10) How many possible outfit combinations come from six shirts, three
slacks, and five ties? *
A 15
B 18
C 30
D 90

Answer:

See below.

Step-by-step explanation:

To find roots of an equation, we use this formula:

[tex]z^{\frac{1}{n}}=r^{\frac{1}{n}}(cos(\frac{\theta}{n}+\frac{2k\pi}{n} )+\mathfrak{i}(sin(\frac{\theta}{n}+\frac{2k\pi}{n})),[/tex] where k = 0, 1, 2, 3... (n = root; equal to n - 1; dependent on the amount of roots needed - 0 is included).

In this case, n = 4.

Therefore, we adjust the polar equation we are given and modify it to be solved for the roots.

Part 2: Solving for root #1

To solve for root #1, make k = 0 and substitute all values into the equation. On the second step, convert the measure in degrees to the measure in radians by multiplying the degrees measurement by [tex]\frac{\pi}{180}[/tex] and simplify.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(0)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(0)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}} = 2(sin(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]

Root #1:

[tex]\large\boxed{z^\frac{1}{4}=2(cos(\frac{19\pi}{36}))+\mathfrack{i}(sin(\frac{19\pi}{38}))}[/tex]

Part 3: Solving for root #2

To solve for root #2, follow the same simplifying steps above but change k  to k = 1.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(1)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(1)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{2\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{2\pi}{4}))\\[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{2}))\\[/tex]

Root #2:

[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{7\pi}{9}))+\mathfrak{i}(sin(\frac{7\pi}{9}))}[/tex]

Part 4: Solving for root #3

To solve for root #3, follow the same simplifying steps above but change k to k = 2.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(2)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(2)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{4\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{4\pi}{4}))\\[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\pi))+\mathfrak{i}(sin(\frac{5\pi}{18}+\pi))\\[/tex]

Root #3:

[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{23\pi}{18}))+\mathfrak{i}(sin(\frac{23\pi}{18}))}[/tex]

Part 4: Solving for root #4

To solve for root #4, follow the same simplifying steps above but change k to k = 3.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(3)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(3)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{6\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{6\pi}{4}))\\[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{3\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{3\pi}{2}))\\[/tex]

Root #4:

[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{16\pi}{9}))+\mathfrak{i}(sin(\frac{16\pi}{19}))}[/tex]

The fourth roots of 16(cos 200° + i(sin 200°) are listed above.

[tex]_9C_7=\dfrac{9!}{7!2!}=\dfrac{8\cdot9}{2}=36[/tex]

Answer:

  146/45

Step-by-step explanation:

Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.

  [tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]

__

Comment on procedure

The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.

Answer:

6.034

Step-by-step explanation:

6 is a whole number.

.034 because it is 34 thousandths, not 34 hundredths.

Answer:

C

Step-by-step explanation:

reciprocal of z=1/z

[tex]z=2(cos \frac{\pi }{4} +i sin\frac{\pi }{4} )=2e ^{i \frac{\pi } {4}\\\frac{1}{z}=\frac{1}{2e^{i \frac{\pi}{4} } }\\\frac{1}{z} =\frac{1}{2} e^{-i\frac{\pi}{4} } \\\frac{1}{z} (cos\frac{\pi}{4} -isin\frac{\pi}{4} ) \\\frac{1}{z}=\frac{1}{2} (\frac{\sqrt{2} }{2} -\frac{\sqrt{2} }{2} )\\\frac{1}{z} =\frac{\sqrt{2} }{4} -i \frac{\sqrt{2 } }{4}[/tex]

Answer:

The value is [tex]T = \$54200[/tex]

Step-by-step explanation:

From the question we are told that

      The  number of shares is  n  =  400

      The rate  of each share is  [tex]k = 135\frac{1}{2} = 135.5[/tex]

Generally the total price is mathematically represented as

     [tex]T = 400 * 135.5[/tex]

      [tex]T = \$54200[/tex]

Answer:

  17 by 21 inches

Step-by-step explanation:

The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...

  L + W = 38

  LW = 357

__

Solution:

  W(38 -W) = 357 . . . . . substitute for L

  -(W^2 -76W) = 357 . . expand on the left

  -(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square

  (W -19)^2 = 4 . . . . . . . write as a square

  W -19 = ±√4 = ±2 . . . take the square root; next, add 19

  W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other

The dimensions are 17 by 21 inches.

Answer:

B. j(kl)

Step-by-step explanation:

(jk)l

We can change the order we multiply and still get the same result

j(kl)

Answer:

Step-by-step explanation:

its B i did it

Answer:

C. -8, -6, -4, -2, ...

Step-by-step explanation:

An arithmetic sequence increases by the same amount every time through addition or subtraction. There is a common difference.

A: -2, 4, -6, 8, ... If there were a common difference, the numbers would not switch between being positive and back to negative. The numbers would either keep going positive or keep going negative.

B: 2, 4, 8, 16, ... The common difference between 16 and 8 is 16 - 8 = 8. The difference between 8 and 4 is 8 - 4 = 4. Since the difference changes between the numbers, this is not an arithmetic sequence.

C. -8, -6, -4, -2, ... The common difference between -2 and -4 is -2 - (-4) = -2 + 4 = 2. The difference between -4 and -6 is -4 - (-6) = -4 + 6 = 2. The difference between -6 and -8 is -6 - (-8) = -6 + 8 = 2. Since the common difference is always two, this is an arithmetic sequence.

Hope this helps!

Answer:

See below.

Step-by-step explanation:

First, recall the meanings of the domain and range.

The domain is the span of x-values covered by the graph.

And the range is the span of y-values covered by the graph.

1)

So, we have here an absolute value function.

As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:

[tex]\{x|x\in\textbb{R}\}[/tex]

(You are correct!)

For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:

[tex]\{y|y\leq 7\}[/tex]

2)

We have here an ellipse.

First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:

[tex]-4\leq x\leq 6[/tex]

So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:

[tex]\{x|-4\leq x\leq 6\}[/tex]

For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:

[tex]-5\leq y\leq 1[/tex]

This represents all the y-values between -5 and 1, including -5 and 1.

In set notation, thi is:

[tex]\{y|-5\leq y\leq 1\}[/tex]

Answer:

P= 2

Step-by-step explanation:

10/7p+13/8+15/2p=-909/56

Combine like terms

10/7p+15/2p=-909/56-13/8

20p+105p/14=-909-13*7/56

125/14p=-909-91/56

125/14p= -1000/56

125/14p*14/125= -1000/56*14/125

simplify

P= 8/4=2

And for #8 n =1 I answered this question it

Search

Answer:

Step-by-step explanation:

A probability density function (pdf) is used for continuous random variables. That is why p is between 0 and 1 (the two extremes - 0 and 1 - exclusive).

X = 100pth percentile of W

Y = 100(1-p)th percentile of W

Expressing Y as a function of X;

Y = 100(1-p)th = 100th - 100pth

Recall that 100pth is same as X, so substitute;

Y = 100th - X

where 100th = hundredth percentile of W and X = 100pth percentile of W  

Answer:

D question,somewhat confusing, itsit's like simultaneous equation,but values are different

Answer:

x = 4 + 2y/3

Step-by-step explanation:

Answer:

Last one

Step-by-step explanation:

The function f is:

● f (x)= √(4x+6)

The function g is:

● g(x) = √(4x-6)

Add them together:

● f+g (x)= √(4x+6 )+ √(4x-6)

Answer:

[tex]\large \boxed{{\sqrt{4x+6} + \sqrt{4x-6} }}[/tex]

Step-by-step explanation:

[tex]f(x)=\sqrt{4x+6}[/tex]

[tex]g(x)=\sqrt{4x-6}[/tex]

[tex](f+g)(x)[/tex]

[tex]f(x)+g(x)[/tex]

Add both functions.

[tex](\sqrt{4x+6} )+ (\sqrt{4x-6} )[/tex]

Answer:

60/220

Step-by-step explanation:

we use combination,

[tex] (\frac{5}{1} ) \times ( \frac{4}{1} ) \times ( \frac{3}{1} )[/tex]

[tex]5 \times 4 \times 3 = 60[/tex]

then, all divided by,

[tex] (\frac{12}{3}) = 220 [/tex]

[tex]60 \div 220[/tex]

The probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The sample contains five milk chocolates, three dark chocolates, and four white chocolates. Therefore, the probability that the first piece is milk chocolate is

[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{5}{12}[/tex]

Now, since the chocolate is been eaten the sample size will reduce from 12 chocolates in total to 11 chocolates in total (four milk chocolates, three dark chocolates, and four white chocolates). Therefore, the probability of the second piece being white chocolate is

[tex]\rm Probability=\dfrac{\text{Number of White choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{4}{11}[/tex]

Now, as the chocolate is been eaten the sample size will reduce from 11 chocolates in total to 10 chocolates in total (four milk chocolates, three dark chocolates, and three white chocolates). Therefore, the probability of the third piece being milk chocolate is

[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{4}{10}[/tex]

Thus, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is

[tex]\rm Probability=\dfrac{5}{12}\times \dfrac{4}{11} \times \dfrac{4}{10} = \dfrac{80}{1320} = 0.06[/tex]

Hence, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.

Learn more about Probability:

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Answer:

Interquartile range is the distance between the first and third of a data.

Step-by-step explanation:

Hope it will help you :)

Answer:

4/7

Step-by-step explanation:

divide both by two for its simplest form

Answer:4/7

Step-by-step explanation

Divide both the numerator and denominator by 2

The result for the numerator is 8/2=4

that of the denominator is 14/2=7

Therefore the resultant answer is 4/7

Answer:

4 units

Step-by-step explanation:

A transformation is the movement of a point from one position to another position. If a shape is transformed all its points are also transformed. Types of transformations are translation, rotation, reflection and dilation.

If a shape is transformed, the length of its sides and shape remains the same, only the position changes.

If Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B, the length of A'B' remains the same which is 4 unit. To prove this:

Let A be at ([tex]x_1,y_1[/tex]) and B be at ([tex]x_2,y_2[/tex]). The length of AB is:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

If AB is translated to the right by 1 unit the new points are A' at ([tex]x_1+1,y_1[/tex]) and B' at ([tex]x_2+1,y_2[/tex]). The length of A'B' is:

[tex]A'B'=\sqrt{(y_2-y_1)^2+(x_2+1-(x_1+1))^2}=\sqrt{(y_2-y_1)^2+(x_2+1-x_1-1)^2}\\\\A'B'=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

AB = A'B' = 4 units

Answer:

(a) 1155.84

(b) 48.2%

(c) D

Step-by-step explanation:

The number of total responses is, N = 38,528.

(a)

It is provided that 3% answered with "a lot".

Compute the actual number of responses consisting of "a lot" as follows:

n (a lot) = N × P (a lot)

            = 38528 × 0.03

            = 1155.84

Thus, the actual number of responses consisting of "a lot" is 1155.84.

(b)

The number of responses consisting of "very little or none" is,

n (very little or none) = 18,566

Compute the percentage of responses consisted of "very little or none" as follows:

[tex]P(\text{very little or none})=\frac{n(\text{very little or none})}{N}[/tex]

                                  [tex]=\frac{18566}{38528}\\\\=0.481883\\\\\approx 0.482[/tex]

The percentage is: 0.482 × 100% = 48.2%.

Thus, the percentage of responses consisted of "very little or none" is 48.2%.

(c)

As the sample size increases the sample statistic value gets closer and closer to the actual population parameter value.

Thus, making the sample statistic an unbiased estimator of the population parameter.

And proving that the sample is a true representative of the population.

Thus, the correct option is (D).

Answer:

[tex] {x}^{2} + 5x + 10[/tex]

Answer:

[tex]\large \boxed{x^2 +5x+10}[/tex]

Step-by-step explanation:

A polynomial is an expression that has variables, coefficients, and constants.

An example of a polynomial can be x² - 6x + 2.

Answer:

Your answer is here.Enjoy dude

Answer:

12.56 unit²

Step-by-step explanation:

The form of the circle is:

Let's bring the given to the form of a circle as above:

As per the form, we got r² = 2², so the radius of circle is 2 units.

The area of circle:

Answer:

7.5 cm²

Step-by-step explanation:

Dimensions of the large ∆:

[tex] base (b) = 3cm, height (h) = 9cm [/tex]

[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]

Dimensions of the small ∆:

[tex] base (b) = 2cm, height (h) = 6cm [/tex]

[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]

Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²

Answer: 1.5 less than 15 is divided by a number d.

Step-by-step explanation:

Answer:

0.56 is the required probability.

Step-by-step explanation:

Time for which signal shows green light = 4 minutes

Time for which signal shows yellow light = 10 seconds

Time for which signal shows red light = 3 minutes

To find:

Probability that the signal will show green light when you reach the destination = ?

Solution:

First of all, let us convert each time to same unit before doing any calculations.

Time for which signal shows green light = 4 minutes = 4 [tex]\times[/tex] 60 seconds = 240 seconds

Time for which signal shows yellow light = 10 seconds

Time for which signal shows red light = 3 minutes = 3 [tex]\times[/tex] 60 seconds = 180 seconds

Now, let us have a look at the formula for probability of an event E:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Here, E is the event that green light is shown by the signal.

Number of favorable cases mean the time for which green light is shown and Total number of cases is the total time (Time for which green light is shown + Time for which Yellow light is shown + Time for which red light is shown)

So, the required probability is:

[tex]P(E) = \dfrac{240}{240+10+180}\\\Rightarrow P(E) = \dfrac{240}{430}\\\Rightarrow \bold{P(E) \approx 0.56 }[/tex]

Answer:

x = 6

Step-by-step explanation:

∠ DBC + ∠ ABC = ∠ ABD , substitute values

5x - 4 + 8x - 3 = 79

13x + 1 = 79 ( subtract 1 from both sides )

13x = 78 ( divide both sides by 13 )

x = 6

Answer:

3

Step-by-step explanation:

f(x)=3x-3

g(x)=-x^2+4,

f(2) = 3(2) -3 = 6-3 =3

g(-2) = -(-2)^2+4 = -4+4 = 0

f(2)-g(-2)= = 3-0 = 3

Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

We have a line of best fit:

h = –21.962x + 114.655

As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.

Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

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Answer:

combined like terms and then follow  the order of operations.

Step-by-step explanation:

Answer:

B. More

Step-by-step explanation:

This is according to the law of large numbers

An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.

Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.

An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed

Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.

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Answer:

The steps 1-7 have been explained

Step-by-step explanation:

The steps are;

1) We will verify that the population standard deviations are known and that the population is normally distributed which means the sample size must be a minimum of 30.

2) We will state the null and alternative hypothesis

3) We will determine the critical values from the relevant tables

4) From the critical values gotten, we will determine it's corresponding region where it can be rejected.

5)We will calculate the value of the test statistic from the formula;

z = [(x1' - x2') - (μ1 - μ2)]/√[((σ1)²/n1) + ((σ2)²/n2)]

6) If the value of the test statistic gotten from step 5 above falls in the region of rejection noted in step 4,then we will reject the null hypothesis

7) After rejection of the null hypothesis, we will now give a decision/conclusion on the claim.