Ten thousand marbles were produced on a production line the first 100 marbles off the line were taken and tested for roundness does this sampling result in a simple random sample

[tex]\bf \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[cos(\alpha)+isin(\alpha)]}{r_2[cos(\beta)+isin(\beta)]}\implies \cfrac{r_1}{r_2}[cos(\alpha - \beta)+isin(\alpha - \beta)] \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \begin{cases} z1=9[cos(225^o)+i~sin(225^o)]\\\\ z2=3[cos(45^o)+i~sin(45^o)] \end{cases}\implies \cfrac{z1}{z2}\implies \cfrac{9[cos(225^o)+i~sin(225^o)]}{3[cos(45^o)+i~sin(45^o)]} \\\\\\ \cfrac{9}{3}[cos(225^o-45^o)+isin(225^o-45^o)]\implies 3[cos(180^o)+i~sin(180^o)] \\\\\\ 3[(-1)+i~(0)]\implies -3+0i[/tex]

Answer:

-1

Step-by-step explanation:

Use DeMoivre's Theorem for division of complex polar numbers.  Set it up like this:

[tex]\frac{9(cos225+sin225i)}{3(cos45+sin45i)}[/tex]

The rule is

[tex]\frac{z_{1} }{z_{2} }cis(\theta_{1}-\theta _{2} )[/tex]

Our z1 is 9 and our z2 is 3, so the division of those gives you 3.  The subtraction of the angles 225 - 45 = 180, therefore:

3 cis 180° = 3(cos 180 + sin 180 i)

The cos of 180 is -1 and the sin of 180 is 0, so 3(-1 + 0) = -3

Answer:

195 yd²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = half the product of the diagonals

one diagonal = 13 + 13 = 26, the other diagonal = 7.5 + 7.5 = 15, thus

A = 0.5 × 26 × 15 = 195 yd²

Answer:

3/40

Step-by-step explanation:

3/8 numbers less than four

1/5 chance for brown

And=Multiplication

Or=Addition

3/8×1/5=3/40

Answer:

251.047804213 miles

Step-by-step explanation:

c1 t=3.5+1     speed 40 mph

c2 t=3.5       speed  50 mph

c1 40 *4.5= 180

c2 50 *3.5= 175

a^2+ b^2= c^2

180^2+175^2=c^2

32400+30625=c^2

63025=c^2

251.047804213=c

Answer:

It is 188 miles

Step-by-step explanation:

This is correct on Odyssey :)

Answer:

  136

Step-by-step explanation:

The two scales are supplementary, so the value on the second scale is ...

  180° -44° - 136°

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{small}{large}\qquad \stackrel{ratio}{\cfrac{3}{4}}\qquad \qquad \cfrac{3}{4}=\stackrel{areas}{\cfrac{\sqrt{a}}{\sqrt{100}}}\implies \cfrac{3}{4}=\cfrac{\sqrt{a}}{10}\implies 30=4\sqrt{a} \\\\\\ \cfrac{30}{4}=\sqrt{a}\implies \left( \cfrac{30}{4} \right)^2=a\implies \cfrac{900}{16}=a\implies \cfrac{225}{4}=a[/tex]

The area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Let's suppose the area of the smaller figure is x

Area of larger figure = 100 square units

The ratio of the areas:

= x/100

We also have:

Two similar figures have a side ratio of 3:4

= 3/4

Square it we will get ratio of the area

= 9/16

x/100  =  9/16

x = 900/16  = 225/4 or 56.25 square units

Thus, the area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.

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Answer:  The correct option is (A) [tex]5x^2-2x+4.[/tex]

Step-by-step explanation:  We are given to select the polynomial that represents the following difference :

[tex]D=(8x^2+9)-(3x^2+2x+5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the required difference, we need to subtract the coefficients of the same powers of the unknown variable x.

From (i), we get

[tex]D\\\\=(8x^2+9)-(3x^2+2x+5)\\\\=8x^2+9-3x^2-2x-5\\\\=(8-3)x^2-2x+(9-5)\\\\=5x^2-2x+4.[/tex]

Thus, the required difference is [tex]5x^2-2x+4.[/tex]

Option (A) is CORRECT.

Answer:

[tex]\frac{63}{55}[/tex]

Step-by-step explanation:

Evaluate by substituting x = - 7 into f(x) and value obtained into g(x)

f(- 7) = (- 7)² + 6 = 49 + 6 = 55

g(55) = [tex]\frac{55+8}{55}[/tex] = [tex]\frac{63}{55}[/tex]

Part A:

You may choose the two lines connecting the origin and points A and B, and choose the portion of the space between them.

The line between the origin and A is

[tex]y = 3x[/tex]

We want everything below this line (line included), so the first inequality is

[tex]y \leq 3x[/tex]

The line between the origin and B is

[tex]y = \dfrac{1}{3}x[/tex]

We want everything above this line (line included), so the second inequality is

[tex]y \geq \dfrac{1}{3}x[/tex]

Create a system with these two inequalities and you'll have an area including only points A and B

Part B:

To verify the solutions, we can plug the coordinates of A and B in this system and check that we get something true: the coordinates of point A are (1,3), while the coordinates of point B are (3,1). The system becomes:

[tex]A:\begin{cases}3 \leq 3\cdot 1\\3 \geq \frac{1}{3}\cdot 1\end{cases},\quad B:\begin{cases}1 \leq 3\cdot 3\\1 \geq \frac{1}{3}\cdot 3\end{cases}[/tex]

Which means

[tex]A:\begin{cases}3 \leq 3\\3 \geq \frac{1}{3}\end{cases},\quad B:\begin{cases}1 \leq 9\\1 \geq 1\end{cases}[/tex]

And these are all true. So, the system is satisfied, which means that the points belong to the shaded area.

Part C

If you draw the line, you'll see that the only points that lay below the line are B and C. In fact, if we plug the coordinates we have

[tex]B:\ 1 <3\cdot 3 - 6 \iff 1 < 3,\quad C:\ -3 < 3\cdot 3 - 6 \iff -3 < 3[/tex]

And this are both true. You can check the coordinates of all other points, and see that they won't satisfy the inequality y<3x-6

Your answer is c, hope it helps!

The measurement at point X to the nearest [tex](\frac{1}{16})''[/tex]  from the beginning of the ruler is option (C) [tex]8(\frac{5}{8} )''[/tex].

A ruler is a device with measurement markings on it used for measuring drawing straight lines. Rulers have measurements in imperial and metric, imperial-only, or metric-only.

For the given situation,

The markings on a standard ruler represent the fractions of an inch. The smallest ticks on a ruler are the sixteenth-inch ticks.

The distance between a sixteenth-inch tick and the other larger ticks is [tex]\frac{1}{16}[/tex].

The very first line on the left hand side of the ruler is the [tex]\frac{1}{16}[/tex] of an inch mark.

The point x is pointed at [tex]8[/tex] inches and at 10th division.

1st division = [tex]\frac{1}{16}[/tex]

So, 10th division = [tex]\frac{10}{16} = \frac{5}{8}[/tex]

Hence we can conclude that the measurement at point X to the nearest [tex](\frac{1}{16})''[/tex] from the beginning of the ruler is option (C) [tex]8(\frac{5}{8} )''[/tex].

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Answer:

Experiment, observational study, survey

Step-by-step explanation:

The first one is an experiment.  The vet selects random samples and compares the effects of the injection to the nose drips.

The second one is an observational study.  The reaction of the dogs to the treats is being observed.

The third one is a survey.  The owners are given specific questions to answer.

The terms 'survey', 'experiment', and 'observational study' are methods of data collection in mathematics, specifically in statistics. A 'survey' collects data systematically from a group of individuals, an 'experiment' tests hypotheses in controlled conditions, and an 'observational study' records data without influencing the subjects of the study.

The terms 'survey', 'experiment, and 'observational study' represent distinct methods of data collection in statistics. A survey is a data collection tool used to gather information about individuals systematically. An experiment involves carrying out a procedure under controlled conditions to test a hypothesis. An observational study refers to a study where researchers observe and record data without influencing the subjects of the study.

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Answer:

A

Step-by-step explanation:

[tex]s_x[/tex]  is the standard deviation of x.

The standard deviation is gotten by:

1. find the average of x-values (add up all the values and divide by number of numbers, which is 5)

2. subtract the average, x bar, from each of the values, square it,  and add up the difference

3. Divide that final answer by n, which is 5

4. Take the square root of the answer

Now, let's find the average (x bar):

x bar = [tex]\frac{2+6+9+14+19}{5}=10[/tex]

Doing steps 2 & 3 together:

[tex]\frac{(2-10)^2+(6-10)^2+(9-10)^2+(14-10)^2+(19-10)^2}{5}\\=35.6[/tex]

Doing step 4:

[tex]\sqrt{35.6} =5.967[/tex]

Correct answer is A

Answer:

∠C=90°

∠A=67°

∠B=23°

Step-by-step explanation:

For angle C:

  Thales' Theorem states that an angle inscribed across a circle's diameter is always a right angle.

  Therefore, since AB is the diameter(hypotenuse) then angle C is the right angle. (90°)

For Angle A:

  The measure of arc BC= 134 degrees. We can just use a formula for an inscribed triangle. ∠A = 1/2 (mBC)

  ∠A= (1/2)134

  ∠A= 77°

For angle B:

  All triangle angles all add up to 180. We can just subtract angles A and C from 180°:

  ∠B = 180-(90+67)

  ∠B = 23°

Answer:

[tex]\frac{9}{10}[/tex]

Step-by-step explanation:

4 = Red

3 = Blue

2 = White

1 = Yellow

What is probability that it is not yellow ?

[tex]\frac{9}{10}[/tex]

Because only 1 marble is yellow and they are 9 other colours apart from yellow it must be [tex]\frac{9}{10}[/tex]

Answer:

[tex]\frac{9}{10}[/tex]

Step-by-step explanation:

Probability of an event occurring is

P = [tex]\frac{outcomerequired}{total outcomes}[/tex]

P( yellow) = [tex]\frac{1}{10}[/tex]

P( not yellow ) = 1 - [tex]\frac{1}{10}[/tex] = [tex]\frac{9}{10}[/tex]

Idk if ya still need it or if this will help but this is what i put for mine

 Concepts that I had previously  learned about are quite important because math goes hand and hand. if you try to skip something and go ahead you'll most likely get confused because there could of been something highly important to that would help you understand whats ahead. in the previous unit it tells you about triangles and their description like a right triangle-90 degree angle and where legs and hypotenuse is located, this unit has had a ton about right triangles.

Previous concepts learned in mathematics provide a necessary foundation for understanding more complex topics such as trigonometry and the properties of right triangles. This is exemplified in how the Pythagorean theorem and understanding of sine, cosine, and tangent in a right triangle, inform the understanding of trigonometric principles. Hence, learning in mathematics is a progressive and integrated process.

Reflecting on working with right triangles and trigonometric concepts, it's clear that concepts learned previously were extremely important to success in this unit. Mathematics is interconnected, and concepts build upon one another. Take for example, the Pythagorean theorem, a fundamental principle in geometry that establishes a relationship between the sides of a right-angled triangle. This theorem set the stage for understanding trigonometric concepts.

Another important previous learning that helped in understanding trigonometry is the concept of the sine, cosine, and tangent of an angle in a right triangle. Knowledge of these terms and ability to calculate them, as represented in a right triangle, feeds into the understanding of trigonometric principles.

Furthermore, the problem-solving strategies applied in mathematics aid in integrating concepts. Identifying physical principles and solving for unknowns is crucial and this reasoning prowess comes from continuous practice over previous sections.

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Answer:

The length of each piece will be [tex]\frac{1}{6}\ yd[/tex]

Step-by-step explanation:

we know that

To find the length of each piece, divide the total length of the board by four

so

[tex]\frac{(2/3)}{4}=\frac{2}{12}\ yd[/tex]

Simplify

[tex]\frac{2}{12}=\frac{1}{6}\ yd[/tex]

Answer:

3

Step-by-step explanation:

1 person eats 2/5 of a pizza

6 people eat 2/5 * 6 pizzas

But what value is 2/5 * 6?

You could do it this way

12/5 = 2 2/5

This number is telling you that you need 2/5 of a pizza over 2.

The group should order 3 pizzas. There will be left overs, but that won't matter. Everyone will get at least 2/5 of a pizza.

for this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle. So:

[tex]tg (A) = \frac {6} {8} = \frac {3} {4}[/tex]

Answer:

[tex]tg (A) = \frac {3} {4}[/tex]

Answer:

1,595.34

Step-by-step explanation:

A=33

2a2=3·3

2·24.782≈1595.34454

Answer:

Step-by-step explanation:

Rewrite this expression as   (27^(1/3) )².  this is equivalent to:

( ∛27 )² or (∛27)(∛27).

If you wish to evaluate this expression, it is ( 3 )( 3 ) = 9.

Answer:

27²/3 = 243 Hope this helps :D

In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.

So, in your case, we have

[tex]\sin(Z) = \dfrac{XY}{XZ}[/tex]

In order to find XY, we have

[tex]XY = \sqrt{XZ^2-YZ^2} = \sqrt{1600-1024}=\sqrt{576} = 24[/tex]

So, the ratio for the sine is

[tex]\sin(Z) = \dfrac{XY}{XZ} = \dfrac{24}{40} = \dfrac{3}{5}[/tex]

Answer:

D) None are true

Step-by-step explanation:

- Data sets with influential points can be linear or nonlinear.

- Influential points can increase the coefficient of determination.

- Outliers are influential only if they have a big effect on the regression equation.

Hope his helps

-Amelia

In regression analysis, statement III is not true. All outliers are not necessarily influential data points. And statement II is not always true

Hence, option I is correct.

Statistics is a discipline of mathematics that deals with all aspects of data. Statistical knowledge aids in the selection of the appropriate technique of data collection and the use of those samples in the appropriate analysis process in order to effectively create the results. In short, statistics is an important procedure that assists in making data-driven decisions.

Since we know that,

A point with a significant residual is considered an outlier.

An influential point is one that has a significant impact on the regression. Surprisingly, these are not synonymous. A point can be an outlier without having any influence. Without being an anomaly, a point can be influential.

Therefore,

statement I can be true - data sets with influential points can indeed be non-linear.

And statement II is not always true - influential points can either increase or decrease the coefficient of determination, depending on whether they are positively or negatively correlated with the response variable.

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Answer:

90 cents

Step-by-step explanation:

If a crate holds 48 bottles and you want to make exactly $34 on selling them, before you find out exactly how much to charge for each bottle, you have to subtract the amount you paid for the crate from the profit.  The unknown here is the cost per bottle that you have to make in order to reach your goal of $34.  If you have 48 bottles of water and you want to know how much to charge PER bottle, the algebraic expression for that would be 48x.  Now from that profit of 48x you need to subtract the $9.20 and set it equal to what you'd like to earn:

48x - 9.20 = 34.00

Solve this by adding 9.2 to both sides, and then dividing by 48.  That gives you a cost per bottle of 90 cents.  Plug .90 in for x in the equation above and see that the left side does indeed equal the right side.

To make a profit of $34 per crate along with the original cost of $9.20, the concession stand should charge $0.90 per bottled water.

The question is asking for the price the concession stand should charge per bottle of water in order to make a profit of $34.00 per crate. We start by determining the total desired income from each crate, which is cost plus profit ($9.20 cost + $34.00 profit = $43.20 total income per crate). Next, we divide the total income per crate by the number of bottles in each crate, which is 48. So, $43.20 / 48 = $0.90. Therefore, the concession stand should charge customers $0.90 per bottle of water to achieve the desired profit of $34.00 per crate.

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The answer is 3.67pi

Find the angle for the arc and divide it by 360 and multiply it by the circumference You calculate the circumference.

Variance = 864

Standard Deviation= 29.4

Answer:

Standard Deviation = 29.40

Variance = 864

Step-by-step explanation:

A contractor records all of the bedroom areas, in square feet of a 5 bedroom house as : 100, 100, 120, 120, 180

To calculate the standard deviation first we have to calculate the mean of the data

( 100 + 100 + 120 + 120 + 180 ) / 5

= 620 / 5 = 124

Then for each number subtract the mean and square the result :

-24, -24, -4, -4, 56

square the result = 576, 576, 16, 16, 3136

Now work out the mean of these squared differences.

( 576 + 576 + 16 + 16 + 3136 ) / 5 = 4320 / 5 = 864

This value is Variance, so the variance = 864

Now we take the square root of 864 to get standard deviation

[tex]\sqrt{864}[/tex] = 29.39 rounded to 29.40

Standard Deviation = 29.40

Variance = 864

You can do substitution 2x-2=x^2 -x -6; isolate all terms on one side 0= x^2 -x-2x -6+2; combine like terms x^2 -3x -4=0; factor the quadratic (x-4)(x+1)=0; each term is zero x-4=0 so x=4 and x+1=0 so x=-1. Now, y=2•4-2=6 and y=2•(-1) -2= -4 ; solutions for the system are ( 4,6) and ( -1, -4)

Answer:

(4,6) or (-1,-4)

Step-by-step explanation:

since both equations about x are equal to y, you can make x^2-x-6=2x-2

solve this quadratic equation, you get x=4 or -1

substitute x into y=2x-2

you get y=6 when x=4, or y= -4 when x=-1

Answer: 240 minutes should be it

Answer:

Step-by-step explanation:240 minutes should be it

Answer:

This equation has no solution.

Step-by-step explanation:

Perform the indicated multiplication:  5(y+1)-7 = 3(y-1)+2y

We get 5y + 5 - 7 = 3y - 3 + 2y.  Subtracting 5y from both sides yields -2 = -3, which is never true.  This equation has no solution.

Final answer:

Upon expanding and simplifying the equation 5(y+1)-7 = 3(y-1)+2y, it leads to a false statement -2 = -3, indicating there is no solution.

Explanation:

A student asked how to describe the solution for the equation 5(y+1)-7 = 3(y-1)+2y. The first step to solving this would be to expand and simplify the equation. Let's do this:

Multiply through the parentheses: 5y + 5 - 7 = 3y - 3 + 2y

Combine like terms on both sides: 5y - 2 = 5y - 3

Attempt to isolate y, but upon subtracting 5y from both sides, you get -2 = -3

This is a false statement, showing that the original equation has no solution.

Final answer:

To find the cost for each call minute, set up a system of equations and solve for x and y. The cost per call minute for Scott is approximately $0.087, and the cost per call minute for Maria is approximately $0.072.

Explanation:

To find the cost for each call minute, we can set up a system of equations using the given information. Let's assume the cost per call minute for Scott is x and for Maria is y. The total cost for Scott is 95x + 207y = $23.55, and the total cost for Maria is 162x + 124y = $17.26.

Using these equations, we can solve for x and y. After solving, we find that the cost per call minute for Scott is approximately $0.087, and the cost per call minute for Maria is approximately $0.072.

Answer:

The simplified form is -26x^2 + 56x -15

Step-by-step explanation:

We need to solve the expression:

3x(-2x+7)-5(x-1)(4x-3)

Multiplying the terms outside the bracket with the terms inside the bracket.

=-6x^2+21x-5(x(4x-3) -1(4x-3))

= -6x^2+21x-5(4x^2-3x-4x+3)

= -6x^2+21x-5(4x^2-7x+3)

Now multiply -5 with the terms inside the bracket

= -6x^2+21x -20x^2 +35x -15

Now, Combining the like terms:

= -6x^2 -20x^2 +21x+35x -15

Adding the like terms

= -26x^2 + 56x -15

So, the simplified form is -26x^2 + 56x -15

Answer: [tex]-26x^2+56x-15[/tex]

Step-by-step explanation:

The first  step is to apply Distributive property.

You also need to remember the Product of powers property, which states the following:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Applying these properties:

[tex]3x(-2x+7)-5(x-1)(4x-3)=\\=-6x^2+21x-5(4x^2-3x-4x+3)\\=-6x^2+21x-20x^2+15x+20x-15[/tex]

And finally, you need to add the like terms.

Therefore, you get:

[tex]=-26x^2+56x-15[/tex]