Using horizontal strip, determine the area of the region bounded by curves x² + 4y - 8 = 0 and x =
2y​

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

Assuming that conditions have been met for the interval, we use the formula [tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex] where [tex]\bar{x}[/tex] represents the sample mean, [tex]t[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] is the sample size.

The critical value of [tex]t[/tex] for an 80% confidence level with degrees of freedom [tex]df=n-1=25-1=24[/tex] is equivalent to [tex]t=1.317836[/tex]

Thus, we can compute the confidence interval:

[tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}\\\\CI=32.64\pm1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\\\\CI\approx\{30.17,35.11\}[/tex]

Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.

Part B

The margin of error is [tex]\displaystyle t\frac{s}{\sqrt{n}}=1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\approx2.47[/tex]

hope you can understand

Answer:

x + 7 = 15

Step-by-step explanation:

I hope the answer above was correct :)

Answer:

x + 7 = 15

Step-by-step explanation:

7 more is adding 7 to "a number" which is x. The sum is 15 so it shouldnt be that hard to put it all together

Answer:

[tex]g(x)=\log_3(x+4)[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:

  [tex]f(x)=\log_3x[/tex]

From inspection of the graph:

If there was a vertical translation, the end behaviors of both g(x) and f(x) would be the same in that the both functions would be increasing from -∞ in quadrant IV.

As the x-intercepts of both functions is different, and g(x) increases from -∞ in quadrant III, this indicates that there has been a horizontal translation of 4 units to the left.

Therefore:

[tex]g(x)=f(x+4)=\log_3(x+4)[/tex]

Further Proof

Logs of zero or negative numbers are undefined.

From inspection of the graph, [tex]x=-3[/tex] is part of the domain of g(x).

Therefore, input this value of x into the answer options:

 [tex]g(-3)=\log_3(-3)-4\implies[/tex] undefined

 [tex]g(-3)=\log_3(-3)+4\implies[/tex] undefined

 [tex]g(-3)=\log_3(-3-4)=\log_3(-7)=\implies[/tex] undefined

 [tex]g(-3)=\log_3(-3+4)=\log_3(1)=0[/tex]

Hence proving that [tex]g(x)=\log_3(x+4)[/tex]

The equation that represents g(x) is:  [tex]g(x) = log_3(x + 4)[/tex]

The correct answer is: the fourth option:

[tex]g(x) = log_3(x + 4)[/tex].

Here, we have to find the equation that represents g(x) using f(x), we need to consider how the graph of g(x) is related to the graph of f(x).

The graph of f(x) = log base 3 of x starts from negative infinity in quadrant four, passes through (0, 1), and increases to positive infinity.

The graph of g(x) is increasing from negative infinity in quadrant two, passes through (0, -3), and increases to positive infinity.

So, we can see that the graph of g(x) is the graph of f(x) shifted 4 units to the left along the x-axis.

Therefore, the equation that represents g(x) is:

[tex]g(x) = log_3(x + 4)[/tex]

The correct answer is: the fourth option:

[tex]g(x) = log_3(x + 4)[/tex].

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Answer:

21.25 m/s

Explanation:

AVERAGE SPEED=

= \frac{s1 t1+ s2t2 + s3t3}{t1 + t2 + t3}=

t1+t2+t3

s1t1+s2t2+s3t3

= \frac{20 \times 10 + 30 \times 5 + 15 \times 5}{10 + 5 + 5}=

10+5+5

20×10+30×5+15×5

= \frac{200 + 150 + 75}{20}=

20

200+150+75

= \frac{425}{20}=

20

425

= 21.25 ms=21.25ms

The table that includes that information correctly when the problem says an object's displacement is 88.8 m is table B.

It should be noted that a displacement simply means the vector quantity that illustrates how far a particular place is.

In this case, the table that includes that information correctly when the problem says an object's displacement is 88.8 m is table B.

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Answer:A  dude if you already know it say it to make it easier for people don't be lazy

Step-by-step explanation:

Answer:

Hi,

Answer B

Step-by-step explanation:

after 1.484 s the ball hit the ground à 22.019 feet

yes the ball will be at a height of 2.93506334 feet when time is 1.348 s and height is 20 feet

no the max height happens at 11.0 has no thing to do with hitting the grat 2.937 s the ball is at -68.2754 feet

ound

Answer:

8x

Step-by-step explanation:

(3x+1)+(3x-1), the 1's cross out, so it is 3x+3x=6x. 6x+2x=8x.

Answer:

8x

Step-by-step explanation:

got it right!!!

Answer:

In terms of Pi: [tex]3\pi + 6[/tex] km

Exact value (rounded): 15.42477 km

Approximated (3.14): 15.42 km

Step-by-step explanation:

Hello!

A semicircle's perimeter can be found using the formula: [tex]P = \pi r + 2r[/tex]

We can plug in the values to solve for the perimeter.

In terms of Pi, it is [tex]3\pi + 6[/tex],

Exact value of Pi, it is 15.42477

Approximation of Pi (3.14), it is = 15.42

Answer:

The power output is 6 W. The resistance is 6 Ω.

Step-by-step explanation:

Power output= 6V * 1 A= 6W

Resistance= 6V/1A= 6 Ω

Answer:

Yes

Step-by-step explanation:

vdhdhdhdhdhshsbsbsbsjshshsjajjssjsusususu

The equation of the function g(x) will be g(x) = (1/2) x². Then the correct option is B.

The complete question is attached below.

Functions are found all across mathematics and are required for the creation of complex relationships.

The function f(x) is given below.

f(x) = x²

Then the function g(x) will be

g(x) = a · x²

Then the value of will be

From the graph, at x = 2, g(x) will be 2.

Then we have

2 = a · 2²

a = 1/2

Then the equation of the function g(x) will be g(x) = (1/2) x².

Then the correct option is B.

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Answer:

Hi,

Step-by-step explanation:

I suppose you want an integer solution.

Let's say

a the number of gallons of 35% alcohol

b the number of gallons of 50% alcohol

[tex]\dfrac{35}{100}*a+\dfrac{50}{100}*b=\dfrac{40}{100}*6\\\\35*a+50*b=240\\\\7a+10b=48\\\\b=\dfrac{48-7a}{10}\\\\a=4+10*n\\\\b=\dfrac{48-7*(4+10*n)}{10}=2-7*n\\\\As\ b\ must\ be\ a\ positive\ number \ n=0\\\\so\ b=2\ and\ a= 4[/tex]

Answer:

[tex]\frac{2}{3}x^{12}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{6x^{18}}{9x^6}=\frac{6}{9}*\frac{x^{18}}{x^6}=\frac{2}{3}*x^{18-6}=\frac{2}{3}x^{12}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x^{18}}{9x^6}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2}{3}x^{18-6}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2}{3}x^{12}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2x^{12}}{3}[/tex]

Answer

Let x be that number We know x + 5 = 12 ( the number plus five equals to 12)=> x = 5-12 = 7 so, that number is 7.

explanation:

Hope this helps:)

:3

have a good day or a beautiful day:3

Answer:

he will buy 4 tickets

Step-by-step explanation:

firts u have to mutilpy 7.50 by a number and start at 1 and go up till u get 30

hope this helps:)!!

Answer:

No (2, 11) is not a solution.

Step-by-step explanation:

y = 3x - 2

Plug in the points:

11 = 3(2) - 2

Solve:

11 = 6 - 2

11 = 4

11 does not equal 4.

Hope this helps.

Answer:

(2,11) is not a solution

Step-by-step explanation:

Substitute the value of x and y in the equation.

  y = 3x - 2

Substitute(2,11)

   11= 3*2 -2

        = 6 - 2

    11 ≠ 4

(2,11) is not an solution of the equation

Answer:

10.63

Step-by-step explanation:

To find the Hypotenuse we need to use Pythagorean Thereom. So plugging in the formula the square root of A squared plus B squared you get 10.63

Answer:

Step-by-step explanation:

To solve the triangle means to find ALL unknown elements of Δ ( sides and angles )

JH² = 8² + 7² = 113

JH = √113 ≈ 10.63 m

m∠H = β

[tex]\frac{8}{7}[/tex] = tan β ; β = arctan [tex]\frac{8}{7}[/tex] = [tex]tan^{-1}[/tex] [tex]\frac{8}{7}[/tex] ≈ 48.814°

m∠H ≈ 49 °

m∠J = 90° - 49° = 41 °

Answer:

2ax + b + C

where C is a constant.

Answer:

20 or 40 or 50

(there are many others)

Step-by-step explanation:

A counterexample is an example that shows the statement is not true. The statement in this question is that if a number is a multiple of 10 (10, 20, 30, 40, 50, 60...) then it is a multiple of 30. Some numbers are, like 60 and 90, but not all numbers. So for example (counterexample) 20 is a multiple of 10 but NOT a multiple of 30.

40 is a multiple of 10, but NOT a multople of 30.

50 is a multiple of 10, but NOT a multiple of 30.

Answer:

6

Step-by-step explanation:

Answer: D

Step-by-step explanation:

An example of exponential function is  p(x) = 500(1.02)x Option D

An exponential function is a mathematical function of the form f(x) = [tex]a * b^x[/tex], where 'a' and 'b' are constants, and 'x' is the variable. The function p(x) = [tex]500(1.02)^x[/tex] is in this form

Where 'a' is 500, 'b' is 1.02, and 'x' is the variable.

The variable 'x' is an exponent, which makes it an exponential function. Option D

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Answer:

y₁ - y₂ = (-7/9)(x₁ - x₂)

Step-by-step explanation:

The general structure for an equation in point-slope form is:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope and the "x" and "y" values come from each point. To find "m", plug the values of each point into the equation.

Point 1: (4, -3)                   Point 2: (-5,4)

y₁ - y₂ = m(x₁ - x₂)                                  <---- Original equation

-3 - 4 = m(4 - (-5))                                 <---- Plug values in for "x" and "y"

-7 = m(4 - (-5))                                      <---- Simplify left side

-7 = m(9)                                               <---- Simplify within parentheses

-7/9 = m                                              <---- Divide both sides by 9

I don't exactly understand what "fully simplified point-slope form" means because if all of the variables are plugged in, you wouldn't be left with an equation. It may just be asking for the slope, which in this case would make the equation look like this:

y₁ - y₂ = (-7/9)(x₁ - x₂)  

It may want you to find the equation in slope-intercept form (y = mx + b), and you would have to find "b". Sorry I don't quite understand what exactly you are looking for.

Answer:

38%

Step-by-step explanation:

Total: 93

Find percentage

Rain: 24

Snow: 11

24 + 11 = 35

Find what percentage of 90 35 is.

35 of 90 can be written as:

35

----

90

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

35           100

----   ×         ----

90            100

= ( 35 * 100/90) * 1/100 = 38.89/100

Therefore, the answer is 38.89%

Answer:

w = 5

Step-by-step explanation:

24w = (14)10

2w + 4 = 10 + 4

2w = 10

w = 5

Answer:

its it a

Step-by-step explanation:

Step-by-step explanation:

13 pounds of sugar for $6.

for a single pound of sugar we need to divide everything by 13 to keep the same ratio (relationship).

1 pound cost then 6/13 = 0.461538462... ≈ $0.46

Reason:

See the screenshot below. I used GeoGebra to plot the points.

The sub group of points D, E, F form a bowl shaped region. Imagine a small parabola passing through these points. Point E is either the local min or very close to it. This is because point E is at the bottom of the bowl shape.

Answer:

(3, 0)

Step-by-step explanation:

Given:

Rotation rule for -90°:  (x, y) → (y, -x)

As the center of rotation is not the origin, we cannot simply apply the above rule.

To rotate an image around a point other than the origin:

1.  Subtract each point of the image from the point of rotation:

⇒ Point of rotation - point of image

⇒ (-2, 6) - P = (-2, 6) - (-8, 1)

                    = (6, 5)

2. Rotate this about the origin by applying the rotation rule:

⇒ (x, y) → (y, -x)

⇒ (6, 5) → (5, -6)

Add the point of rotation to each rotated point of the image:

⇒ (5, -6) + (-2, 6) = (3, 0)

Therefore, the location of the image of P (-8, 1) after a counterclockwise rotation of 90° about (-2, 6) is (3, 0).