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Answer:  see attachment

Step-by-step explanation:

Put the numbers in order from smallest to biggest:

1, 2, 2, 3, 3, 3,         3, 4, 4, 4, 5, 6

        ↓              ∨                ↓

       Q1        Median          Q3

Q1 median = (2+3)/2 = 2.5  <---- left side of box plot

Median = (3+3)/2 = 3          <---- Vertical Line of box plot

Q3 median = (4+4)/2 = 4    <---- right side of box plot

Answer:

43.8 meters

Step-by-step explanation:

12 x 3.65

Answer:

13

Step-by-step explanation:

let the number be x

how Cindy worked it out :

(x -6) ÷ 3 = 25

x -6 = 75

x = 81

How she should have worked it out:

(x - 3) ÷ 6

(81 - 3) ÷ 6

78 ÷ 6 = 13

Answer:

b=(2a-1)/(3a-1)

Step-by-step explanation:

a=(b-1)/(3b-2)

3ab-2a=b-1

3ab-b=2a-1

b(3a-1)=2a-1

b=(2a-1)/(3a-1)

Answer:

[tex]\large \boxed{\mathrm{1/2 \ boxes}}[/tex]

Step-by-step explanation:

Subtract the fractions.

[tex]\frac{9}{16}-\frac{1}{16}=\frac{8}{16} =\frac{1}{2}[/tex]

Vicky had 1/2 of a box more baking powder yesterday.

Answer:

Step-by-step explanation:

Trapezoid area is the Average of the parallel lines times the width

A = ½(18 + 42)(12) = 360 ft²

The area of the garden plot is 360 ft².

A trapezoid is a four-sided closed 2D figure which has an area and its perimeter. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid.

Here, the length of parallel sides = 18ft. and 42 ft.

         Width of plot = 12 ft.

Area of Trapezoid = 1/2 X (b₁+b₂) X h

                              = 1/2 X (18 + 42) X 12

                              = 6 X 60

                             = 360 sq. ft.

Thus, the area of the garden plot is 360 ft².

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Answer:

Hey there!

The first graph is the correct answer. A point on the parabola is equally far from the focus as it is to the directrix.

Let me know if this helps :)

The graph that  accurately displays a parabola with its directrix and focus is the first graph.

Suppose the considered function whose graph is to be made is  f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values  f(x) are plotted on the vertical axis.

They are together plotted on the point  (x,y) = (x, f(x))

This is why we usually write the functions as:  y = f(x)

A point shown in the graphs on the parabola is equally far from the focus as it is to the directrix.

Therefore, The first graph is the correct answer.

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Answer: -n+(-n-1)

Step-by-step explanation:

Expression will be -n + (-1)

Series

-4 +(-5)+(-6)+(-7)+(-8)+(-9)+(-10)+(-11)+(-12)+(-13) and so on

Here number -n has + (-n-1) being added to it

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Answer:

2.67

Step-by-step explanation:

To solve this problem do 16.02 / 6.

Answer:

Hello your question is incomplete attached is the missing part the second curve ; y = 3x is incomplete so i would solve the problem taking the second curve as ; y = 3x + 8 ( giving you the general methodology )

answer : y = ( 5,32) , x = ( -1,8 )

area of shaded region = 90.673

Step-by-step explanation:

The given curves ; [tex]y = x^2 - 4x\\y = 3x +8[/tex]

solving the above curves simultaneously

[tex]x^2-4x = 3x + 8[/tex]

x^2 - 7x - 8 = 0

( x + 1 )(x - 8 ) = 0

hence  X = ( -1 , 8 )

Therefore y = 3x + 8

when x = -1 ,  y = -3 + 8 = 5

when x = 8 ,  y = 24 + 8 = 32

hence y = ( 5, 32 )

attached below is the sketched region

Integrating the curves to determine the shaded area in respect to x = ( -1, 8)

∫ [( 3x +8 ) - ( x^2 - 4x ) ] dx

∫ ( -x^2 +7x + 8 ) dx

= { - x^3/3  + 3x^2 + 8x }

= { - 8^3/3 + 3(64) + 64} - { -1^3/3 + 3 - 8 }

= {-170.66 + 192 + 64 } - { -1/3 - 5 }

= -170.66 + 192 + 64 + 5.333 = 90.673 ( area of the shaded region )

Answer: -3

Step-by-step explanation: 2x = -2 then you subtract 1 from that which is the same as adding negative one so -2 - 1 or -2 + -1 = -3

Complete Question

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is  7.5

Answer:

The minimum sample size is  [tex]n =97[/tex]

Step-by-step explanation:

From the question  we are told that

 The margin of error is  [tex]E = 1.25[/tex]

   The  standard deviation is  [tex]s = 7.5[/tex]

Given that the confidence level is  90% then the level of significance is mathematically represented as

             [tex]\alpha = 100 - 90[/tex]  

             [tex]\alpha =10\%[/tex]  

             [tex]\alpha =0.10[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table  

    The value is  [tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]

   The  minimum sample size is mathematically evaluated as

         [tex]n = \frac{Z_{\frac{\alpha }{2} * s^2 }}{E^2 }[/tex]

=>        [tex]n = \frac{1.645^2 * 7.5^2 }{1.25^2 }[/tex]

=>        [tex]n =97[/tex]

Answer:

16, 16(sqrt3)

Step-by-step explanation:

30-60-90 triangles follow a rule where the hypotenuse is 2 times the shortest leg, and the longer leg is sqrt3 times the shorter leg.

So, the sides are x, 2x, and (sqrt3)x.

If 2x = 32, then x = 16.

Therefore the two legs are 16 and 16(sqrt3)

you can search up 30-60-90 triangle for more information

Answer:

4 consecutive goals

Step-by-step explanation:

If 3 of last 10 field goals = 30%

Which is equivalent to

(Number of goals scored / total games played) * 100%

(3 / 10) * 100% = 30%

Number of consecutive goals one has to score to raise field goal to 50% will be:

Let y = number of consecutive goals

[(3+y) / (10+y)] * 100% = 50%

[(3+y) / (10+y)] * 100/100 = 50/100

[(3+y) / (10+y)] * 1 = 0.5

(3+y) / (10+y) = 0.5

3+y = 0.5(10 + y)

3+y = 5 + 0.5y

y - 0.5y = 5 - 3

0.5y = 2

y = 2 / 0.5

y = 4

Therefore, number of consecutive goals needed to raise field goal to 50% = 4

Answer:

Step-by-step explanation:

8-2=6

answer is 6

Answer:

2 x 4

Step-by-step explanation:

She need to travel 4 times before she reach the same points again

Answer:

x = 3

Step-by-step explanation:

-40 = -8 (x + 2)

-8 (x + 2) = -40   --- divide both sides by - 8

-8 (x + 2)           -40

--------------   =   ----------

      -8                  -8

x + 2 = 5    --- subtract 2 from both sides

x + 2 - 2 = 5 - 2   then simplify

x = 3

Answer:

x=3

Step-by-step explanation:

First, write out the equation as you have been given it:

[tex]-40=-8(x+2)[/tex]

Then distribute the -8 to the terms inside the parenthesis:

[tex]-40=-8x-16[/tex]

Next, add 16 to both sides:

[tex]-40+16=-8x-16+16\\-24=-8x[/tex]

Finally, divide both sides by -8:

[tex]\frac{-24}{-8}=\frac{-8x}{-8}\\3=x[/tex]

Therefore, x=3.

Answer:

A

Step-by-step explanation:

The height is always perpinducular to the base. The height here is perpendicular to line segment A.

Answer:

A

Step-by-step explanation:

Answer:

Hello,

Step-by-step explanation:

HCF(100,150,250)=50*HCF(2,3,5)=50*1=50

Part of each fruits for a student:

2 oranges, 3 cirtrus and 5 guavas.

Answer:

6.25

Step-by-step explanation:

(x-a)^2=x^2-2ax+a^2

2a=5

a=2.5

2.5 ^ 2 = 6.25

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]

Answer:

the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days

Step-by-step explanation:

Given that :

Mean  = 265

standard deviation = 14

The formula for calculating the z score is [tex]z = \dfrac{x -\mu}{\sigma}[/tex]

x = μ + σz

At middle of 50% i.e 0.50

The critical value for [tex]z_{\alpha/2} = z_{0.50/2}[/tex]

From standard normal table

[tex]z_{0.25}=[/tex] + 0.67  or -0.67  

So; when z = -0.67

x = μ + σz

x = 265 + 14(-0.67)

x = 265 -9.38

x = 255.62

when z = +0.67

x = μ + σz

x = 265 + 14 (0.67)

x = 265 + 9.38

x = 274.38

the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days

Answer:

x could be 3 or 1

Step-by-step explanation:

x²+3=4x

x²-4x+3=0

(x-3)(x-1)

x could be 3 or 1

The values could be 1 or 3.

In this exercise, you're required to write a mathematical (algebraic) expression for the given word problem and determine which values could be the unknown number.

Translating the word problem into an algebraic expression, we have;

[tex]n^{2} = 4n - 3\\\\n^{2} - 4n + 3 = 0[/tex]

We would solve the quadratic equation by using the factorization method;

[tex]n^{2} - 3n -n + 3 = 0\\\\n(n - 3) - 1(n - 3) = 0\\\\(n - 1)(n - 3) = 0[/tex]

Therefore, the values could be 1 or 3.

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9514 1404 393

Answer:

  y = -1

Step-by-step explanation:

We assume you want the line with a slope of zero. That is a horizontal line, so y is a constant. In order to make the line go through the point with y=-1, the equation of the line is ...

  y = -1

Answer:

D. (-7, 3)

Step-by-step explanation:

The equation given is in point-slope form.

Point-slope form is:

y-y1=m(x-x1)

This is where:

y1 is the y-coordinate of a point it goes through

m is the slope of the line

x1 is the x-coordinate of a point that it goes through

That said, in the given equation:

y1=3

m=4

x1=-7

Note that a point is (x-coordinate, y-coordinate)

Therefore, (-7, 3) is the point that lies on the line.

9514 1404 393

Answer:

  D.  (0, 6)

Step-by-step explanation:

The origin is where the axes cross. The coordinates of that point are (0, 0). The distance of a point (x2, y2) from point (x1, y1) is given by the distance formula ...

  d = √((x2 -x1)² +(y2 -y1)²)

When (x1, y1) = (0, 0), this reduces to ...

  d = √(x² +y²)

We want to find (x, y) such that d=6. This can be a little easier if we square both sides of the equation to eliminate the radical.

  x² +y² = 6² = 36

This is the equation of a circle of radius 6 centered at the origin: all points that are distance 6 from the origin. So, any point on the circle will be at a distance of 6 from the origin.

__

The sum of squares in each case is ...

  A. 3² +0² = 9 . . . inside the circle

  B. 4² +2² = 20 . . . inside the circle

  C. 5² +3² = 34 . . . inside the circle

  D. 0² +6² = 36 . . . on the circle at a distance of 6 from the origin

  E. 4² +4² = 32 . . . inside the circle

  F. 1² +5² = 26 . . . inside the circle

Answer:

Step-by-step explanation:

The formula for calculating the Margin of error of a dataset is expressed as;

Margin of error = [tex]Z*\sqrt{\frac{p(1-p)}{n} } \\\\[/tex] where;

Z is the z-score of 95% confidence interval = 1.96

p is the sample proportion/mean = 0.75

n is the sample size = total number of people = 1000

Note that when the confidence interval is not given, it is always safe to use 95% confidence.

Substituting this values into the formula we have;

[tex]ME = 1.96*\sqrt{\frac{0.7(1-0.7)}{1000} } \\\\ME = 1.96*\sqrt{\frac{0.7(0.3)}{1000} } \\\\ME = 1.96*\sqrt{0.00021} } \\\\ME = 1.96*0.01449\\\\ME = 0.0284[/tex]

Hence the margin error for the dataset is 0.0284

Answer:

The confidence interval consist of positive values, it implies that the mean length of male babies at birth is more than that of female babies.

Step-by-step explanation:

Consider the hypothesis for testing the difference in the mean length of male babies and female babies​ at birth:

H₀: There is no significant difference between the mean length of male babies and female babies​ at birth, i.e. μ₁ - μ₂ = 0.

Hₐ: There is a significant difference between the mean length of male babies and female babies​ at birth, i.e. μ₁ - μ₂ ≠ 0.

The decision rule based on the confidence interval is:

If the (1 - α)% confidence interval does not consist of the null value, i.e. 0 then the null hypothesis will be rejected.

The confidence interval for the difference in the mean length of male babies and female babies​ at birth is:

CI = (0.2 in, 2.7 in)

The confidence interval does not consist of the null value, i.e. 0.

Thus, the null hypothesis will be rejected.

Hence, concluding that there is a significant difference between the mean length of male babies and female babies​ at birth.

Since the confidence interval consist of positive values, it implies that the mean length of male babies at birth is more than that of female babies.

Answer:

4

Step-by-step explanation:

Original coordinates:

A (0, 2)

B (2, 3)

The scale is what number the original coordinates was multiplied by to reach the new coordinates

1. Divide

(0, 8) ÷ (0, 2) = 4

(8, 12) ÷ (2, 3) = 4

AB was dilated by a scale factor of 4.