Justifying a Claim Based on a Confidence Interval for a Population Proportion

Based on the simulation, what proportion of the 95 percent confidence intervals capture the population proportion of 0.3? Explain how you determined your answer.​

Answer:

QR = 15

Step-by-step explanation:

Opposite sides of parallelograms are congruent. This means that their lengths are the same.

Hence,

PS = 15 = QR.

Answer:

The length of side x in the given triangle is 12 m.

Step-by-step explanation:

To calculate length x in the given triangle, use the Area Sine Rule.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Area Sine Rule} \\\\$A=\dfrac{1}{2}ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides enclosing the angle. \\\end{minipage}}[/tex]

The given values are:

Substitute the given values into the formula:

[tex]\implies 42=\dfrac{1}{2} \cdot 14 \cdot x\cdot \sin30^{\circ}[/tex]

Multiply 1/2 · 14 = 7:

[tex]\implies 42=7x\sin30^{\circ}[/tex]

Divide both sides of the equation by 7:

[tex]\implies 6=x\sin30^{\circ}[/tex]

Calculate sin30°:

[tex]\implies 6=\dfrac{1}{2}x[/tex]

Multiply both sides of the equation by 2:

[tex]\implies 12=x[/tex]

Therefore, the length of side x in the given triangle is 12 m.

Answer:

D

Step-by-step explanation:

9(4x + 8) ← multiply each term in the parenthesis by the 9 outside

= 36x + 72

Yes, both tests can be reported to denote a significant difference. The T-test is used for normally distributed data, whereas the Mann-Whitney U test is used for non-normally distributed data.

Yes, both the Student's T-test and the Mann-Whitney U test can be used to denote a significant difference. The Student's T-test is used to compare the means of two normally distributed samples and determine if the difference in means is statistically significant. The Mann-Whitney U test is used to compare the means of two non-normally distributed samples and determine if the difference in means is statistically significant. Both tests are used to test the null hypothesis that the means of the two samples are the same. If the null hypothesis is rejected, it can be concluded that the difference between the means is statistically significant. Both tests provide a measure of the strength of the evidence against the null hypothesis, which can be used to determine if the difference between the means is significant.

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{(11, 16), (12, 14), (14, 14), (11, 13), (21, 12)}

This is because the the number 11, an x-value, is used twice and if an x-value is used more than once then it is not a function. A function is a relation between sets where there is only one output for each input

The missing reasons for the proof are given as follows:

1) AB/DB = CB/EB - Given

2) ∠ABC ≅ DBE - Opposite Angles

3) ΔABC ~ ΔDBE - Angle - Side - Side Postulate.

The Angle-Side-Side (ASA) Postulate states that if two angles and a side of one triangle are congruent to two angles and the corresponding side of another triangle, then the two triangles are congruent.

In other words, if two triangles have the same orientation and their corresponding angles and sides match in size, the two triangles are identical. The ASA Postulate can be used to determine the congruence of triangles and to prove theorems and solve problems in geometry and related fields.

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We can see that the triangle is given as one of the angles is 90 degrees . The triangle is a right-angle triangle, and scalene also.

A right-angled triangle is a triangle having one of its angles with measure of 90°

The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.

We can see that the triangle is given as one of the angles is 90 degrees and the other two angles are 36 and 54 degrees.

If one of the angles is 90°  then the triangle is a right-angled triangle.

Also, the length of the two sides is given as 8.66 units and 5.1.

We have already concluded that the triangle is a right-angle triangle, so all the three sides of the triangle must be different.

This implies that the triangle is scalene also.

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Answer: No.

Step-by-step explanation: Unless I read and calculated wrongly, it should be equal to 2b^4/(a^3b^2c^2-2)a^4c^2   -1/256

It  takes for the account to reach $200 is 4 years.

Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only quantity.

Given that aldonia deposits $150 into an account that pays 7.3% annual interest compounded quarterly.

[tex]A = P(1 +\frac{r}{n})^n^t[/tex]

where:

A = the total account balance after t years

P = the initial deposit $150

r = the annual interest rate =0.073

n = the number of compounding periods per year, which is 4 (quarterly) in this case

t = the number of years the money is in the account

Now let us substitute the values

[tex]A = 150(1 + \frac{0.073}{4} )^4^t[/tex] is the equation to represent Caldonia's account balance after t years.

Now let us determine the number of  years it will take for the account to reach $200.

[tex]200 = 150(1 + \frac{0.073}{4} )^4^t[/tex]

200=150(1+0.01825)^4t

[tex]1.333=1.018^4^t[/tex]

Take log on both sides

log1.333=4tlog(1.018)

0.1248=4t 0.0077

0.1248=0.0309t

Divide both sides by 0.0309

t=4.038

Hence, it takes 4 years to reach account balance of $200

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Answer:

16, 64, 256

Step-by-step explanation:

The angle of elevation is 66.50 degrees

From the question, we have the following parameters that can be used in our computation:

Rise = 46 ft

Length = 20 ft

The angle of elevation, x is calculated as

tan(x) = 46/20

Evaluate

tan(x) = 2.3

Take the arc tan of bth sides and evaluate

x = 66.50

Hence, the angle is 66.50 degrees

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The explicit function of the sequence is a(n) = 2(5)^n-1

The definition of the function is given as

2, 10, 50, 250, 1250

The above definitions imply that we simply multiply 5 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a(1) = 2

Common ratio, r = 5

So, we have

a(n) = a * r^n-1

This givs

a(n) = 2(5)^n-1

Hence, the sequence is a(n) = 2(5)^n-1

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A x=3 hope it helps-parker have a nice day

the value of "t" will be 28 degrees for the given circle.

The following four properties and their proofs were introduced:

1: The angles at the center and at the circumference of a circle are subtended by the same arc.

2: Angles at the circumference are subtended by a diameter.

3: Angles at the circumference of a circle subtended by the same arc.

Given, a circle with an angle between two secants of 28 degrees.

From the intersecting Secant theorem of a circle:

The angle between secant = bigger arc -smaller arc)/2

In our case,

28 = (3t -t)/2

2t/2 = 28

t = 28

therefore, the value of "t" will be 28 degrees for the given data.

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The value of x is given as follows:

x = 10.

In a parallelogram, the consecutive angles are supplementary, meaning that the sum of their measures is of 180º.

The measures of the consecutive angles for the parallelogram in this problem are given as follows:

6x and 12x.

Hence the value of x is obtained as follows:

6x + 12x = 180

18x = 180

x = 180/18

x = 10.

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x=6 is the solution to the equation 18 - x - x - x = 0.

Two or more expressions with an Equal sign is called as Equation.

One way to build a subtraction equation using the indicated expression is:

18 - x - x - x = 0

Add the like terms

18 - 3x = 0

Now let us solve for x

we can isolate x on one side of the equation by subtracting 18 from both sides:

-3x = -18

Divide both sides by -3 to find the value of x:

x = 6

Therefore, a solution to the equation 18 - x - x - x = 0 is x = 6.

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Answer:

Total distance flown = 5.2 miles

Step-by-step explanation:

The path of the helicopter is that of a right triangle with the first stretch of 2 miles as one leg and the other stretch 90° left as the other leg.

The return trip direct to starting point is the hypotenuse of the right triangle

By the Pythagorean theorem if c is the hypotenuse and a, b are the two legs

c² = a² + b²

Letting a = 2mi and b= 1mi,

c² = 2² + 1²

c² = 4 + 1

c² = 5

c = √5  (only positive square root considered)

c =2.236 mi

c = 2.236 mi to the nearest tenth

Total distance = 2 + 1 + 2.236

= 5.236

= 5.2 mi to the nearest tenth

Answer:

y = -x - 1

Step-by-step explanation:

y = mx +c

y = -x + c [ m = slope]

As the line passes through (4,-5)

-5 = -4 + c [Substituting value of x and y]

c = -1 [Solving the above equation]

Total cards = 4 (6,7,8,9), If the card is not 9, the required card will be (6,7,8), Number of cards that are not 9 is 3, Probability = expected/total P( 5) = 3/4 and the probability of picking 5 is 16.67%.

What is Probability?

There are a total of 6 numbers in the grid, and only one of them is 5. Therefore, the probability of selecting 5 is:

P(5) = 1/6

To write this as a percentage, we multiply by 100:

P(5) = 1/6 * 100% = 16.67%

Therefore, the probability of picking 5 is 16.67%.

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Answer:

Step-by-step explanation:

C is chosen 12 times (7 + 5)

You have 50 total picks.

So the experimental probability is 12/50.

Answer: [tex]370.08 m^2[/tex]

Step-by-step explanation: Lets do the easy part first. We see that there is a proven square in the center of the figure with side lengths of 12. The area formula is [tex]l*w[/tex] and since its a sqaure we can just multiply a side length by itself.

[tex]12*12 = 144[/tex]

^^ Thats the area of the square.

We now have to do the more difficult part which is finding the area of the semi circles. I combined the semi circles to form 2 circles with diameter 12. Now we know that the area of a circle is [tex]\pi r^2[/tex] and that the diameter is [tex]2r[/tex] so we just divide 12 by 2 to get the radius which is 6. Now we use the area formula and multiply it by 2 because there are 2 circles.

[tex]A = 2(3.14)(6^2)[/tex]

which is

[tex]226.08[/tex]

Now add it to the area of the square to get the area of the figure.

[tex]226.08+144 = 370.08[/tex]

put units and thats it!

Answer:

[tex]x = - \frac{2}{9} [/tex]

Answer:   [tex]\text{x} = \boldsymbol{-\frac{2}{9}}[/tex]

2 goes in the green box up top

9 goes in the gray box down below.

=========================================

Work Shown:

[tex]-2(4+3\text{x}) = 3(\text{x}-2)\\\\-8-6\text{x} = 3\text{x}-6\\\\-6\text{x}-3\text{x} = -6+8\\\\-9\text{x} = 2\\\\\text{x} = \boldsymbol{-\frac{2}{9}}\\\\[/tex]

Answer:

5 mx plus b which you have to do 5 plus m to get 5m which is ur answer

In a case whereby Mr. Ahmed has 31 students in his class. There are 14 boys and 17 girls.

From the question we were told that there are 14 boys in the class wehereby there the whole class has 31 students

Then we can conclude that te  ratio of the part-to-whole relationship for boys= 14/31.

From the question, there are 17 girls in the class, then we can conclude that  the ratio of the part-to-whole relationship for girls = 17/31.

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complete question:

Mr. Ahmed has 31 students in his class. There are 14 boys and 17 girls.

The ratio

describes the part-to-whole relationship for boys.

The ratio

describes the part-to-whole relationship for girls.

The measure of angle 3 from the diagram is 115 degrees

The given figure is a line geometry. An angle is defined as the point where two lines meet.

Given that the measure of <5 is 115 degrees, the measure of <3 is calculated as shown below:

m<3 = m<5 = 115 degrees

This angles are equal since they are alternate exterior angles.

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The amount of free space inside the cylindrical container would be

92 cm³.

A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

We know, The volume of a cylinder is πr²h and the volume of a

sphere is (4/3)πr³.

Therefore, The amount of empty space that will be there is the volume the spherical balls subtracted from the volume of the cylinder which is,

= [tex][\pi{(2)^2\times10] - [(\frac{4}{3})\pi(2)^3] cm^3[/tex]

= [tex]40\pi - (32/3)\pi cm^3[/tex].

= [tex]92 cm^3[/tex].

Q. A toy company sells 3-packs of sphere-shaped bouncy balls the height of the cylindrical package is 10 cm and the radius of each ball is 2 cm, If the company ships the three bouncy balls in a cylindrical container like the one shown, how many empty space will there be in the container?

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The missing values in table should be completed as follows;

X(input)         Y(output)

10                     19

12                     23

Rule: y = 2x - 1.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (3, 5), a linear equation of this line in slope-intercept form can be calculated by using the point-slope form as follows:

y - 5 = (11 - 5)/(6 - 3)(x - 3)

y - 5 = 6/3(x - 3)

y = 2(x - 3) + 5

y = 2x - 1

When x(input) = 10, the y(output) is given by:

y = 2x - 1

y = 2(10) - 1

y = 20 - 1

y = 19.

When y(output) = 23, the x(input) is given by:

y = 2x - 1

23 = 2x - 1

2x = 24

x = 12.

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The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to any one of its sides because it serves as a measure of the inradius, or the radius of the circle inscribed within the polygon. In a regular polygon, all sides are congruent and all interior angles are equal, so the apothem is the same for all sides.

To see this, imagine drawing radii from the center of the polygon to each vertex, and then drawing the perpendicular bisector of each side. These perpendicular bisectors will all intersect at the same point, which is the center of the polygon. The apothem is the length of the line segment connecting this center point to any one of the sides of the polygon.

The apothem is useful in finding the area of a regular polygon. By using the formula for the area of a regular polygon in terms of the apothem and the number of sides, one can find the area of a regular polygon without having to find the exact shape of the polygon.

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Answer:

42x + 24

Step-by-step explanation:

6(7x + 4)

42x + 24