The number of DVDs in a random person's home collection is counted for a sample population of 80 people. The mean of the sample is 52 movies, the entire population is known to have a standard deviation of 12 movies. Assuming a 99% confidence level, find the margin of error.

A) 59.4671

B) 2.6296

C) 38.6536

D) 3.4547​

Answer:

-1

Step-by-step explanation:

The y-intercept is where the line crosses the y-axis.

Answer:

[tex]\huge\boxed{\sf y-intercept = -1}[/tex]

Step-by-step explanation:

Here,

Since, this is the point where x = 0 and where the line passes through the y-axis.

[tex]\rule[225]{225}{2}[/tex]

Answer:

See below.

Step-by-Step Explanation:

5) 8x+9-6x-7

8x + 2 - 6x (Subtract the numbers)

2x + 2 (Combine like terms)

2 (x + 1)  (Common factor - Factor by grouping twice)

6) 2y-6+5y+9

2y + 3 + 5y (Add the numbers)

7y + 3 (Combine like terms)

7) 3x+8+4x-9

3x - 1 + 4x (Subtract the numbers)

7x - 1      (Combine like terms)

8) 9y+16-12y+24

9y + 40 - 12y (Add the numbers)

-3y + 40 (Combine like terms)

9) 7g-5-8g+12

7g + 7 - 8g (Add the numbers)

-g + 7 (Combine like terms)

10) 11c-8+5c-8

11c - 16 + 5c (Subtract the numbers)

16c - 16 (Combine like terms)

16 (c - 1)   (Common factor - Factor by grouping twice)

11) 5(2x + 3) (This one was a bit blurry, I am assuming that's a addition sign.)

10x + 15 (Distribute)

12) 5(-2x+3)

-10x + 15 (Distribute)

Hope this helps!

Answer: those are the answers its a long time.

Question  5  Answer: 2(x+1)

8x+9−6x−7

Multiply and combine like terms.

2x+2

Factor out 2.

2(x+1)

Questio 6 Answer : 7y + 3

2y−6+5y+9

Combine 2y and 5y to get 7y.

7y−6+9

Add −6 and 9 to get 3.

7y+3

Question 7  Answer: 3x+8+4x−9

Combine 3x and 4x to get 7x.

7x+8−9

Subtract 9 from 8 to get −1.

7x−1

Question 8 Answer: - 3y + 40

9y+16−12y+24

Combine 9y and −12y to get −3y.

−3y+16+24

Add 16 and 24 to get 40.

−3y+40

Question 9 Answer: -g + 7

7g−5−8g+12

Combine 7g and −8g to get −g.

−g−5+12

Add −5 and 12 to get 7.

−g + 7

Question 10 Answer: 16 ( c - 1 )

11c−8+5c−8

Combine 11c and 5c to get 16c.

16c−8−8

Subtract 8 from −8 to get −16.

16c - 16

Question 11 Answer: 10x +15

5(2x+3)

Use the distributive property to multiply 5 by 2x+3.

10x+15

Question 12 Answer: 15 - 10x

5(−2x+3)

Use the distributive property to multiply 5 by −2x+3.

−10x+15

The value of n is 12. and m is 6root5

We have given the diagram,

The measurement of m,

n = 12

According to the altitude theorem

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse.

24/n = n/6

The Cross multiply

24 * 6 = n²

144 = n²

n² = 144

n = √144

n = 12

[tex]m^2=6^2+n^2[/tex]

[tex]m^2=6^2+12^2\\m^2=36+144\\m^2=180[/tex]

[tex]m=\sqrt{180} \\m=2\cdot \:3\sqrt{5}\\m=6\sqrt{5}[/tex]

Hence the value of n is 12.

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Answer:

12

Step-by-step explanation:

Step-by-step explanation:

[tex] = { ({16}^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]

[tex] = { ({( {2}^{4}) }^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]

[tex] = {2}^{4 \times \frac{3}{2} \times \frac{1}{2} } [/tex]

[tex] = {2}^{ \frac{12}{4} } [/tex]

[tex] = {2}^{3} [/tex]

[tex] = 2 \times 2 \times 2[/tex]

[tex] = 8[/tex]

The answer is B.

72

x varies directly as y

hence x=k y

k=6

y=12

x=6×12

x=72

The solutions of the given equation are x= (√5+3)/2 & x= (-√5+3)/2

If ax²+bx+c = 0 is a quadratic equation ,where a,b,c are real numbers, Then the solution is x = (-b±√(b²-4ac))/2a , where a≠0

The given equation is, 4x²-12x+9 = 5

So, 4x²-12x+9 = 5

⇒ 4x²-12x+9-5 = 0

⇒ 4x²-12x+4 = 0

Comparing this equation with ax²+bx+c = 0 we get,

a = 4, b = -12, c = 4

Applying sridharacharya formula we get,

x = (-(-12)±√((-12)²-4×4×4))/(2×4)

  = (12±√(144-64)/8

  = (12±√80)/8

  = (3±√5)/2

The values of x are (√5+3)/2 & (-√5+3)/2

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C. For the first card, there are three ways to choose the number of card.

For the another, there two options, and likewise there's only 1 choice of card. So there are 3 × 2 × 1 = 6 ways that the calculation can be chosen.

Doing this for the other attributes, we get 6 × 6 × 24 × 6 ways. But the order of cards does not count in a set of card, so we divide by 3! 6 * 6 * 24 × 6 ÷ 3! = 864. It means there are 864 sets for part.

D. The cards may have the same number, color, shapess, orshading.

However, also there are 6 × 24 × 6 × 3! = 144 sets of cards, If all the colors are thesame. How ever, also there are 144 sets of cards.

If all the calculation are the same. We get the same number for shape and shadings, so there are 4 × 144 = 576 sets of cards.

what is Probability?

Probability is branches of mathematics concerning numerical descriptions of how to the likely an event is to occurs, or how to the likely it is that a proposition is true. The probability of an event is a numbers between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the events and 1 indicates certain of cards.

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Step-by-step explanation:

2y+9= 4

2y=-5

y=-5/2

y= -2and 1/2

When we simplify (3 + √5)(3 + √2), the result obtained is:

9 + 3√2 + 3√5 + √10

a√b × c√d = (a × c)√(b × d)

(3 + √5)(3 + √2)

Expand by clearing the bracket

3(3 + √2) + √5(3 + √2)

9 + 3√2 + 3√5 + √10

Thus,

(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10

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Answer:

the area of rectangle is 270 cm and its length is 18 cm

the breath of the perimeter of given rectangle respectively

used concept

area of rectangle l into b where is is v is breadth of the rectangle perimeter of rectangle 2 into l + b where I and b stands for same as the

solution

let's the length of rectangle is equal to l is equal to 18 cm

breath of rectangle is is equal to b is equal to

area of rectangle is equal to 270 CM

now according to the question and l into b is equal to a

18 into b is equal to 1070

b is equal to 270 upon 18

b is equal to 15 CM

p no no perimeter of the rectangle is equal to 2 into l + b

2 multiply 18 + 15

2 X 33

is equal to 66 cm

therefore the breath and the perimeter of rectangle are 15 cm and 66 respectively

The expression for P(red) is (x - 5)/x

The given parameters are:

Apple = x

Green = 5

The number of red apples is:

Red = Apple - Green

This gives

Red = x - 5

The expression for P(red) is then calculated as:

P(Red) = Red/Apple

This gives

P(Red) = (x - 5)/x

Hence, the expression for P(red) is (x - 5)/x

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The slope- intercept is y> (1-4x) / 5 and y< 2x + 6

A  statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

4x – 5y < 1  and 1/2y – x < 3

Solving

4x – 5y < 1

-5y < 1- 4x

-y < (1-4x) / 5

y> (1-4x) / 5

Now, the second inequality,

1/2y – x < 3

1/2y< 3+x

y< 2x + 6

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Answer:

07698+96965#5_(-&)!:86539'6";

The solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The given equation will be solved as:-

= 3x² + 8x - 10  

Using the formula of factors:-

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

x = [tex]\dfrac{-8\pm\sqrt{64-(-120)}}{2\times 3}[/tex]

x = [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].

Therefore the solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].

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Answer:

The function h(x) = -5√x is decreasing on the interval (–∞, 0) is true, Option A is correct.

A relation is a function if it has only One y-value for each x-value.

The given function h of x equals negative 5 times the square root of x.

h(x) = -5√x

The value of h(x) decreases as the value of x increases.

The function h(x) is a decreasing function over the interval (–∞, 0) because it is a negative function over the interval.

Hence, the function is decreasing on the interval (–∞, 0) is true.

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Answer:

x = (√10  -3)/2  and (-√10  -3)/2

Step-by-step explanation:

(2x+3)^2 = 10

To solve the equation, take the square root of each side

sqrt((2x+3)^2) = ±√10

2x+3 = ±√10

Subtract 3 from each side

2x+3-3 = ±√10  -3

2x = ±√10  -3

Divide each side by 2

2x/2 = (±√10  -3)/2

x = (±√10  -3)/2

There are two solutions

x = (√10  -3)/2

and (-√10  -3)/2

Answer:

[tex]\large {\textsf{A and D}}\ \implies \sf \sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]

Step-by-step explanation:

Given: (2x + 3)² = 10

In order to find the solutions to the given equation, we can take the (square) roots of the equation to find the zeros, which are also known as the x-intercepts. This is where the zeros intersect the x-axis.

Note: when taking the square roots of a quadratic equation, remember to use both the positive and negative roots.

Step 1: Square both sides of the equation.

[tex]\sf \sqrt{(2x + 3)^2} = \sqrt{10}\\\\\Rightarrow 2x+3=\pm\sqrt{10}[/tex]

Step 2: Separate into possible cases.

[tex]\sf x_1 \implies 2x+3=-\sqrt{10}\\\\x_2 \implies 2x+3=\sqrt{10}[/tex]

Step 3: Solve for x in both cases.

[tex]\sf \bold{x_1} \implies 2x+3=-\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=-\sqrt{10}-3\\\\\Rightarrow 2x=-\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{-\sqrt{10}-3}{2}\\\\\Rightarrow x_1=\dfrac{-\sqrt{10}-3}{2}\\\\[/tex]

[tex]\sf \bold{x_2}\implies 2x+3=\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=\sqrt{10}-3\\\\\Rightarrow 2x=\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{\sqrt{10}-3}{2}\\\\\Rightarrow x_2=\dfrac{\sqrt{10}-3}{2}[/tex]

Therefore, the solutions to this quadratic equation are: [tex]\sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]

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In total 180 chairs are ordered for the cost $6000.

The total cost of chairs=$6,000.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Let x be the chairs ordered each at $20 and y be the chairs ordered each at $40.

Then equation will be 20x+40y=6000-------(1)

Given that, twice as many $20 chairs as $40 chairs were ordered.

That is 2x=y⇒2x-y=0--------(2)

Multiply equation (2) by 40.

That is 80x-40y=0--------(3)

By adding equation (2) and (3) we get

20x+40y+80x-40y=6000

⇒100x=6000

⇒x=60

Substitute x=60 in equation (2)

That is, 2x=y

⇒y=120

Total number of chairs=x+y=60+120=180 chairs.

Hence, in total 180 chairs are ordered for the cost $6000.

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Answer:

has no x^2 term

Step-by-step explanation:

Has no x^2 term   <====== that would make it an exponential function, not linear

Answer:

the answer is C.64

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

because the

The time it takes = 3 hours 12 minutes

Rate is a ratio which compares two quantities of different units.

Analysis:

Speed = 5 miles/hour

distance covered = 16 miles

speed taken = distance covered/time taken

time taken = 16/ 5 = 3.2 hours = 3 hours 12 minutes

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There are 32 subsets of the set h.

We have given that h={A,E,I,O,U},

We should count the elements of the set, then put that number as the exponent of 2.

A set A is a subset of another set B if all elements of set A are elements of set B. In other words, set A is contained inside set B.

Remember that 2 should always be the base in finding the number of subsets: 2^5=32

Therefore there are 32 subsets of the set h.

Here set h is denoted by small h but the set is always denoted by capital letters.

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The probability of P(20s | Chocolate) and P(chocolate | 30s) x P(vanilla | 30s) will be 0.26 and 0.25, respectively.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Adults were polled to determine whether they preferred vanilla or chocolate ice cream. The survey findings for three age groups are displayed in the table.

There are 127 people who enjoy chocolate, and 33 of them are in their 20s is given as,

P(20s | Chocolate) = 33 / 127 = 0.26

There are 122 persons in their 30s, and 53 of them prefer chocolate 69 others prefer vanilla is given as,

P(chocolate | 30s) x P(vanilla | 30s) = 53/122 x 69/122 = 0.25

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Answer:

  f(-2) = 0

Step-by-step explanation:

The value of the function for a particular x-value can be read from the graph.

The graph is a map showing the value of f(x) for each value of x for which the function is defined. The x-values are identified by the numbers on the horizontal x-axis. The corresponding function values are found by referencing the vertical y-axis.

To find the function value f(x) for x=-2, we locate the vertical grid line marked with -2 at the x-axis. We then locate the point on the graph of the function where it crosses that vertical grid line. Tracking horizontally from that point to the vertical y-axis, we can read the function value from the vertical scale.

The attachment has a red arrow pointing to the intersection of the graph with the grid line x=-2. That point of intersection lies on the x-axis, where the y-value is 0. That means ...

  f(-2) = 0

__

Additional comment

On this graph, the axis crossing point (x=0, y=0) is not labeled. It is halfway between x=-1 and x=1. Similarly, it is halfway between y=-1 and y=1. Based on this and on experience with similar graphs, you can assume that the axis crossing has coordinates (x, y) = (0, 0).

An expression can either be an equation or an inequality.

The correct classification of the terms are:

Expression; 4x+20

Inequality: 4x+20>40

Equation: 4x+20=40

We have given that,

{20,18,8,18,10,8,4}

{12,14,16,20,4,8,10}

{12,16,4,20,8,6,8}

To determine the correct classification, we make use of the following highlights

When an expression has the =, then the expression is an equation.

When an expression has any of the following signs>, <, >=, <= or != , then the expression is an inequality.

When the expression is neither an equation nor an inequality, then it is just an expression.

Hence, the correct classifications are:

Expression; 4x+20

Inequality: 4x+20>40

Equation: 4x+20=40

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Reason:

I'm assuming that the swimmer travels along the 50 meter side

Divide 1500 over 50 to get 1500/50 = 30, which tells us that the swimmer must make 30 trips.

Answer:

(-2, -4)

Step-by-step explanation:

You can complete the square of the equation to get

y+(4/2)^2 = x^2+4x+(4/2)^2

y+4 = x^2 + 4x + 4

y+4 = (x+2)^2

y = (x+2)^2 - 4

This gives the form y = a(x-h)^2 + k where (h, k) is the vertex of the equation. You can also arrive at the same conclusion by making some observations of the equation. (x+2)^2 minimum value is going to be 0 since and negative values resulting from x+2 is going to become positive because of the square. So the minimum value is when x+2 is 0 or when x is equal to -2 and when it's at that minimum value of 0 it's going to have 4 subtracted from it which gives the vertex of (-2, -4)

A figure can be graphed on a coordinate plane as a set of points located on specific places, specified by  their coordinates.

The cartesian coordinate plane is an infinite 2 dimensional plane and each point of a cartesian plane is tracked by a location.

Now, the perpendicular distance of point from the horizontal axis and vertical axis are respectively usually named x-axis and y-axis. The location is then written as (a,b) where;

a is that point's shortest distance from the y-axis and called x-coordinate of that point.

b is that point's shortest distance from the x-axis, and called y-coordinate of that point.

Thus, those given geometric figures can be graphed on a coordinate plane as a set of points located on specific places, specified by  their coordinates.

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Answer:

45

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

Depending on where you start, the protractor can read in different ways. Since the measure of this angle started from the left, you read the numbers at the top. If the measure would have started from the right, you read the numbers below.

A good rule of thumb is that if the angle appears to be greater than 90 degrees, or an obtuse angle, you would choose the only answer choice that is above 90 degrees.

Hope this helps!

Using proportions, it is found that his net pay is of $158,040.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

His first discount is for the retirement account, hence the taxable amount is:

T = 240000 - 20500 = $219,500.

He pays 28% of that in taxes, hence his net pay is of 100 - 28 = 72% of  $219,500, hence:

N = 0.72 x 219500 = $158,040.

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