A recent study of 28 city residents showed that the mean of the time they had lived at their present address was 9.3 years. The standard deviation of the population was 2 years. Find the 90% confidence interval of the true mean? Assume that the variable is
approximately normally distributed. Show all your steps

Answer:

10- I can't really help you with that one you have to just draw it on your own.

11- a triangle can only have 1 obtuse angle because the other 2 need to be acute to connect 3 sides.

12- x=20 degrees,y=64 degrees,z=116 degrees

Step-by-step explanation:

11- 1 obtuse angle because the other 2 need to be acute to connect 3 sides.

12- x=20 degrees because of the other 20 degree angle opposite to it. y=64 degrees because 180-(20+96)=64 (all angles in a triangle add to 180). z=116 degrees because supplementary angles add to 180 degrees and Y and Z are supplementary.

The domain and range of the function f of x are equal to : (C) D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}

A Domain can be defined as the values or numbers that are accepted or allowed in a particular function.

A domain is very important when dealing with a function.

In conclusion, The domain and range of the function f of x are equal to (C) D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}

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The probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The area of the rectangle = 30×21 = 630 square m

The total outcomes = 630 square m

The favorable outcomes = area of the circle + area of the trapezoid

= π(5)² + [(11+15)/2]×5

= 78.53 + 65

= 143.53 square m

Probability(a point chosen randomly inside the rectangle is either in the circle or in the trapezoid):

= 143.53/630

= 0.227 ≈ 0.23

Thus, the probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.

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Answer:

0.13

Step-by-step explanation:

I guessed and got it correct. Sorry, I cant show work, I hope it helped!! <3

Answer:

[tex]x^{\frac{5}{3}} y^{\frac{1}{3} }[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{x^{5} y}[/tex] = [tex]x^{\frac{5}{3}} y^{\frac{1}{3} }[/tex]

Answer:

125cm³

Step-by-step explanation:

To find volume, we multiply length × width × height

(length × breadth × height)

here, we know our length to be 5cm, our width to be 5cm, and our height to be 5cm

length : 5cm

width/breadth: 5cm

height: 5cm

so, we can multiply our values together (we can plug in our known values to the volume formula of length × width × height)

length × width × height

5  ×   5  ×  5= 125

*note: we write volume as cubed (unit³)

So, we know our volume is 125cm³

hope this helps! have a lovely day :)

Answer:

0

Step-by-step explanation:

You need to restrict the domain to one side of the axis of symmetry.

The probability that the contestant wins at least one car is 3/5.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

For 1 car, we consider two possible outcomes:

P(1 car) = 2/6 x 4/5 + 4/6 x 2/5

P(1 car) = 8/15

For no car in either door

P(no car) = 4/6 x 3/5

P(no car) = 2/5

The probability that the contestant wins at least one car is the sum of the probability of one car and the probability of two cars:

P(2 cars) = 2/6 x 1/5

= 1/15

P(1 car) + P(2 cars) = 8/15 + 1/15

= 3/5

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Hello,

Answer: D

Step-by-step explanation:

F(x) = (1/5)ˣ

F(3) = (1/5)³ = 1³/5³ = 1/125

⇒ Answer D

Answer:

Domain: (-infinity, infinity)

Range: [10, infinity)

Step-by-step explanation:

So the domain is easy to determine, because the only reason the domain would be restricted is in like logarithmic equations, radical equations, etc... So in this case the domain is all real number (-infinity, infinity) or all real numbers.

The range of this function is a bit different since it's an absolute function, so  when the value inside the absolute values goes from -infinity to 0, it's actually decreasing, despite the value technically increasing. But there is a x-5 and that actually doesn't change the range, it simply shifts it to the right by 5 units, so the vertex is there, because that's when the value inside of it goes from being a negative to a positive number. the +10 does change the range, because normally an absolute value function has a vertex at (0, 0) and in this case it's slightly different since it has a vertex when x=5 since the x has 5 subtracted from it. But the +10 is moving that up. Since the lowest value of the absolute value will be 0, any negative number becomes positive. So the vertex is shifted up 10 units, thus the range is [10, infinity)

According to the AA similarity theorem, the statement that must be true is: D. ∠Z ≅ ∠W and ∠X ≅ ∠U.

The AA similarity theorem states that if two angles in one triangle is congruent to two corresponding angles in another triangle, then both triangles are similar.

For △ZYX ~ △WVU, any two pairs of corresponding angles must be congruent.

Therefore, the statement that must be true based on the AA similarity theorem is: D. ∠Z ≅ ∠W and ∠X ≅ ∠U.

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Answer:

(a)  -1

(b)  4

(c)  14

(d)  61

Step-by-step explanation:

A piecewise function is a function which has different definitions for different intervals of x.

Given:

[tex]f(x)=\begin{cases}5x-1 \quad \textsf{if }-5\leq x \leq 3\\x^3-3 \quad \textsf{if }\:\:\:\:\:\:3 < x \leq 4\end{cases}[/tex]

f(x) has 2 definitions:

Definition 1

[tex]5x-1[/tex] when x is more than or equal to -5 and less than or equal to 3.  This is a linear function.

Definition 2

[tex]x^2-3[/tex] when x is more than 3 and less than or equal to 4.  This is a cubic function.

Part (a)

We have to find f(0), so when x = 0.

x = 0 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

[tex]f(x)=5x-1[/tex]

Substitute x = 0 in this definition:

[tex]\implies f(0)=5(0)-1=-1[/tex]

Part (b)

We have to find f(1), so when x = 1.

x = 1 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

[tex]f(x)=5x-1[/tex]

Substitute x = 1 in this definition:

[tex]\implies f(0)=5(1)-1=4[/tex]

Part (c)

We have to find f(3), so when x = 3.

x = 3 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

[tex]f(x)=5x-1[/tex]

Substitute x = 3 in this definition:

[tex]\implies f(0)=5(3)-1=14[/tex]

Part (d)

We have to find f(4), so when x = 4.

x = 4 satisfies the condition 3 < x ≤ 4 so the corresponding function is

[tex]f(x)=x^3-3[/tex]

Substitute x = 4 in this definition:

[tex]\implies f(4)=(4)^3-3=61[/tex]

3,2

because each input only has one output and 2 has 0 and 3 so it is not a function that leaves 3,2.

Answer:

Recognize the equation as that of a horizontal line passing through the y-axis at −3

The attached graph represents the graph of the function g(x)

The function f(x) is an absolute value function.

An absolute value function is represented as:

y = a|x - h| + k

Where

Vertex = (h, k)

From the graph, we have:

(h, k) = (-3, -2)

So, we have:

y = a|x + 3| - 2

Also, we have:

(x, y) = (-1, 0)

So, we have:

0 = a|-1 + 3| - 2

This gives

0 = 2a - 2

Solve for a

a = 1

Substitute a = 1 in y = a|x + 3| - 2

y = |x + 3| - 2

This means that

f(x) = |x + 3| - 2

We have:

g(x) = 2f(x)

This means that:

g(x) = 2(|x + 3| - 2)

So, we have:

g(x) = 2|x + 3| - 4

See attachment for the graph of g(x)

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Answer:

y < x + 1

Step-by-step explanation:

identify 2 points along the line (-1,0) and (0,1)

gradient = [tex]\frac{0-1}{-1-0} =1\\\\the \ y \ intercept = 1\\\\y=x+1\\\\[/tex]

let us choose point (0,0) which is within our origin and substitute

0 = 0 +1

0 = 1

but we know 0 < 1

so the region is well represented by : y < x + 1

Answer:

y > x + 1

Step-by-step explanation:

→ As the line is upward sloping we can eliminate the 2 negative equations options

y < x + 1 or y > x + 1

→ As the region shaded is above the line y = x + 1, it must be y > x + 1

Answer:

Step-by-step explanation:

The inequality that represents the given graph is: D. y ≥ 2/3x + 2.

Using two points on the line, (0, 2) and (-3, 0), find the slope (m).

Slope (m) = change in y / change in x

Slope (m) = (2 - 0)/(0 - (-3))

Slope (m) = 2/3

The y-intercept (b) is the y-value of the point where the line intercepts the y-axis = 2.

Substitute m = 2/3 and b = 2 into y ≥ mx + b:

y ≥ 2/3x + 2

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Answer:

if there's a graph for f(x):

if you're given a graph it means that at the x-coordinate x=1 the corresponding y-value is y=7. Another way to think of this is it's giving you the ordered pair. f(x-value) = y-value which gives you (x,y).

if there's an equation for f(x):

if you're given an equation, you're still looking to find the y-value but instead of looking on a graph, you're plugging 1 in for x in the equation which, after solving the equation, will equal 7.

basically, at x=1, the y-coordinate is 7

Answer:

575g

Step-by-step explanation:

Since we need the ans in grams first ensure that both values are in the same unit.

So convert 0.4 kg into grams by multiplying it with 1000grams.

This gives us 400g

175+400=575g

Step-by-step explanation:

Answer:

sin 2x + cos x =  2 sin x cos x + cos x = (2 sin x + 1)cos x

Step-by-step explanation:

Given the expression: sin 2x + cos x,

then we can use the formula: sin 2x = 2 sin x cos x, which gives:

sin 2x + cos x =  2 sin x cos x + cos x = (2 sin x + 1)cos x

So there you have two expressions in terms of sin x and cos x, as requested. :D

The mean of the data set is 42.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

Given:

20, 32, 34, 36, 40, 42, 44, 48, 55, 65

Mean = 20+32+ 34+ 36+ 40+ 42+ 44+ 48+ 55+ 65/10

Mean = 416 / 10

Mean = 41.6

Mean = 42

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Answer:

Step-by-step explanation:

The total amount of interest earned is the sum of the amounts of interest earned by each of the accounts.

Let x represent the amount invested at 8%. Then 2x is the amount invested at the lower rate of 6%. The interest earned by each investment is the product of the amount and the interest rate. The total earned is ...

  0.08x +0.06(2x) = 2920

We can simplify this equation, then divide by the x-coefficient.

  0.20x = 2920 . . . . . . . . . . . simplify

  x = 14600 . . . . . . . . . . divide by 0.2

  2x = 29200 . . . . . . . . multiply by 2

Jolene invested $29,200 at 6%, and $14,600 at 8%.

Answer:

The value of x =2 and y= 2, because they are congruent and 2+2=4

Answer:

The value of x =2 and y= 2, because they are congruent and 2+2=4

Step-by-step explanation:

hope this helps :)

Answer:

- 3/5

Step-by-step explanation:

(y2-y1) / (x2-x1)

(6,0) & (1,3)

(3-0) / (1-6)

3/-5

- 3/5

Answer:

33 %

Step-by-step explanation:

3200 - 2400 = 800

800 / 2400 x 100

1 /3 x 100

100/ 3

33 %

Answer:

The answer is A)

Step-by-step explanation:

There is a domain restriction meaning the denominator should not equal to zero. If you substitute 6 and -1 into x for A) :

(1-1)(-6+6)=0

The Denominator can't be zero

Hope it helps!