Consider the following scores. (i) a score of 40 from a distribution with mean 50 and standard deviation 10 (ii) a score of 45 from a distribution with mean 50 and standard deviation 5 How do the two scores compare relative to their respective distributions

Answer:

The value of this expression when a = 3 and b = -2 is -1.

Step-by-step explanation:

The expression is:

[tex]X=\frac{3a^{-2}b^{6}}{2a^{-1}b^{5}}[/tex]

Compute the value of X for a = 3 and b = -2 as follows:

[tex]X=\frac{3a^{-2}b^{6}}{2a^{-1}b^{5}}[/tex]

    [tex]=\frac{3\cdot (3)^{-2}\cdot (-2)^{6}}{2\cdot (3)^{-1}\cdot (-2)^{5}}\\\\=\frac{(3^{-1})\times (-2)^{6}}{2\cdot (3^{-1})\cdot (-2)^{5}}\\\\=\frac{(-2)^{1}}{2}\\\\=-1[/tex]

Thus, the value of this expression when a = 3 and b = -2 is -1.

ANSWER:

C. Place the compass on point A. Open the compass to a point between point P and point B.

EXPLANATION:

A perpendicular is a line that would be at a right angle to line BA.

The next step is to chose a radius that is greater than PB or PA so as to construct the bisector. And this can be done by placing the compass on point A, and open the compass to a point between point P and point B.

Use this radius to draw an arc above and below the line, and repeat the same using B as the center with the same radius. This would form two intersecting arcs above and below line BA. Join the point of intersection of the arcs by a straight line through P. This is the bisector of line BA through point P.

Answer:

1.28

Step-by-step explanation:

Margin of error is also called confidence interval, and it shows how much the results from sample reflects the characteristics of the larger population.

The following steps are used to calculate margin of error.

- obtain population standard deviation (σ) and sample size (n)

- divide standard deviation by square root of sample size

- multiply result by z score consistent with the given confidence. In this case confidence is 80% and z score for it is 1.28

Margin of error= z * (σ ÷ √n)

Margin of error = 1.28 * (10 ÷ √100)

Margin of error= 1.28 * (10 ÷ 10) = 1.28

Answer:

g(x) = x² + 4x + 5

h(x) = 3x - 5

To find (g+h)(x) add h(x) to g(x)

That's

(g+h)(x) = x² + 4x + 5 + 3x - 4

Group like terms

(g+h)(x) = x² + 4x + 3x + 5 - 4

Simplify

We have the final answer as

Hope this helps you

Answer:

cars are dum

Step-by-step explanation:

Answer:

Range of wages is £140 to £525.

Mean wage = £226

Step-by-step explanation:

Given:

Weekly wages paid to the staff are :

£245, £140, £525, £163, £195, £174 and £140.

To find:

Range of these wages = ?

Mean wage = ?

Solution:

First of all, let us learn about the range of wages and mean wage.

Range of wages has a minimum pay and a maximum pay.

Here, if we have a look £140 is the minimum pay and

£525 is the maximum pay.

So, range of wages is £140 to £525.

Mean wage means the average of all the wages given to the staff.

Mean is defined as the formula:

[tex]\text{Average/Mean =} \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}[/tex]

Here, Sum of all observations mean sum of the wages of all the staff members.

Number of observations mean the number of staff members i.e. 7 here.

Applying the formula:

[tex]\text{Average/Mean =} \dfrac{\text{245+140+525+163+195+174+140}}{\text{7}} \\\Rightarrow \text{Average/Mean =} \dfrac{\text{1582}}{\text{7}}\\\Rightarrow \text{Average/Mean =} 226[/tex]

So, the answer is:

Range of wages is £140 to £525.

Mean wage = £226

Answer:

(4,0,-7)

Step-by-step explanation:

The initial position was (0,0,0) since it was the origin

Now, we have a movement of positive x at a distance of 4 units, with a distance of z a total of 7 units(negative since downward)

The current position is thus;

(4,0,-7)

Thus correlates to (x,y,z) and our y has remained zero as there is no movement along the y-axis

The value of x from the diagram is 50 degrees. Vertical angles are angles that meets at a point of intersection.

Vertical angles are angles that meets at a point of intersection. From the given diagram 150 and 50+2x are vertical angles showing that they are equal to each other. Hence;

50 + 2x = 150

2x = 150 - 50

2x = 100

Divide both sides by 2

2x/2 = 100/2

x = 50

Hence the value of x from the diagram is 50 degrees

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Hi there! :)

Answer:

2nd choice. f(x) = 4 sin x + 2

Step-by-step explanation:

Recall that the transformations form of a sine function is:

y = ±a sin(b(x-h)) + k

Where:

'a' changes the amplitude

'b' changes the period

'h' is a horizontal shift

'k' is a vertical shift, or a change in the midline.

In this instance, the function has a midline of y = 2, which means an equation representing this must have a 'k' value of 2.

The only equation that contains this value is:

f(x) = 4 sin x + 2.

Answer:

I'm pretty positive the answer is B.   f(x) = 4sinx + 2

Step-by-step explanation:

Since d = 2 and the amplitude is 4 and there is nothing else effecting the function you are going up the graph 2 vertically and the amplitude will just go up and down 4 with you midline being at y = 2.

Answer:

3 PM

350 miles

Step-by-step explanation:

Let's say t is the number of hours since 8 AM.

The distance traveled by Winston is:

w = 50t

The distance traveled by Alice is:

a = 70(t−2)

When w = a:

50t = 70(t−2)

50t = 70t − 140

140 = 20t

t = 7

Winston and Alice will be at the same place 7 hours after 8 AM, or 3 PM.

The distance they travel is 350 miles.

Answer:  21 ft³

Step-by-step explanation:

Let x represent the height of the box.

Then the 5 ft width of cardboard is (5 - 2x) when creating the box

and the 9 ft length of cardboard is (9 - 2x) when creating the box.

Volume = length x width x height

            = (9 - 2x)(5 - 2x)(x)

            = 45x - 28x² + 4x³

Using Calculus to solve for x, set the derivative equal to zero and use the quadratic formula to solve for x:

V' = 45 - 56x + 12x²

0 = 12x² - 56x + 45

x = 3.6, x = 1.0

Use those values to find the width, length, and volume:

height(x)   ×  width (5 - 2x)   ×  length (9 - 2x) = Volume

  3.63       ×       -2.26*                                            

     1          ×          3               ×         7              =    21

*width cannot be negative so the height cannot be 3.63

Answer:

The answer to your question is 24 cm³

Step-by-step explanation:

Data

Initial volume = 2/5

Additional volume = 42 cm³

Final volume = 4/7

the total volume of the glass = ?

Process

1.- Write a proportion to help you solve the problem

                  42 cm³  -------------------- 4/7 of the total

                   x            -------------------  7/7

2.- Solve the proportion

                  x = (7/7 x 42) / 4/7

3.- Simplification

                  x = 42 / 4/7

                  x = 168/7

                 x = 24 cm³                  

Answer:

y = mx + c

since m = 0

c = 9

Step-by-step explanation:

y = mx + c

since m = 0

c = 9

SLOPE THESE DAYS

Answer:

a) The velocity of the ball after 2 seconds is -91 feet per second, b) The velocity of the ball after falling 364 feet is 155 feet per second, c) The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is [tex]y = 6\cdot x^{2}-7\cdot x +1[/tex].

Step-by-step explanation:

a) The velocity function is obtained after deriving the position function in time:

[tex]v (t) = -32\cdot t -27[/tex]

The velocity of the ball after 2 seconds is:

[tex]v(2\,s) = -32\cdot (2\,s) -27[/tex]

[tex]v(2\,s) = -91\,\frac{ft}{s}[/tex]

The velocity of the ball after 2 seconds is -91 feet per second.

b) The time of the ball after falling 364 feet is found after solving the position function as follows:

[tex]435\,ft - 364\,ft = -16\cdot t^{2}-27\cdot t + 435\,ft[/tex]

[tex]-16\cdot t^{2} - 27\cdot t + 364 = 0[/tex]

The solution of this second-grade polynomial is represented by two roots:

[tex]t_{1} = 4\,s[/tex] and [tex]t_{2} = -5.688\,s[/tex].

Only the first root is physically reasonable since time is a positive variable. Now, the velocity of the ball after falling 364 feet is:

[tex]v(4\,s) = -32\cdot (4\,s) - 27[/tex]

[tex]v(4\,s) = -155\,\frac{ft}{s}[/tex]

The velocity of the ball after falling 364 feet is 155 feet per second.

c) Let consider the equation for a second order polynomial that passes through (0, 1) and its first derivative that passes through (1, 0) and represents the give equation of the tangent line. That is to say:

Second-order polynomial evaluated at (0, 1)

[tex]c = 1[/tex]

Slope of the tangent line evaluated at (1, 0)

[tex]5 = 2\cdot a \cdot (1) + b[/tex]

[tex]2\cdot a + b = 5[/tex]

[tex]b = 5 - 2\cdot a[/tex]

Now, let evaluate the second order polynomial at (1, 0):

[tex]0 = a\cdot (1)^{2}+b\cdot (1) + c[/tex]

[tex]a + b + c = 0[/tex]

If [tex]c = 1[/tex] and [tex]b = 5 - 2\cdot a[/tex], then:

[tex]a + (5-2\cdot a) +1 = 0[/tex]

[tex]-a +6 = 0[/tex]

[tex]a = 6[/tex]

And the value of b is: ([tex]a = 6[/tex])

[tex]b = 5 - 2\cdot (6)[/tex]

[tex]b = -7[/tex]

The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is [tex]y = 6\cdot x^{2}-7\cdot x +1[/tex].

Answer:  width = 2.4 in, length = 5

Step-by-step explanation:

The max area of a right triangle is half the area of the original triangle.

Area of the triangle = (6 x 8)/2  = 24

--> area of rectangle = 24 ÷ 2 = 12

Next, let's find the dimensions.

The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.

length = 10 ÷ 2 = 5

Use the area formula to find the width:

A = length x width

12 = 5 w

12/5 = w

2.4 = w

The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.

Let the length and width of the rectangle be x and y.

Then Area of the rectangle = xy

Now, from the triangle we can conclude that

[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]

Put the value of y in Area we get

[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]

Differentiating it w.r.t x we get

[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]

Put A'(x)=0 for maximum /minimum value

[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]

Now, [tex]A''(3)=-\frac{8}{3} <0[/tex]

Therefore the area of the rectangle is maximum for x=3 inch

Now,

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

Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.

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In any coordinate pair, the first number is the x-value and the second number is the y-value.

To find the slope, simply take the difference of the y values and divide by the difference in the x values: (14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is -5/3.

It is find the slope of the line.

The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

The slope is always calculated from the rise divided by the run. Typically, the equation is presented as:

m = Rise/Run

If you have two points, the points should be [tex]P_{1} (x_{1} ,y_{1} )[/tex] and [tex]P_{2} (x_{2} ,y_{2} )[/tex]  So, the equation would be:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

In any coordinate pair, the first number is the x-value and the second number is the y-value.

The difference of the y values and divide by the difference in the x values:

m=(14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is  -5/3.

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Answer:

Total hectares needed = 13.3 billion hectares of ecological footprint.

Step-by-step explanation:

Country X's per capita ecological footprint = 3.2 hectares

Country Y's per capita ecological footprint = 0.6 hectares

Earth's population = 7 billion

Average footprint between the two nations = 1.9 (3.2 + 0.6) hectares

If everybody in the world (i.e. the earth's population) has an ecological footprint the size of the average footprint between these two countries, i.e. = 1.9 per capita of earth's population,

Therefore, the total hectares of ecological footprint needed will be equal to 7 billion x 1.9

= 13.3 billion hectares of ecological footprint.

Hi there!! (✿◕‿◕)

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

Hillsboro: 700 houses sold

Lowell: 100 houses sold

700 + 100 = 800

Hillsboro and Lowell: 800 houses sold

Other: 600

800 + 600 = 1,400

Clay County: 1,400 houses sold

800/1,400 = 4/7

Hope this helped!!  ٩(◕‿◕｡)۶

Answer:

4/7

Step-by-step explanation:

Well first we need to find the total amount of houses sold in Clay County.

700 + 100 + 600

= 1,400

Now we need to find the total of houses sold in Lowell and Hillsboro.

700 + 100

= 800

Now we can make the fraction,

800/1400

and simplify

400/700

200/350

20/35

4/7

Thus,

the fraction of houses sold in Hillsboro and Lowell in Clay County is 4/7.

Hope this helps :)

If the path is perpendicular to the field it is zero.

If the path is along the field it is positive or negative depending on it's direction.

See the attached picture.

Answer:

x=-11

Step-by-step explanation:

x+8=-3

x=-3-8 :- collect like term

since we are adding two negative numbers, we will let the number be negative but add them.

x=-11

Hope it helps :)

Answer:

x=-11

Step-by-step explanation:

x+8=-3

collect like terms;

x=-3-8

x=-11

The approximate volume only applies when pi = 3.14

Use either answer, but not both of course.

===============================================

Work Shown:

V = volume of cylinder

V = pi*r^2*h

V = pi*2^2*8

V = pi*32

V = 32pi .... exact volume in terms of pi

V = 32*3.14

V = 100.48 .... approximate volume when we use pi = 3.14

Answer:

Option D

x = 27; m∠FDG = 62°; m∠GOF = 118°

Step-by-step explanation:

To solve this, we will need the help of the following laws of geometry:

1. We can see that the shape formed is quadrilateral. The sum of the interior angles of a quadrilateral = 360 degrees.

2. The angle between a radius and a tangent = 90 degrees. as a result of this, <OGD = <OFD = 90 degrees.

Once we have values for all the angles of the quadrilateral, we can set up an equation using the first rule mentioned above.

2x+8 + 4x+10 +90 +90 = 360 (Sum of interior angles of a quadrilateral = 360)

6x = 162

x=27 degrees

Now we have the value of x, we can find FDG and GOF as follows:

FDG = 2x + 8 = 2(27)+8 =62

FOG = 4x + 10 = 4(27)+ 10 =118

Answer:

perimeter = 56 in

area = 192 sq. in.

Step-by-step explanation:

area of a triangle = 0.5 * b * h

b = 12

h = 8

At = (0.5 * 12 * 8)  = 48

Area of a square

As = 12 * 12 = 144

total area = At + As

total area = 48 + 144

total area = 192 sq. in.

perimeter = add all sides

12 + 12 + 12 + 10 + 10 = 56 in

hope it helps

Answer:   90°

Step-by-step explanation:

As known ∡EGC=(arcEC+arcDF)/2

arcEC+arcDF=70°*2

5x+10+11x+2=140

16x+12=140

16x=128

x=128:16

x=8

So arcDF=11*x+2=11*8+2=90°

The measure of arc DF is 90°.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

Given,  Circle A with chords EF and CD that intersect at point G,

arc EC = 5x + 10°

arc DF = 11x + 2°

∠EGC = 70°

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite

so

∠EGC=(1/2)[arc EC+arc DF]

substitute the values

70 = 1/2(5x + 10 + 11x + 2)

70 = 1/2(16x + 12)

140 = 16x + 12

16x = 128

x = 128/16 = 8

so ac DF = 11x + 2

arc DF = 11(8) + 2

arc DF= 88 + 2 = 90°

Hence the value of arc DF is 90°.

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Answer:

$1116

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x)=3x+15

let  f(x)=y

y=3x+15

flip x and y

x=3y+15

3y=x-15

y=1/3 x-5

or f^{-1}x=1/3 x-5

Answer:

see graph

Step-by-step explanation:

A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.

Answer:

Its d [tex]x^{2} -6x+7=0[/tex]

Step-by-step explanation:

A= [tex]2+\sqrt{3\\}[/tex]

B= [tex]3\sqrt{2}[/tex]

C= [tex]-3+\sqrt{2}[/tex]

Answer:

D. x^2 - 6x + 7 = 0.

Step-by-step explanation:

The roots are 3 plus or minus sqrt(2). That means the equation is...

(x - [3 + sqrt(2)]) * (x - [3 - sqrt(2)])

= [x - 3 - sqrt(2)] * [x - 3 + sqrt(2)]

= x^2 - 3x - xsqrt(2) - 3x + 9 + 3sqrt(2) + xsqrt(2) - 3sqrt(2) - (sqrt(2))^2

= x^2 - 3x - 3x + 9 - 2 - xsqrt(2) + xsqrt(2) + 3sqrt(2) - 3sqrt(2)

= x^2 - 6x + 7.

Hope this helps!

Answer:

A) (3, 2)

Step-by-step explanation:

y = 4x - 10

y = 2

Substitute y with 2 in the first equation and solve for x.

y = 4x - 10

2 = 4x - 10

12 = 4x

3 = x

Solution: x = 3, y = 2

Answer: A) (3, 2)

Set up two equations:

Let a = adults and c = child:

a +  c = 289 ( rewrite as a = 289 - c)

1.50c + 4a = 746

Replace a with the rewritten formula:

1.50c + 4(289-c) = 746

SImplify:

1.50c + 1156 - 4c = 746

Combine like terms:

-2.50c + 1156 = 746

Subtract 1156 from both sides:

-2.50c = -410

Divide both sides by -2.50

c = -410 / -2.50 = 164

Number of children = 164

Number of adults = 289 - 164 = 125

Answer:

[tex] x+y = 289[/tex] (1) total people entered

[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected

From the first equation we can solve for x and we got:

[tex] x = 289-y[/tex] (3)

Replacing (3) into (2) we got:

[tex] 1.5(289-y) +4y = 746[/tex]

And solving for y we got:

[tex] 433.5 -1.5 y +4y = 746[/tex]

[tex] 2.5 y= 312.5[/tex]

[tex]y=\frac{312.5}{2.5}= 125[/tex]

And then using (3) we can solve for x and we got:

[tex] x= 289-125= 164[/tex]

So then we have:

number of children = 164

number of adults = 125

Step-by-step explanation:

Let x the number of children and y the number of adults. From the info given we can set up the following equations:

[tex] x+y = 289[/tex] (1) total people entered

[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected

From the first equation we can solve for x and we got:

[tex] x = 289-y[/tex] (3)

Replacing (3) into (2) we got:

[tex] 1.5(289-y) +4y = 746[/tex]

And solving for y we got:

[tex] 433.5 -1.5 y +4y = 746[/tex]

[tex] 2.5 y= 312.5[/tex]

[tex]y=\frac{312.5}{2.5}= 125[/tex]

And then using (3) we can solve for x and we got:

[tex] x= 289-125= 164[/tex]

So then we have:

number of children = 164

number of adults = 125