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Explanation:(x)(x)=x^2 and(x)(x)(x)=x^3

Using the z-distribution, it is found that since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.

At the null hypothesis, it is tested if there is not enough evidence that the proportion is below 85%, that is:

[tex]H_0: p \geq 0.85[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the proportion is below 85%, that is:

[tex]H_0: p < 0.85[/tex]

The test statistic is given by:

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

In which:

For this problem, the parameters are:

[tex]p = 0.85, n = 250, \overline{p} = \frac{203}{250} = 0.812[/tex]

Hence the test statistic is:

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

[tex]z = \frac{0.812 - 0.85}{\sqrt{\frac{0.85(0.15)}{250}}}[/tex]

z = -1.68

Using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -1.68, the p-value is of 0.0465.

Since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.

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Based on the distance of the pitcher's mound from the home plate, the path of the ball, and the height the ball was hit, the distance the outfielder threw the ball is C. 183.0 ft.

Based on the shape of a mound, the law of cosines can be used.

The distance the ball was thrown by the outfielder can therefore be d.

Distance is:

d² = 60.5² + 226² - (2 x 60.5 x 226 x Cos(39))

d ²= 33,484.42ft

Then find the square root:

d = √33,484.42

= 182.9874

= 183 ft

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Complete the square.

[tex]z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0[/tex]

[tex]\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4[/tex]

Use de Moivre's theorem to compute the square roots of the right side.

[tex]w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)[/tex]

[tex]\implies w^{1/2} = \pm \dfrac{\sqrt7}2 \exp\left(\dfrac i2 \tan^{-1}(4\sqrt3)\right) = \pm \dfrac{2+\sqrt3\,i}2[/tex]

Now, taking square roots on both sides, we have

[tex]z^2 + \dfrac12 = \pm w^{1/2}[/tex]

[tex]z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2[/tex]

Use de Moivre's theorem again to take square roots on both sides.

[tex]w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)[/tex]

[tex]\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}[/tex]

[tex]w_2 = -\dfrac{3+\sqrt3\,i}2 = \sqrt3 \, \exp\left(-i \dfrac{5\pi}6\right)[/tex]

[tex]\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}[/tex]

Answer:

The equation of the line passing through point __0___ and point __1___ plotted below in point-slope form is y+3 =-(x-4

Thee diagonal of the rectangle is 13.86 cm long.

We are given that;

Width of a rectangle is 9 less than twice its length. Thus, if length is L, then;

W = 2L - 9

Area formula for a rectangle is;

A = Length * Width

We are given area of rectangle = 96 cm²

Thus;

L(2L - 9) = 96

2L² - 9L = 96

2L² - 9L - 96 = 0

Using online quadratic equation calculator gives;

L = 9.53 cm

Thus;

W = 2(9.53) - 9

W = 19.06 - 9

W = 10.06 cm

The diagonal of the triangle will be gotten from Pythagoras theorem;

D = √(9.53² + 10.06²)

D = √192.0245

D = 13.86 cm

Thus, we conclude that the diagonal of the rectangle is 13.86 cm long.

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Answer:

31

Step-by-step explanation:

The numbers in the sequence increase by (n+1)^2. So the sequence is (1, 1+1^2 (which is 2), 2+2^2 , 6+3^2, 15+4^2, 31+5^2, 56+6^2) and the fifth term of that sequence is 15+4^2, which is 31

The unknown number(x) in the series is 31.

The given series 1, 2, 6, 15, x, 56, 92.

We need to find the value of x.

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, and mathematical analysis.

The numbers in the series increase by (n+1)².

So the sequence is 1, 1+1² (which is 2), 2+2², 6+3², 15+4², 31+5², 56+6² and the fifth term of that sequence is x=15+4²=31.

Therefore, the unknown number(x) in the series is 31.

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Answer:

18.8 inches

Step-by-step explanation:

The circumference is [tex]\displaystyle{C = 2\pi r}[/tex]. The diameter is two times of radius which can be expressed as [tex]\displaystyle{d = 2r}[/tex].

We can rewrite the equation of circumference as [tex]\displaystyle{C = \pi d}[/tex]. Thus, substitute d = 6 in:

[tex]\displaystyle{C = 6\pi}\\\\\displaystyle{C = 18.849}[/tex]

Rounding to the nearest tenth, we will get:

[tex]\displaystyle{C = 18.8 \ \sf \ inches}[/tex]

Hence, the circumference is 18.8 inches.

Answer:

A

Step-by-step explanation:

given the points

(0, 0 ) , (2, 4 ) , (4, 8 )

note that the y- coordinate is twice the value of the x- coordinate , so

y = 2x

Answer:

Rhoda and Ming are both correct, but Ming's prediction is closer because the result is accurate to two decimal places.

Step-by-step explanation:

Answer:

Step-by-step explanation:

parallel lines are the same so they dont touch u-u

perpendicular lines do touch eachother and intersect

The required two differences between constructing parallel lines and constructing perpendicular lines are,
1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.

Parallel lines are defined as the pair of lines in which points on both the lines are equidistant from each other, and the line never intersects each other.

The differences between constructing parallel lines and constructing perpendicular lines are as follows.

1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.

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The value of k such that the graph of f and the graph of g only intersect one is equal to 2.

The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

Herein we have a system formed by two nonlinear equations, a quadratic equation and a cubic equation. Given the constraint that both function must only intersect once, we have the following expression:

f(x) - x² - k · x = 4       (1)

g(x) - x² - k · x = x³ + 2 · k        (2)

x³ + 2 · k = 4

x³ + 2 · (k - 2) = 0

If f and g must intersect once, then the roots must of the form:

(x - r)³ = x³ + 2 · (k - 2)

x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)

Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:

2 · (k - 2) = 0

k - 2 = 0

k = 2

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

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Step-by-step explanation:

answer=18^2/3

according to the congruent triangles are present there.

so divide corresponding sides

The feasible reason for inequality y>2 is attached.

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Answer:

below

Step-by-step explanation:

1) 4 < 7

28 < 49

168 < 294

1680 < 2940

2) 11 > -2

16 > 3

19 > 6

15 > 2

3) -4 < -2

-10 < -8

-18 < -16

-20 < -18

4) -8 < 8

2 > -2

-1 < 1

5) When you multiply by a negative number, the inequality sign flips.

Answer:

SAS and SSA

Kindly award branliest

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Congruency refers to the criteria of making two identical shapes that can hide each other properly when overlapped.

The criterias that guarantee congruence are :

[tex] \qquad \large \sf {Conclusion} : [/tex]

The correlation coefficient between U and V is -0.5587 and it illustrates to at there's a negative relationship between U and V.

The data shows that:

E(x) = 1

E(y) = 2

E(z) = 3

Var(X) = 2² = 4

Var(Y) = 4² = 16

Var(Z) = 5² = 25.

Cov(U, V) = 16

Var(U) = Var(Z - Y)

= 25 - 0 + 16

= 41

The correlation coefficient will be:

= -16/✓(20 × 41)

= -0.5587

The correlation coefficient between U and V is -0.5587 and it illustrates to at there's a negative relationship between U and V.

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Answer:

B

Step-by-step explanation:

Every (x,y) pair is equal to each other, thus making them proportional :)

Answer: W

Step-by-step explanation: I remember learning this in school> you can tell it’s a function because no numbers repeat themselves etc .

Answer:

x = -9

Step-by-step explanation:

12 + 2x + 24 = 27 + x

(12 + 24) + 2x = 27 + x

36 + 2x = 27 + x

subtract 27 from both sides

36-27 + 2x = 27-27 + x

9 + 2x = x

subtract x from both sides

9 + x = 0

subtract 9 from both sides

x = -9

(the steps could've been faster but that shows the most work)

check:

12 + 2(-9) + 24 = 27 + (-9)

36 - 18 = 18

18 = 18

True!

so -9 is correct

Answer:

Step-by-step explanation:

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

In the case above, the value of the overhead rate for the second quarter is $17,640.

Note that:

In the case above, for one to be able to calculate the predetermined overhead rate, a person need to divide the value of the  estimated overhead costs which is $52,500 by that of the estimated direct labor hours .

Predetermined overhead rate=Estimated overhead costs/ estimated direct labor hours

Predetermined overhead rate=$52,500/  12,500

Predetermined overhead rate=$4.20/DLH overhead rate

Hence:  $52,500/ 12,500 =   $4.20/DLH overhead rate.

Since the Overhead that was applied at standard hours was said to be allowed, then:

= $4.2 x 2,400 x 1.75

= $17,640.

Therefore, In the case above, the value of the overhead rate for the second quarter is $17,640.

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Answer:

6 gallons

Step-by-step explanation:

the total area to be painted :

= The total surface area - area of the floor

= area of the walls + area of the ceiling

area of the walls :

= [perimeter of the room] ×height

= [2 × (30+20)] × 12

= 1 200

area of the ceiling :

= length × width

= 30 × 20

= 600

the total area to be painted :

= 1200 + 600

= 1800

The number of gallon of paint needed to cover the room :

= 1800 ÷ 300

= 6

Answer:

3rd grade

Step-by-step explanation:

Given that the values are different types (fractions, decimals, and percentages), it would be helpful to convert them to the same type of value.

Converting everything to percentages seems more convenient.

Since 61.24% is already a percentage, we simply have to convert 0.52, 25/36, and 0.5274444 (I wrote 0.5274 like this since the 4 is a repeating value).

To convert 0.52, we simply multiply by 100:

0.52 * 100 = 52%

For 25/36, we need to know its decimal form and multiply by 100 to find the percentage:

25 / 36 = 0.6944 * 100 = 69.44%

For 0.5274444, we also multiply by 100:

0.5274444 * 100 = 52.74444

Thus, we have 52% (2nd grade), 69.44% (3rd grade), 61.24% (4th grade), and 52.74444% (5th grade).

3rd grade has the highest portion of students

0.1 or 10%

The numbers between 1 and 50 that end in 6 are as follows:

6, 16, 26, 36, 46

There are therefore 5 numbers between 1 and 50 that end in 6.

This means there are 5 out of 50, or 5/50.

5/50 is 0.1 as a decimal, or 10% in percentage form.

The conclusion of the Hypothesis Conclusion is; that there is sufficient evidence to support the claim that the fund has moderate risk.

We are given;

Sample size; n = 36

Population standard deviation; σ₀ = 10

Sample standard deviation; s = 4.95

Significance level; α = 0.05

Claim: Standard deviation less than 10

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis needs to contain an equality and the value mentioned in the claim. If the claim is the null hypothesis, then the alternative hypothesis states the opposite of each other. Thus;

Null Hypothesis; H₀: σ = 10

Alternative Hypothesis; H₁: σ < 10

Compute the value of the test statistic:

χ2 = [(n - 1)/(σ²)] * s²

χ2 = [(36 - 1)/(10²)] * 4.95²

χ2 = 8.576

The critical value of the left-tailed test is given in the row with df = n - 1 = 36 - 1 = 35 and in the column with 1 − α = 0.95 of the chi-square distribution table online, we have;

χ2_{1 - α} = 21.77

The rejection region then contains all values smaller than 21.77

If the test statistic is in the rejection region, then reject the null hypothesis:

8.576 < 13.848

Thus, we will reject H₀ and conclude that there is sufficient evidence to support the claim that the fund has moderate risk.

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The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.

Given that BD is diameter of the circle and angle BAC is 100°.

We are required to find the central angle, major arc, minor arc, m BEC, BC.

Angle is basically finding out the intensity of inclination of something on the surface.

In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.

Major arc of a circle is that arc whose length is larger than all other arcs in the circle.

In our circle the major arc is arc BED.

Minor arc of a circle is that arc whose length is smaller.

In our circle the minor arc is arc ADC.

We know that arc's length is 2πr(Θ/360)

In this way BC=2π*(BD/2)*100/360

=(5π*BD)/18

We cannot find angle BEC.

Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.

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It should be noted that organization was important in the thought process and calculation for an accurate solution.

It should be noted that problem-solving enables us to identify and exploit opportunities in the environment and exert control over the future.

In this case, problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations

Also, good problem solving activities provide an entry point that allows all students to be working on the same problem.

In this case, the open-ended nature of problem solving allows high achieving students to extend the ideas involved to challenge their greater knowledge and understanding and problem solving develops mathematical power.

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Answer:

All Real Numbers

Step-by-step explanation:

The domain is all the x values for a function. As this function is not restricted in any way, the domain is all real numbers. You can put any number in for x and plot it on the graph.