Round 6254 correct to 1 signature figure

The interval estimate for the true population proportion is 45.25% to 64.75% and we can conclude that the majority of the community supports water rationing

The given parameters are:

The error margin is calculated using:

[tex]E = z * \sqrt{\frac{p* (1 - p)}{n}}[/tex]

Where z is the critical value.

At 95% confidence level, the critical value is:

z = 1.96

So, we have:

[tex]E = 1.96 * \sqrt{\frac{0.55 * (1 - 0.55)}{100}}[/tex]

Evaluate

[tex]E = 1.96 * \sqrt{0.002475}[/tex]

Evaluate

E = 0.0975

Hence, the error margin is 0.0975

This is calculated using:

I = p ± E

So, we have:

I = 0.55 ± 0.0975

Expand

I = (0.55 - 0.0975, 0.55 + 0.0975)

Evaluate

I = (0.4525, 0.6475)

Express as percentage

I = (45.25%, 64.75%)

Hence, the interval estimate for the true population proportion is 45.25% to 64.75%

From the simulation,

The values are approximately the interval estimates.

i.e.

45.25% ≈ 45% and 64.75% ≈ 65%

Hence, we can conclude that the majority of the community supports water rationing

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It is a pythagorean triple.

The range of f as shown in the graph is -6 ≤ f(x) ≤ 5. The correct option is A. -6 ≤ f(x) ≤ 5

From the question, we are to determine the range of f.

The range of a function is the set of its possible output values.

The graph of the function, f, is shown in the diagram.

From the graph,

The minimum value of f on the x-axis is -6. That is, f(x) ≥ -6

and

The maximum value of f on the x-axis is 5. That is, f(x) ≤ 5

Combining the two expressions, we get

f(x) ≥ -6 and f(x) ≤ 5

That is,

-6 ≤ f(x) and f(x) ≤ 5

∴ -6 ≤ f(x) ≤ 5

Hence, the range of f as shown in the graph is -6 ≤ f(x) ≤ 5. The correct option is A. -6 ≤ f(x) ≤ 5

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Answer:

In 15 years the final balance will be $632.15

Step-by-step explanation:

The final balance would be $632.15 and the total compound interest would be $332.15. If you have trouble with these kind of questions in the future I suggest using a compound interest calculator that can be found online :)

Answer:

If yo translate ABC down 5 units and to the right 2 units, it coincides with GHI.

Step-by-step explanation:

You just have to follow the directions

Answer:

(Choice B) Add the equations

Step-by-step explanation:

The equations that were given are:

[tex]5x + 3y = 9 \\ 4x - 3y = 9[/tex]

If we add the equequatiothen the y variable would be eliminated:

[tex] +3y + (-3y) = 0[/tex]

If A and B are independent variables, P(A and B) =0.12. Therefore, option B is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that, p(a)=0.60 and p(b)=0.20.

If A and B are independent variables,

P(A and B) =P(P∩B)= P(A) × P(B)

Here, P(P∩B)=0.60×0.20

= 0.12

Therefore, option B is the correct answer.

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Answer:

C

Step-by-step explanation:

To find the area of the base of the prism, you would first multiply 7 1/2 and 2 1/4, which would leave you with 16.875. Next, you would divide by 2, which gives you 8.4375. Rounding up, you would have the answer C.

Answer:

50m^2

Step-by-step explanation:

cut the shape into half. Now you should have a rectangle and a right triangle. Then do 5•7=35 so 35m for the rectangle. Now do the triangle! 10-7=3 so the base is 3 so do 3•5=15m so add them together 15m+35m=50m^2

ALSO IF YOU NEED TO KNOW THE ANGLE X IS: 60*
Hope this helps! ;-)

Answer:

the correct answer is 2nd hope this will help u i have find the value of x also hope it will help

Step-by-step explanation:

[tex] {4}^{x + 3} = 64 \\ {2}^{2(x + 3)} = {2}^{6} \\ 2{ }^{2x + 6} = 2 {}^{6 } \\ 2x + 6 = 2 \\ 2x = 2 - 6 \\ x = \frac{ - 4}{2} \\ x = - 2[/tex]

Answer:

Yes

Step-by-step explanation:

Natural numbers are positive integers such as 1, 2, 3, etc., (sometimes zero as well). As such, they are indeed whole numbers, so the statement is true.

If you know BN and AN, then you can use the fact that ∆ AQB and ∆ ABN are similar. which gives the relation

BN/BQ = AN/AB = AB/AQ

Now

AN/AB = AB/AQ   ⇒   AQ = AB²/AN = 36/AN

and

BN/BQ = AN/AB   ⇒   BQ = (BN • AB)/AN =  6 • BN/AN

where AB = 6 because it's the diameter of the circle, and C(O, 3) means the circle has center O and radius 3.

Answer: 48 feet

Step-by-step explanation:

Answer:

12 feet

Step-by-step explanation:

Containers are generally in the shape of a rectangular prism.

Formula

Answer+Step-by-step explanation:

1)

[tex]x^{2}+4x+1=x^{2}+4x + (4 - 4) + 1[/tex]

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

                  [tex]=(x+2)^2-3[/tex]

then

[tex]x^{2}+4x+1=0[/tex]

[tex]\Longleftrightarrow \left( x+2\right)^{2} -3=0[/tex]

[tex]\Longleftrightarrow \left( x+2\right)^{2} =3[/tex]

2)

[tex]\left( x+2\right)^{2} =3[/tex]

⇔ |x + 2| = √3

⇔ x + 2 = √3 or x + 2 = -√3

⇔ x + 2 = ±√3

⇔ x = -2 ± √3

Answer:

The solution is in the image

Answer:

the top answear

Step-by-step explanation:

the top aka 16^15/5 it should be 16^15 not that 5

Answer:

The answer is "no" because when two numbers with the same bases are divided, their powers are subtracted.

This should have been done instead:

                                     [tex]\frac{6^{15} }{6^5}[/tex] = 6¹⁵ ⁻ ⁵

                                           = 6¹⁰

Hope this helps!

Find the volume of a sphere with a diameter of 16 cm using the formula Volume = [tex]\dfrac{4}{3}[/tex] × π × r³.

In this question we are provided with the diameter of a sphere. We are asked to calculate the volume of the sphere using the radius.

First we will find the radius of the sphere

We know,

[tex] ✭ \: \small\boxed{ \rm{ Radius = \dfrac{Diameter}{2}}}[/tex]

Substituting the values we get

[tex] \small\sf{ Radius = \dfrac{ \cancel{16} \: \: 8}{ \cancel{2}}}[/tex]

[tex] \star \: \small\rm{ Radius = 8 \: cm}[/tex]

Now we will calculate the volume of the sphere

We know,

[tex] ✭ \: \small \boxed{{\rm{ Volume_{(sphere)} = \dfrac{4}{3} × π × r³}}}[/tex]

Where,

Substituting the values we get

[tex] \small\rm{ Volume_{(sphere)} = \dfrac{4}{3} × 3.14 × 8³}[/tex]

[tex]\small\rm{ Volume_{(sphere)} = \dfrac{ \cancel{4}}{3} × 3.14 × 8 \times 8 \times \cancel{ 8 } \: \: 2}[/tex]

[tex] \small\rm {V olume_{(sphere)} = \dfrac{3.14 × 64}{3}}[/tex]

[tex] \small\rm{ Volume_{(sphere)} = \dfrac{200.96}{3} =66.98 \: {cm}^{3} }[/tex]

Hence the volume of the sphere is 66.98 cm³.

[tex] \underline{\rule{71mm}{4pt}}[/tex]

Answer:

6.6 ft

Step-by-step explanation:

The area of a triangle is given by the formula: [tex]A=\frac{1}{2}bh[/tex].

In this case, the base b equals the height h.

[tex]\therefore A=\frac{1}{2}h^2 \rightarrow h=\sqrt{2A}[/tex]

Given: A = 22 ft²

[tex]\therefore h=\sqrt{2A} = \sqrt{2(22 \text{ ft}^2)} = \sqrt{44}\text{ ft} \approx 6.6 \text{ ft}[/tex]

Answer:

Step-by-step explanation:

The coordinates of the rotated image are Z' = (4,-1), Y' = (2,0), X' = (0,4) and W' = (4,3)

The points are given as:

Z ( -1,-4) , Y (0,-2), X (4,0), and W (3,-4)

The rule of rotation around the origin counterclockwise by 90 degrees is

(x,y) => (-y,x)

Using the above rule, we have:

Z' = (4,-1)

Y' = (2,0)

X' = (0,4)

W' = (4,3)

Hence, the coordinates of the rotated image are Z' = (4,-1), Y' = (2,0), X' = (0,4) and W' = (4,3)

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Answer: D

Step-by-step explanation:

The correct answer is (D): Lower high school GPAs correlate to lower college GPAs, with one exception to a low high school GPA and high college GPA.

Grade point average, or GPA, is measured on a scale of 0 to 4. A grade of four is an A, while a grade of zero equals an F.

Given:

The scatter plot illustrates the relationship between high school and college GPAs for a sample of students.

The scatter plot is given in the attached image.

Highest college GPAs are  4, 3.5, 2 and so on.

And their respective high school GPAs are 2, 4, 3.25 and so on.

That means, students with higher high school GPAs have lower college GPAs.

Let students with lower high school GPAs repeat their performance and get low college GPAs.

But here a student has GPA 2 in high school and 4 GPA in college.

That gives us contradiction.

There is one exception, with college GPA as 4 and HS GPA as 2.

All other points show that a lower college GPA could result in lower HS GPA.

Therefore, the correct answer is option D.

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The solution to the system of equation is (4.75, -11)

3.2x + 0.5y = 4.2

-1.6x -0.5y = 3.4

3.2x + 0.5y = 4.2

-1.6x -0.5y = 3.4

add equation(i) to equation(ii)

Therefore,

1.6x = 7.6

divide both sides by 1.6

x = 7.6 / 1.6

x = 4.75

Therefore,

3.2(4.75) + 0.5y = 4.2

0.5y = 4.2 - 15.2

0.5y = -11

y = - 11 / 0.5

y = - 22

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Answer:

The solution is x=4.75  and   y = -22

Step-by-step explanation:

To find the solution to the system of equations, we will follow the steps below:

3.2x + 0.5y = 4.2 --------------------------------------------------------------------------(1)

-1.6x -0.5y = 3.4 ----------------------------------------------------------------------------(2)

add equation (1) and equation (2)

1.6x =7.6

Divide both-side of the equation by 1.6 to get the value of x

1.6x /1.6 =7.6/1.6

x =4.75

substitute x = 4.75 into equation (1) and solve for y

3.2(4.75) + 0.5y = 4.2

15.2 + 0.5y = 4.2

subtract 15.2 from both-side of the equation

15.2 - 15.2 + 0.5y = 4.2-15.2

0.5y = -11

Divide both-side of the equation by 0.5

0.5y/0.5 = -11/0.5

y = -22

The solution is x=4.75  and   y = -22

Answer:

  y = 3x -4

Step-by-step explanation:

The two pairs of x and y values are used to find the slope of the line. That and one of the pairs is used to find the y-intercept. These values are put into the slope-intercept equation to give the equation of the line through the two points.

__

Each (x, y) pair represents a point on a graph. The slope-intercept equation for a line relates all the (x, y) pairs that lie on the line. That equation is ...

  y = mx +b . . . . . . where m is the slope, and b is the y-intercept

The slope is the "steepness" of the line. It is positive when the line goes up to the right, and negative when the line goes down to the right. It is 0 for a horizontal line.

The slope is found from (x, y) pairs using the formula ...

  m = (y2 -y1)/(x2 -x1) . . . . . . where (x1, y1) and (x2, y2) refer to different pairs

  m = (8 -(-1))/(4 -1) = 9/3 = 3 . . . . using the (x, y) values from the table

The y-intercept (b) is the y-value where the line crosses the y-axis. It can be found by rearranging the slope-intercept equation shown above:

  b = y - mx . . . . . . . for a line with slope m and a point (x, y) on the line

Using the first point listed in the table with the value of m we just found, we see that b is ...

  b = -1 - 3(1) = -4 . . . . . . for (x, y) = (1, -1) and m = 3

Now that we have found m=3 and b=-4 for the points in the table, we can put these values in the slope-intercept equation:

  y = mx +b

  y = 3x -4 . . . . . equation of the relationship in the table

Answer:

AC and YX are corresponding sides.

AB and YZ are corresponding sides.

BC and ZX are corresponding sides.

Step-by-step explanation:

Hope this helps and have a nice day