Mrs. Malatlian selects a simple random sample of 28 seniors from the 300 seniors at her school and finds that 20 of
them are planning to participate in the school's annual capture the flag game. She wants to construct a confidence
interval for p= the proportion of all seniors who plan to participate in the game. Which condition has she failed to meet,
if any?
a) The sample was selected at random.
b) np ≥ 10
c) n(1-p) ≥ 10
d) The sample size is less than 10% of the population size.
e) All conditions are met.

Answer:

A) 3.6 meters

B) 3.24 meters

C) 13 Times

Step-by-step explanation:

:)

Considering the expression of a line, the equation of the line that passes through the pair of points (-4,1) and (4, -1) is y=-1/4x +2.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a line, the value of the ordinate to the origin b can be obtained.

In this case, being (x₁, y₁)=  (-4, 1) and (x₂, y₂)= (4, -1), the slope m can be calculated as:

m= (-1 -1)÷ (4 - (-4))

m= (-1 -1)÷ (4 +4)

m= (-2)÷ 8

m= -1/4

Considering point 1 and the slope m, you obtain:

1= (-1/4)× (-4) + b

1= -1 +b

1 +1= b

2= b

Finally, the equation of the line is y=-1/4x +2.

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Answer:

268.2 cm²

Step-by-step explanation:

Create the following ratio for both pentagons:

side : area

9      : 603.45 cm²

4      :  A

We can see that multiplying 603.45 cm² by 4/9 will solve for A, as multiplying 9 by 4/9 will solve for 4.

4 = 9 × (4/9)

A = 603.45 cm² × (4/9)

A = 268.2 cm²

So, the area of the smaller pentagon is 268.2 cm².

The sum of the vertical opposite angle m∠q and the angle m∠r us equal to 85.5°.

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

The line MN and PQ intersect each other, so m∠q and the angle m∠MOP are equal

m∠q = 54°

m∠p = 180° - 54° {sum of angles on a straight line}

m∠p = 126°

m∠p = 4 × m∠r {cross multiply}

m∠r = 126°/4

m∠r = 31.5°

Therefore, the sum of the vertically opposite angle m∠q and the angle m∠r is 54° + 31.5° = 85.5°.

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A similarity transformation is a rigid movement followed by scaling, so this type of transformation can change the position and size, but not the shape.

In geometry, a similarity transformation is a rigid movement followed by scaling, so this type of transformation can change the position and size, but preserve the shape and angles.

Thus, two or more shapes are similar if they have the same shape and corresponding angles, but their corresponding sides are proportional in length.

This type of transformation is often also referred to as dilation.

The rule of dilatation:

[tex]D_{k}[/tex] (x,y) = (kx, ky)

with [tex]D_{k}[/tex] is the coordinate point of the new image and k is the scale factor.

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It takes 10 hours to reach a population of 200,000 at the growth rate of 7% per hour.

We can use the formula for compound interest to calculate the time it takes for the population of bacteria to reach 200,000.

The formula is:
A = P(1+r)^t

Where:
A = final amount (200,000)
P = initial amount (50,000)
r = growth rate (7% per hour expressed as decimal)
t = time (in hours)

We can rearrange the formula to solve for t:
t = log(A/P) / log(1+r)

By plugging in the given values:
t = log(200000/50000) / log(1+ 0.07)

The answer will be in hours, so we need to use a calculator or a log function in a programming language to get the answer.

Alternatively, you can use the rule of 70, which says that the number of years required to double a population at a given growth rate is approximately 70/growth rate. So in this case it is 70/7 = 10 hrs.

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Answer:

3n³-19n²+20n

Step-by-step explanation:

(g×f)(n)= g(n) × f(n)

= (n²-5n)(3n-4)

=3n³-4n²-15n²+20n

=3n³-19n²+20n

The value of g(-2) is 0 and the value of g(4) is -4.

The function g is defined as a piecewise function that assigns a specific value to the input x depending on the range of x.

For x between -8 and -2 (not including -2) the function g assigns 6 as the output, for x between -2 and 4 (not including 4) the function g assigns 0 as the output, and for x between 4 and 10 (not including 10) the function g assigns -4 as the output. Therefore, for input x = -2, the function g assigns 0 as the output and for input x = 4, the function g assigns -4 as the output.

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Complete question :

consider a function g.

given

g(x) = 6    if  -8 ≤ x < -2

g(x) = 0     if  -2 ≤ x < 4

g(x) = -4     if  -4 ≤ x < 10

find the value of g(-2) and g(4)

To make the ratio of red to blue counters 3:1, you will need 3 times as many red counters as blue counters.

If the current ratio is 1:3, then for every 1 red counter, there are 3 blue counters. To make the ratio 3:1, you will need 3 red counters for every 1 blue counter.

So, if you have x red counters and y blue counters, where the ratio of red to blue is 1:3, then you will need 3x red counters and y blue counters to make the ratio 3:1. This means you will need 3x - x = 2x more red counters.

For example, if you have 6 red counters and 18 blue counters, the ratio of red to blue is 1:3. To make the ratio 3:1, you will need 3×  6 = 18 red counters and 18 blue counters. This means you will need 18 - 6 = 12 more red counters.

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Answer:

18 cubic units

Step-by-step explanation:

The volume of prism is equal to:

base area x height

therefore;

V = 1.33333 x 13.5

   = 17.999955 ≈ 18

Answer:

The volume of a prism is given by the formula:

V = Bh

Where V is the volume, B is the area of the base, and h is the height of the prism.

Given the height of 1.33333 and an area of the base of 13.5, the volume can be calculated as:

V = 13.5 * 1.33333

V = 18.08332

So the volume of the prism is 18.08332 cubic units.

Step-by-step explanation:

A. The number of red balls he had was 8  at the beginning.

Duke's starting red ball total can be found by setting up a system of equations. First, let x represent the number of red balls and y represent the number of blue balls.

After 5 days, the equation is x-15=y+10. This equation states that after 5 days, the number of red balls (x) minus 15 will equal the number of blue balls (y) plus 10. After 9 days, the equation is x-27=2y+20.

This equation states that after 9 days, the number of red balls (x) minus 27 will equal twice the number of blue balls (y) plus 20. To solve for x, both equations can be set equal to each other and solved. This results in x=8. Therefore, Duke had 8 red balls at the beginning.

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Answer:

u = -42

Step-by-step explanation:

Now we have to,

→ find the required value of u.

The equation is,

→ -23u = 966

Then the value of u will be,

→ -23u = 966

→ u = 966/-23

→ u = -(966/23)

→ [ u = -42 ]

Hence, the value of u is -42.

The values of x when solved;

a. x≥ 3. 44

b. x≥3. 44

c. x ≤ 8. 8

Inequalities are simply described as relations that makes a non-equal comparison between two numbers, variable or other mathematical expressions.

They are used to compare numbers on the number line on the basis of size

From the information given, we have to determine the value of x in the inequality given;

a. 5 1/2≥1.6x

convert to improper fraction

11/2 ≥1.6x

divide both sides by 1. 6

x≥ 3. 44

b. x≥3 7/16

convert to improper fraction

x≥ 55/ 16

x≥3. 44

c. x≤8 4/5

convert to improper fraction

x≤ 44/ 5

x ≤ 8. 8

Hence, the value are  x≥ 3. 44, x≥3. 44 and x ≤ 8. 8

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The two functions of f(x)= -6x2 + 5 and g(x)= 5 result in the y-intercept of function g(x) being 2 as a result (1. 5)

Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.

given

y-intercept for f(x) is f(0)

so f(0) =

=> 0+5

=>5

so the y-intercept of f(x) is 5

now y-intercept of g(x) is g(0)

so g(0) = 7*0 +2

=>0 +2

=>2

The two functions of f(x)= -6x2 + 5 and g(x)= 5 result in the y-intercept of function g(x) being 2 as a result (1. 5) .

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Answer:B 1 real zero

Step-by-step explanation:

Solutions for the given graph can be be given as function  [tex]$ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.[/tex]

A relation called a "function" is one in which each input has just one Solution.

In the relationship, y is a function of x because there is only one solution y for each input x (1, 2, 3, or 0). Since y = 3 has multiple solution (x = 1 and x = 2), x is not a function of y.

As we can see, f(x) has two inequalities

in first case x ≤ -1.5

And equation is

[tex]$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

m = -2

Line equation

y - 0 =  -2(x - (-1.5))

y = −2x − 3

in second case x ≤ -1.5

And equation is

[tex]$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

m = 0.75

Line equation

y - 0 =  0.75(x - (-4))

y = 0.75x + 3

[tex]$ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.[/tex]

Thus, Solutions for the given graph can be be given as function  [tex]$ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.[/tex]

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Answer: 10

Step-by-step explanation: 1/2 + 3/4= 5/4 or 1 1/4

1 1/4 / 1/8= 10

Answer:

  (d)  4/9

Step-by-step explanation:

You want the probability of drawing D, D from a set of cards {A, D, D} if two are drawn with replacement.

The probability of drawing a D is 2/3. The probability of doing it again is the same. Thus, the probability of doing it twice, assuming the draws are independent, is ...

  P(D, D) = P(D)·P(D) = (2/3)(2/3) = 4/9

P(D, D) = 4/9

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The required value of x can be obtained as per the similarity of triangles as 18.84 units.

A triangle is a two dimensional shape bound by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.

For two similar triangles the ratio of corresponding sides are always equal.

The given diagram shows two similar triangles.

As the ratio of corresponding sides are equal,

The following equation can be written as,

⇒ 26/35 = 14/x

⇒ 26x = 14 × 35

⇒ x = 18.84

Hence, the value of x can be obtained as 18.84 units.

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The total number of possible four-digit PINs that cannot begin or end with a 0 and must be an even number is 10,000 - 900 - 4,500 = 4,500. Thus, the correct answer is c. 4,500.

To determine this:

There are 10 options for the first digit (1-9) and 10 options for the last digit (2, 4, 6, 8). For the middle two digits, there are 10 options for each digit (1-9). Therefore, the total number of possible four-digit PINs is 10 x 10 x 10 x 10 = 10,000.

However, we must subtract the number of PINs that begin or end with a 0, which is 9 x 10 x 10 x 1 = 900. We must also subtract the number of PINs that are odd numbers, which is 9 x 10 x 10 x 5 = 4,500.

Therefore, the total number of possible four-digit PINs that cannot begin or end with a 0 and must be an even number is 10,000 - 900 - 4,500 = 4,500. Thus, the correct answer is c. 4,500.

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The value of x give the sides in the rectangle is 4cm.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has. Based on the information, it's important to note that the perimeter of a rectangle is given as:

= 2(length + width)

Since rectangle a has sides 6cm long and x+2cm long. rectangle b has sides 3cm long and 2x+1 cm long and the perimeter is the same. This will be calculated by equating the perimeter for both rectangle A and B.

2(6 + x + 2) = 2(3 + 2x + 1)

12 + 2x + 4 = 6 + 4x + 2

Collect the like terms

-2x = 8 - 16

-2x = -8

Divide

x = 8/2

x = 4

Therefore, the value of x based on the calculation is 4cm.

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The balance in your account after 5 years, given the annual simple interest rate and the amount deposited, is $ 1, 612. 50

To find the balance on the account after 5 years, you first need to find the simple interest on the account every year ;

= Amount deposited x Simple interest rate

= 1, 500 x 1. 5 %

= $ 22. 50

The interest over 5 years is :

= 22. 50 x 5

= $ 112. 50

The balance is therefore:

= 1, 500 + 112. 50

= $ 1, 612. 50

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Full question is:

A savings account pays an annual simple interest rate of 1.5%. What would be the balance in your account after 5 years, if you deposited $ 1, 500?

A convex polygon is a polygon which has all its interior angles as less than 180° . The correct option is B

Convex polygon is a closed figure where all its interior angles are less than 180° and the vertices are pointing outwards. convex is used to refer to a shape that has a curve.

Therefore from visual inspection of all four options only option B seems to fulfill the criteria mentioned . A convex shape is a shape where all of its parts point outwards. No part of it points inwards,

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The minimum sample size required for the estimate is given as follows:

385.

The bounds of a z-distribution confidence interval, which is used as we have the standard deviation for the population, are given as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which the parameters are given as follows:

Hence the equation for the margin of error is given as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The variance is known to be 3.61, hence the standard deviation is given as follows:

[tex]\sigma = \sqrt{3.61} = 1.9[/tex]

The critical value for a 95% confidence interval is given as follows:

z = 1.96.

Hence the required sample size for a margin of error of M = 0.19 is calculated as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.19 = 1.96\frac{1.9}{\sqrt{n}}[/tex]

[tex]0.19\sqrt{n} = 1.96 \times 1.9[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 1.9}{0.19}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 1.9}{0.19}\right)^2[/tex]

n = 385.

(rounding up, as for a sample size of 384, the margin of error would be slightly above 0.19).

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Answer:

6 -19i

Step-by-step explanation:

5 - 8i + 1 - 11i

Collect like terms

5 + 1 -11i -8i

6 - 19i

Answer: -7x+2x+5-4x=-9x+6

The equation -7x+2x+5-4x=-9x+6 is an example of an equation that has no solution. This is because the left side of the equation, -7x+2x+5-4x, is not equal to the right side, -9x+6.

When we simplify the left side of the equation, we get -7x+2x+5-4x = -9x. We can see that the left side and right side of the equation are not equal and thus have no solution.

In general, an equation has no solution when the two sides of the equation are not equal, and there is no value of the variable that can make them equal.

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 7 : a₁ = 2

Step-by-step explanation:

An explicit formula has the form

[tex]a_{n}[/tex] = a₁ + d(n - 1)

compare with [tex]a_{n}[/tex] = 2 + 7(n - 1)

then a₁ = 2 and common difference d = 7

the recursive rule allows a term to be found by adding d to the previous term, that is

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 7 : with a₁ = 2

Answer:

60

Step-by-step explanation:

Total angle of triangle= 180

so 4x + 5x + 3x = 180

12x = 180

x = 180/12

x = 15

E = 5x = 5×12 = 60

The rate of change of this linear function is -2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁)

From the given table, (-2, 15), (-4, 23) and (-5, 27).

Substitute, (x₁, y₁)=(-2, 15) and (x₂, y₂)=(-4, 23) in (y₂-y₁)/(x₂-x₁), we get

Rate of change =(23-15)/(-4+2)

= 8/(-2)

= -4

Therefore, the rate of change of this linear function is -2.

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