  =  1 - b ;                                          

              →   x² + 2x + 1   = 1 - b ;

_____________________________________________________

And assume "b" would equal "1" ;

 since assuming the question refers to the equation:

     "x²  +  2x  ±   b = 0 " ;  solve for "b" ;  

And:   "b = 1 " ;

Then:  " x² + 2x + 1 = ?  1 - b  ??

       →  then:   " 1 - b = 0 "  ;  Solve for "b" ;

       →  Add "b" to each side of the equation:

                      " 1 - b + b = 0 + b " ;

       →  to get:  " 1 = b "  ;   ↔ " b =  1 "  ;  Yes!

___________________________________________________

Also, to check our work:

_____________________________________________________

Remember, from above:

_____________________________________________________  

" The form of an equation in the perfect square would be:

                →  (x + b)²  =  x²  +  2bx + b² " ;  _____________________________________________________

   →  Let us substitute "1" for all values of "b" :

                  →   "  (x + 1) ²  =   x² + 2*(b)*(1)  +   1²  "  ;

                  →   "  (x + 1)²   =   x²  +  (2*1*1)   +  (1*1) "  ;

                  →   "  (x + 1)²   = ?  x²  +  2  +  1 "  ?? ;  Yes!

                  →  However, let us check for sure!

 _____________________________________________________

→   Expand:  " (x + 1)²  " ;  

→  " (x + 1)² = (x + 1)(x + 1) " ;

_____________________________________________________

   →  " (x + 1)(x + 1) " ;  

_____________________________________________________

Note the following property of multiplication:

_____________________________________________________

 →   " (a + b)(c + d)  =  ac  +  ad  +  bc  +  bd " ;

_____________________________________________________

As such:

_____________________________________________________

         →  " (x + 1)(x + 1) " ;

              =  (x*x) + (1x) + (1x) + (1*1) ;

              =  x²  +  1x + 1x + 1 ;

        →  Combine the "like terms" :

              + 1x + 1x = + 2x ;  

And rewrite:

              =   x²  +  2x + 1 .

_____________________________________________________

"  (x + 1)²   = ?  x²  +  2  +  1 "  ?? ;  Yes!

_____________________________________________________

    →   So:  The answer is:  " 1 " .

_____________________________________________________

   →  " x² + 2x +  1    =  (x + 1)²  " .

_____________________________________________________

Hope this answer helped!

    Best wishes to you in your academic endeavors

            — and within the "Brainly" community!

_____________________________________________________

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \begin{cases} r=-5\\ n=3\\ S_3=147 \end{cases} \implies 147=a_1\left( \cfrac{1-(-5)^3}{1-(-5)} \right)\implies 147=a_1\left( \cfrac{1-(-125)}{1+5} \right) \\\\\\ 147=a_1\cdot \cfrac{126}{6}\implies 147=21a_1\implies \cfrac{147}{21}=a_1\implies 7=a_1[/tex]

The first term of the geometric sequence with a common ratio of -5 and the sum of the first 3 terms being 147 is 7.

The first term of a geometric sequence where the common ratio is -5 and the sum of the first 3 terms is 147. A geometric sequence is denoted by a, ax, ax2, ax3, ..., where 'a' is the first term and 'x' is the common ratio.

Given the common ratio (x) is -5, we can express the first three terms of this geometric sequence as:

First term: a

Second term: a(-5) = -5a

Third term: a(-5)2 = 25a

The sum of these three terms equals 147:

a - 5a + 25a = 147

Combining like terms we get:

21a = 147

Now, dividing both sides by 21 to isolate 'a', we find:

a = 7

Therefore, the value of the first term of the sequence is 7.

Answer: The height of the robot is 200 millimeters

Step-by-step explanation:

Answer:

It is 1,200

Step-by-step explanation:

Answer:

mirena started at sea level, dove down 15 feet then rose up 6 feet

Step-by-step explanation:

she starts at zero the goes up -15 feef and then up 6 feet

Answer:

Morena started at sea level, dove down 15 feet, then rose up 6 feet.

Step-by-step explanation:

The expression is composed by three values. The first value indicates the starting point; which is 0, meaning sea level. The second component is -15, this indicates that Morena dove 15 feet below sea level, so she dove down. The third component is 6, this indicate that she drove up 6 feet, so she rose up. The position of Morena should be at 9 feet below sea level. The equation should be:

X = 0 + (-15) + 6

X = 0 - 15 + 6

X = -15 + 6

X = -9 down sea level

X means the Morena's postion

ANSWER

461.7 yd²

EXPLANATION

The shaded region represents a sector.

The area of the sector is a fraction of the area of the whole circle.

Area of sector

[tex] = \frac{angle \: \: of \:sector }{360 \degree} \times \pi {r}^{2} [/tex]

We substitute the angle of the sector and the radius of the circle to obtain:

[tex] = \frac{167 \degree}{360 \degree} \times \pi \times {17.8}^{2} [/tex]

[tex] = 461.7 {yd}^{2} [/tex]

Therefore the area of the shaded region to the nearest tenth is 461.7 square yards.

Answer:

Area of shaded sector = 461.5 yd²

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where 'r' is the radius of circle

To find the area of given circle

Here r = 17.8 yd

Area = πr²

 = 3.14 * 17.8²

 = 3.14 * 316.84

 = 994.8776 yd²

To find the area of shaded region

Central angle of sector = 167°

Area of sector = (167/360) * area of circle

 =  (167/360) *994.8776

 = 461.52 ≈ 461.5 yd²

William Jones

The number pi (π) is a platonic concept and has been used for 4000 years. The number pi can be approached but never reached. In general, this number means the constant ratio of the circumference to the diameter of any circle. Ancient Babylonians, Egyptians, and even Archimedes, one of the greatest mathematicians of the ancient world tried to approximate the value of pi, but in the 1700s, mathematicians began using the Greek letter π that was introduced by William Jones, in his second book Synopsis Palmariorum Matheseos or A New Introduction to the Mathematics base. Then, this symbol was popularized and adopted in 1737 by the greatest mathematician Leonhard Euler.

Answer:

  A.  4.20% compounded quarterly

Step-by-step explanation:

The effective annual multiplier on an account with annual interest rate r compounded n times per year is ...

  (1 +r/n)^n

When doing multiple evaluations of the same expression, it is convenient to let a spreadsheet or calculator do them from a list of inputs. In the attached, we round the result to 4 decimal places to make comparison easier.

The highest effective rate is 4.2% compounded 4 times per year.

____

Example calculation

  (1 +0.042/4)^4 = 1.0105^4 = 1.0426661426550625 ≈ 1.0427

Answer:

A) Account 1: Interest is compounded quarterly at an annual rate of 4.20%

Answer:

  A.  4

Step-by-step explanation:

Pick two terms with consecutive x-values and find their ratio. That is the common ratio.

 for x = 2 and x = 1,

 r = 32/8 = 4

The common ratio is 4.

_____

You can check other pairs of terms if you want to confirm.

  r = 2048/512 = 4 . . . . for x=5 and 4.

Answer:

Hi!

The correct answer is A. 4.

Step-by-step explanation:

To find the common ratio of an geometric sequence of set A = {a₁, a₂, a₃, ..., aₙ} you can use the formula:

[tex]r=\frac{a_{i+1}}{a_i}[/tex]

If you pick x = 4 to find the ratio, you have to replace in the formula:

[tex]r=\frac{a_{4+1}}{a_4} =\frac{a_{5}}{a_4}[/tex] // replace the values

[tex]r= \frac{2048}{512} = 4[/tex]

The common ratio of this geometric sequence is 4.

Answer:

√129

Step-by-step explanation:

The distance formula between two points is:

d² = (x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²

Plugging in:

d² = (4 − (-4))² + (-1 − 7)² + (-2 − (-3))²

d² = 8² + 8² + 1²

d² = 129

d = √129

1. To sketch the function f(x) = (2/3)x - 3, we first need to find two points that we can later join to sketch the line, for example the x- and y-intercepts.

a) The x-intercept occurs when f(x) = 0, so if f(x) = 0, then:

f(x) = (2/3)x - 3

0 = (2/3)x - 3

3 = (2/3)x (Add three to both sides)

3*(3/2) = x (Multiply both sides by 3/2)

9/2 = x

We have now found the x-intercept at (9/2, 0)

b) The y-intercept occurs when x = 0, so:

f(x) = (2/3)x - 3

f(0) = (2/3)*0 - 3

f(0) = -3

Now we know that the y-intercept is at (0, -3)

c) All that's left is to sketch the graph axes and label them, plot the two points, join them together using a ruler and label their coordinates.

2. The Domain is the range of x-values for which the function exists, and the Range is the range of y-values for which the function exists.

Since there haven't been any constraints specified, we can say that both the Domain and Range are (-∞, ∞), since the graph continues forever both along the x- and y-axis.

(Note that this isn't always the case and would change if, for example, the question stipulated that there was a domain of [0, 5] and you had to find the range. Then, you would calculate the value of y at each end of the domain (if x = 0, y = -3 and if x = 5, y = 1/3) - in my example, the range would thus be [-3, 1/3].)

Answer:

  Yes

Step-by-step explanation:

(3/8)·64 = 24 seats in the first class carriage are being used.

(7/13)·(78)·3 = 126 seats in the standard carriages are being used, for a total of ...

  24 + 126 = 150 . . . occupied seats

The number of available seats is ...

  64 +3·78 = 298

so half the seats on the train will be 298/2 = 149 seats.

  150 > 149, so more than half the seats on the train are being used.

Answer:

Is the graph shown the initial triangle, or the translated one?

Step-by-step explanation:

Answer:

t = 5.48

Step-by-step explanation:

f(x) = -5x² + 200

given f(t) = 50 when x = time(t)

Hence,

50 = -5t² + 200

5t² = 200 - 50

5t² = 150

t² = 30

t = √30 = 5.48

The number of seconds are 5.48, the correct option is C.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We are given that;

f(x) = –5x2 + 200

Now,

To find the time when the ball is 50 meters from the ground, we need to solve the equation:

f(x) = 50

Substituting f(x) with -5x^2 + 200 and simplifying, we get:

-5x^2 + 200 = 50

-5x^2 = -150

x^2 = 30

x = ±√30

Since x represents time, we only consider the positive value of x. Therefore,

x ≈ 5.48

Therefore, by the quadratic equations the answer will be 5.48

Learn more about quadratic equations;

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Answer:

(-7,4)

Step-by-step explanation:

goal: (y-k)^2=4p(x-h)

y^2-8y=4x+12    Rearranged and added 4x and 12 on both sides

y^2-8y+(-8/2)^2=4x+12+(-8/2)^2 complete square time (add same thing on both sides)

y^2-8y+(-4)^2=4x+12+(-4)^2 (simplify inside the squares)

(y-4)^2=4x+12+16  (now write the left hand side as a square)

(y-4)^2=4x+28

(y-4)^2=4(x+7)    factored...

vertex is (-7,4)

Answer:

(-7,4)

Step-by-step explanation:

Answer: 24%

Step-by-step explanation:

2610+8120 = The undergraduates and graduates combined.

That is 10730. You are figuring out the probability the student is a graduate when those two graduates are combined, because that is all the data given. So you would do 2610/10730 in your calculator, resulting in 24.324324324%. As it says rounded to the nearest percent in parentheses, it has to round to the whole number, 24%, and .3 rounds down.

Answer:

the minimum value is 1/2x^2+4x+15/2 (write down the work below)

Step-by-step explanation:

f(x)=1/2*(x+3)*(x+5)=0

multiply the parenthesis by  1/2

(1/2x+3/2)*(x+5)

multiply the parenthesis

1/2x^2+5/2x+3/2x+15/2

calculate the equation

1/2x^2+4x+15/2 is you're answer  

Given that the raffle prize is to be divided equally, the amount of money each person will receive will be equal to the total raffle prize (14x^(2)/15) divided by the number of people (7x). Thus, we get:

(14x^(2)/15) / 7x

= (14x^(2)/15) * (1/7x)

= 14x^(2)/15*7x

= 14x^(2)/105x

= 2x/15 (Divide both the numerator and denominator by 7x)

Therefor, each person would receive 2x/15 dollars.

If you know how to cancel when dealing with fractions, you can get to this step much easier, however this way also works. The idea with cancelling would be that when you had (14x^(2)/15) / 7x, you would recognise that 14x^2 may be divided by 7x straight away to get 2x. Then you would have 2x/15 as your answer.

Answer:

  $5308.79

Step-by-step explanation:

The future value can be computed from ...

  FV = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual interest rate, n is the number of times per year it is compounded, and t is the number of years.

Filling in the given numbers, we have ...

  FV = $5000(1 +.03/12)^(12·2) ≈ $5308.79

Myron's withdrawal will be in the amount of $5308.79.

Answer:

The answer is A.) u < 200

next one is B.) u > 200

The alternative hypothesis in your testing would be: u < 20; u > 200.

An alternative hypothesis can be defined as a statement in statistical inference which is used in contradictory form against what is stated in the null hypothesis.

Alternative hypothesis is the alternative t a null hypothesis in hypothesis testing.

Therefore, the alternative hypothesis in your testing would be: u < 20; u > 200.

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Answer: The first box is circle and second box is rectangle.

Step-by-step explanation:

If you are asking about the shape of the cross section for a right circular cylinder, that is the case. A parabola or triangle can't be sliced so the cross section is parallel or perpendicular to the base.

If the cross section is parallel to the base, it is a circle.

If the cross section is perpendicular to the base, it is a rectangle.

Answer with Step-by-step explanation:

Tara can spend at most $700

Restaurant charges $450 for the first 25 people and  $15 for each additional guest

Let x be the number of additional guest

⇒ 450+15x<700

⇒ 15x<250

⇒ x<250/15

⇒ x<16.67

Hence, Maximum additional guest can be 16

25+16=41

Hence,  the greatest number of people who can attend the shower is:

41

Answer:

Explanation:

When 4 people are chosen at random, the probability that exactly 3 of them favor the new building project may be thought as four cases:

- the first one is against and the other three are in favor

- the second one is against and the other three are in favor

- the third one is against and the other three are in favor

- the fourth one is against and the other three are in favor.

Each one of those probabilities are equal to:

          ↑                          ↑

      one against          three in favor

Since, there are four equal results: 4 × 0.09611875 = 0.384475

Rounded to 2 significant digits that is 0.38.

The probability that exactly 3 out of 4 people randomly selected from a poll, where 65% of people are in favor of a certain building project, are also in favor of it is approximately 0.3835 or 38.35%.

This question is about the calculation of probability related to a poll result. To calculate the probability that exactly 3 of 4 randomly chosen people favor the new building project, we should consider this as a binomial probability problem, because each person either supports the project or not, and each person is independent of the others. Accordingly, the probability that exactly 3 out of 4 people are in favor is given by the formula:

P(X=3)=C(4,3)*(0.65)^3*(1-0.65)^(4-3)=4*(0.65)^3*(0.35)=(4*0.2746*0.35)=0.3835

So, the probability that exactly 3 of them favor the new building project is approximately 0.3835 or 38.35%.

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Answer:

B) 16 ft, 10.5 in

Step-by-step explanation:

There are a few different ways you can work this. Since we want to know the difference between length and heigh of the model and we are given skull length of the model, it makes a certain amount of sense to find the corresponding measurements of the actual skeleton.

The actual skeleton's length was 40 ft and its height was 13 ft, so the difference between these dimensions is ...

40 ft - 13 ft = 27 ft

The actual skull is 5 ft long, so the difference is ...

(27 ft)/(5 ft) = 5.4

times the length of the skull.

The same ratio will apply to the model, so the difference between the model height and model length is 5.4 times the length of the model skull:

desired difference = 5.4 × 3 ft 1.5 in = 16.2 ft + 8.1 in

= 16 ft 10.5 in