What type of number is expressed in the form a bi?.

The expression that equals to 9[tex]\sqrt[3]{10}[/tex] is 5[tex]\sqrt[3]{10}[/tex] + 4[tex]\sqrt[3]{10}[/tex] so option 2 is correct.

Given expression:

Second option:

=  5[tex]\sqrt[3]{10}[/tex] + 4[tex]\sqrt[3]{10}[/tex]

Take cube root 10 as common

= [tex]\sqrt[3]{10}[/tex](5+4)

= ∛10(9)

= ∛10*9

= 9∛10.

which is equal to given expression.

Therefore the expression that equals to 9[tex]\sqrt[3]{10}[/tex] is 5[tex]\sqrt[3]{10}[/tex] + 4[tex]\sqrt[3]{10}[/tex] so option 2 is correct.

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The stronger the evidence is against the null hypothesis, the higher the divergence from it.

What do you mean by null hypothesis ?

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is [tex]H_{0}[/tex]. To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts employ the null hypothesis,

The null hypothesis states that the percentage of the population who works full time is 0.45.

As a result, 450 persons who are randomly selected from a population of 1000 work full-time.

A different hypothesis states that the ratio is higher than 0.45.

In the options provided, the proportion for the first option is 300/1000, or 0.3.

In the second choice, 500/1000 equals 0.5

Third alternative: 700/1000 = 0.7

Therefore, the stronger the evidence is against the null hypothesis, the higher the divergence from it.

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The equation of a line is typically written as y = MX + b  where m is the slope and b is the y-intercept.

First of all, remember what the equation of a line is:

y = MX + b

Where:

To start, you know what m is; it's just the slope, which you said was. So, you can right away fill in the equation for a line somewhat to read:

Y = x + b.

Now, what about b, the y-intercept?

To find b, think about what your (x, y) point means:

(,). When x of the line is, y of the line must be.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: b is what we want, the 0 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specifically passes through the point (,).

So, why not plug in for x the number and for y the number This will allow us to solve for b for the particular line that passes through the point you gave.

In arithmetic, the slope or gradient of a line is various that describes each direction and the steepness of the line. The slope is regularly denoted through the way of the letter m; there may be no clear way to question why the letter m is used for slope, however, its earliest use in English seems in O'Brien (1844) who wrote the equation of a straightaway line as "y = MX + b" and it is able to additionally be decided in Todhunter (1888) who wrote it as "y = MX + c".

The slope is calculated by locating the ratio of the "vertical exchange" to the "horizontal alternate" amongst (any) two incredible elements on a line. on occasion the ratio is expressed as a quotient ("upward push over run"), giving an equally extensive range for each first-rate point on the same line. A line that is reducing has a terrible "upward thrust". the line can be sensible – as set with the aid of a street surveyor, or in a diagram that fashions a road or a roof either as a definition or as a plan.

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I, III, and IV  quadrants.

What do the four graph quadrants represent?

The x and y and y-coordinates are both positive in quadrant I. X and Y coordinates in quadrant II are opposite one other. X and Y coordinates are both positive in quadrant III. In quadrant IV, the x-coordinate and y-coordinate are both positive.

Why are the first and third quadrants used?

Typically, we assume that after a projection is made on the horizontal plane, it spins clockwise. We employ first angle and third angle projection for this purpose. Because only within these two quadrants will we receive both viewpoints following the horizontal plane's clockwise rotation.

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Solutions for the inequality y is less than or equal to two-thirds times x minus 4 will exist in the I, III, and IV quadrants.

What do the four graph quadrants represent?

In quadrant I, the x and y coordinates are both positive. In quadrant II, the X and Y coordinates are orthogonal. In quadrant III, both the X and Y coordinates are positive. The x- and y-coordinates are both positive in quadrant IV.

What is the inequality's y-intercept?

Inequality y image result

Any straight-line's equation, known as a linear equation, can be written as y = mx + b,

Where m is the slope of the line and b is the y-intercept.

This line's y-intercept is the value of y at the point where the line intersects the y-axis.

We usually assume that after a horizontal plane projection, it spins clockwise. For this, we use first and third-angle projections. Because only within these two quadrants will we receive both viewpoints after the horizontal plane rotates clockwise.

Solutions for the inequality y is less than or equal to two-thirds times x minus 4 will exist in the I, III, and IV quadrants.

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The variance of 1 means that the values of the given data set are relatively more than the expectations.

According to the question,

We have the following information:

Variance of 1

Now, we know that the variance of 1 means that the values in the data set are relatively more than our expectations.

Now, we also know that if the the variance for a given data set is less than 1 then it can be considered that the variance is relatively low.

Hence, the variance of 1 means that the values of the given data set are relatively more than the expectations.

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Check the picture below.

so the chord we see in the picture in "green", has a length of XQ + QY, now, we can just use the pythagorean theorem to get the length of XQ, keeping in mind that the point of tangency at Q is always a right-angle, and thus that means that XQ = QY, so whatever the green chord is, is just really 2 * XQ.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{9}\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{XQ}\\ \end{cases} \implies \sqrt{9^2 - 7^2}=XQ \\\\\\ \sqrt{32}=XQ\implies 4\sqrt{2}=XQ\hspace{5em} \underset{\textit{\LARGE XY}}{\stackrel{(2)4\sqrt{2}}{{\Large \begin{array}{llll} 8\sqrt{2}\approx 11.31 \end{array}}}}[/tex]

Answer:

[tex]8\sqrt{x} 2 - 11.31\\[/tex]

The given function is f(x) = 1/x - 1, with x and y intersecting (1,0) and the graph is attached below.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

The given function is f(x) = 1/x - 1

f(x) = 1-x / x

Now put x = 0 to get the y-intercept

f(x) = ∞

It doesn't touch y-axis.

Putting f(x) = 0

1-x /x = 0

⇒1-x = 0

⇒x = 1

So the x-intercept is 1.

Hence, is f(x) = 1/x - 1, with x and y intersecting (1,0) and the graph is attached below.

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The formula to calculate the discount in cell D2 of worksheet will be     D2-(D1*0.10).

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Rather than being stated as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Here,

Since we have to give 10% discount,

=D2-(D1*0.10)

D2-(D1*0.10) is the formula to calculate the discount in cell D2 of the worksheet.

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The function f(x) = x(x+4√x) is concave down on (0, 9/4) and  concave up or (9/4, ∞)

According to the question,

Given equation is f(x) = x(x+4√x)

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

Derivative the function with respect to x

f'(x) = 2x - 6√x

Derivative the function again ,

f''(x) = 2 - 3/√x

Domain of f(x): x ≥ 0.

Let f''(x) = 0

Putting f"(x) = 0,

2x1/2 = 3

=> x = 9/4

f'(x) Doesn't exist for x = 0 and at x = 0

we have not inflection point, because x < 0 not in domain.

For 0 <x< 9/4,

f''(x) < 0 and graph concave down or (0, 9/4)

For x > 9/4 f''(x) > 0 and graph concave up or (9/4, ∞)

f(9/4) = -135/16. So, point (9/4, -135/16) is point of inflection

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The expression will become cos²(7x) = [tex]\frac{1}{2}[/tex](1 + cos14x).

Power reduction formulas like double angle and half angle formula are used to simplify the calculations requires to solve a given expression.

Power reduction formulas allow us to reduce the power on one of the trigonometric functions when the power is an even integer.

The trigonometric power reduction identities allow us to rewrite expressions involving trigonometric terms with trigonometric terms of smaller powers.

The power reduction formula is

cos²θ = [tex]\frac{1}{2}[/tex](1 + cos2θ)

sin²θ =[tex]\frac{1}{2}[/tex](1 - cos2θ)

For the given equation we will use cosine formula.

Therefore

cos²(7x) = [tex]\frac{1}{2}[/tex](1 + cos2(7x))

cos²(7x) = [tex]\frac{1}{2}[/tex](1 + cos14x).

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The number of days taken by 12 men, 18 women and 28 boys is 108 days.

Here we have to find the number of days required to do the work by 12 men, 18 women, and 28 boys in 8 hours.

It is given that 6 men, 8 women, and 16 boys together can do a work in 288 days working 6 hours.

The ratio of efficiency of men, women, and boys is 3:2:1.

Let d be the number of days taken by 12 men, 18 women, and 28 boys.

Work done formula:

Work done = number of people × efficiency × number of days

Let us assume that the number of days taken by 12 men, 18 women and 28 boys be d.

So from this, we have:

(6× 3 + 8× 2 + 16×1) 288 × 6 = ( 12×3 + 18×2 + 28×1) d × 8

( 18 + 16 + 16) 288 × 6 = ( 36 + 36 + 28) d× 8

50 × 288 × 6 = 100 × 8 × d

d = 108

Therefore the number of days taken is 108 days.

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The complete question is:

if 6 men. 8 women and 16 boys together can do a piece of work in 288 days by working 6 hours each day how many days can 12 men, 18 women, and 28 boys complete the same & work by working 8 hours each day? The work efficiency of men, women, and boys proportion 3:2:1 respectively. ​

a)The expected number of ER admissions per week is 800.

b)The probability they will make 800 or more ER admissions during a typical week is 1.

We have given that on average the number of admission on weekdays is 100

So, in five days number of admission are =5×100=500

Now, in weekend we have given that 150 admissions comes per day

So, in two days number of admission are =2×150=300

So, Total number of admissions =500+300=800 admissions.

b)We can see that total number of admissions are 800 on average, so it is the average number of admissions.

Here, we can see that this is the event of 100% occurrence. There are no chances of failure.

So, maximum probability of getting 800 or more ER admissions is 1.

Hence, a)ER admissions are 800 b)The probability of 800 or more admission is 1.

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Answer:

fishing + camping = 15

not fishing + camping = 10

The lower limit that she traveled in three second is 33.45 feet and the upper limit that she traveled in three second is 43.45 feet

The speed of a runner increased steadily during the first three seconds of a race

Therefore the time = 3 seconds

Her speed at half-second intervals is given in the table

We know,

Speed = Distance / Time

Similarly

Distance = Speed × Time

Δt = 0.5 seconds

Then the lower limit of total distance traveled = 0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4)

Add the terms and multiply it

= 0.5 × 66.9

= 33.45 feet

The upper limit of total distance traveled = 0.5( 6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)

= 0.5 × 86.9

= 43.45 feet

Hence, the lower limit that she traveled in three second is 33.45 feet and the upper limit that she traveled in three second is 43.45 feet

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The number of students taking classes at Zeke's Karate altogether is 108 students.

Given that, at Zeke's Karate, there are 5 times as many youth students as adult students taking classes this session.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

The ratio of youth students to adult students is x:5x.

If there are 72 more youth students than adult students this session

So, 5x=x+72

⇒ 5x-x=72

⇒ 4x=72

⇒ x=18

Now, 5x=5×18 =90

Total students = 18+90=108

Therefore, the number of students taking classes at Zeke's Karate altogether is 108 students.

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The probability that the student is satisfied with the tentbook is given by 56% or 0.56

Given that,

Let A denotes the event that student used book by Professor A

Similarly B and C

let X be the event that student is satisfied

P [ Student is satisfied given he used a book by professor A ]=

= P[x / A ] = 200/500

= 0.4

Also

P[X/B] = 150/300 = 0.5

P [X/C] = 160/200 = 0.8

Also P(A ) = P(B ) = P(e) = 1/3

The probability that the student is satisfied with the textbook is givenby

P( x ) = P(A). P (x / A ) + P(B ). P( X/B ) + P(e ) P(x/e )

=1/3(0.4) + 1/3(0.5) + 1/3(0.8)

= 0.56667

Hence, The probability that the student is satisfied with the textbook is given by 56%

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The two facts that we can double to find 8 × 4  is (4 and 4) .

The Double Facts are the number that repeat two time .

For Example : 2 × 2  , 4 + 4 .

The two facts of a number that is doubled is represented as :

2 * b = c

the value of c is given as 8*4 = 32   .

2 * b = 32

dividing both sides of the equation 2 * b = 32 by 2 , we get

b = 32/2 ,

Simplifying further ,

we get ,

b = 16 .

which in double can be written as 4 × 4 ,

that means 2(4×4) = 2(16) = 32 .

Therefore , The two facts that we can double to find 8 × 4  is 4 and 4 .

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Angle of elevation in degrees is [tex]28.1[/tex]° .

Define angle of elevation.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

According to the question ,

Roof shape = isosceles triangle

base length = 30 m

and two sides each =  17 m.

Let it be in the middle ,such that the two 17 m beams will have the same angle of elevation .

Now , we have to find the angle of elevation such that we can split the roof in half vertically to create a right angled triangle.

The base will now be 15 m, and the hypotenuse will be 17.

Therefore we use a trigonometry function to solve for the angle. We know the hypotenuse and the side adjacent to the angle, so we can use cosine.

Now ,by trignometric formulas :

[tex]cos([/tex]Ф[tex])[/tex][tex]= \frac{adjacent side }{hypotenuse}[/tex]

[tex]cos([/tex]Ф[tex])=\frac{15}{17}[/tex]

Ф=cos inverse of [tex]\frac{15}{17}[/tex]

Ф[tex]= 28.1[/tex]°

Hence the angle is 28.1° .

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If the shoes that bridget purchased were all priced the same, each pair of shoes cost $37.52

Bridget purchased 3 pairs of shoes online.

The total bill of $126. 81 included a $7. 50 shipping charge and 6% tax on the total purchase

tax = 6% of x

= 3(6/100) x  = 0.18x

x - the price of each pair of shoes;

3 x + 7.50 + 0.06 * 3 x = 126.81

3 x + 0.18 x + 7.50 = 126.81

3.18 x = 126.81 - 7.50

3.18 x = 119.31

x = 119.31 : 3.18

x = 37.52

Therefore, If the shoes that bridget purchased were all priced the same, each pair of shoes cost $37.52.

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Possible combinations that can be formed a committee of 5 male and 2 female with at least 3 men that must be at the committee from 13 members is 28000.

What is combination?

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.

C (n, r) = n! (r! n-r!)

According to the given question:

8 males, 3 at a time = Comb (8,3) = 56

5 females, 2 at a time = Comb (5,2) = 10

So, the base combination of 5 males & 2 females from 8 possible males and 5 possible females = 56 x 10 = 560.

However, the total combinations are further expanded by the condition that 3, 4 or 5 of the 5 male members must be present

This expansion factor is the Comb (5,3) x Comb (5,4).

So, Comb (5,3) x Comb (5,4) = 10 x 5 = 50

Therefore, the combined total are 560 x 50 = 28,000 possible combinations of 5 of 8 possible males & 3 females of 5 possible females with 3, 4 or 5 of the males being present.

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Null hypothesis assumes that there is no relationship between the two variables( dependent and independent ).

As given in the question,

Following hypothesis assumes that there is no relationship between variables.

a. Alternate hypothesis: There is a relation between two variables.

b. Null hypothesis : There is no relation between two dependent and independent variables.

c. Secondary : It depends on the primary hypothesis.

d. Research : It is study of systematic inquiry after colleting data.

e. Substantive : research based on particular subject.

Therefore, null hypothesis assumes there is no relation between two variables.

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Answer: I got you

The answer is 2,160

Step-by-step explanation: I multiplied

Answer:

5) Perimeter = 41 ft

Step-by-step explanation:

Now we have to,

→ find the perimeter of triangle.

Formula we use,

→ P = a + b + c

Then the perimeter will be,

→ a + b + c

→ 8 + 15 + 18

→ 41 ft

Hence, the perimeter is 41 ft.

The probability that the center is up when the person’s call comes in is 2/5

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Solution:

Let us consider a random variable Y it presents the number of person’s call comes when center is up. Beginning at 12:00 midnight, a computer center is up for 1 hour and then down for 2 hours on a regular cycle.

We need to find  the probability that the center is up when the person’s call comes in.

Let 12:00 midnight be ‘a = 0’, then we will have ‘b = 5’, therefore f(y) = 1/5

For beginning of a = 0, the computer is up for 1 hour, so P(0<Y<1)

The computer is down for 2 hours and then up for another one hour, so P(3<Y<4)

Hence,

The probability that the center is up when the person’s call comes in is given by:

P(0<Y<1) + P(3<Y<4) = ∫f(y) dy + ∫f(y) dy

= (1/5)y + (1/5)y

= (1/5)((1-0)+(4-3))

= 2/5

Therefore, The probability that the center is up when the person’s call comes in is 2/5

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An unbiased sample that is a good depiction of the population as a whole is a representative sample

A representative sample is what?

A subset of a population is referred to as a "representative sample" when it aims to correctly reflect the traits of the broader group.The following characteristics must be present for the sample plan to accurately reflect the population: One of the key characteristics of item control is the evaluation of assessment by components, which contains methods for deciding on the aura of numerous individual units based on test estimations of units on the quality trademark being examined.

Consequently, the representative sample is an objective sample that accurately portrays the population as a whole.

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Total 8 angles are formed when parallel lines are cut by a transversal.There relationships are mentioned below.

When two lines don't intersect, they are said to be parallel. Parallel lines are two lines that run parallel to each other and meet at infinity.

A transversal is formed when a line intersects two lines at distinct points.

When a transversal intersects two or more parallel lines, various angle pairs are formed. As shown in the figure below, a and d are two parallel lines intersected by the transversal l at the points P and Q.

When a pair of parallel lines is transversally cut, 8 angles are formed, as shown in the figure.

The relationship between the angles are:

pair of angles was formed.                        Relationships between angles

Corresponding angle pairs.                  ∠1 = ∠6, ∠4 = ∠8, ∠2 = ∠5, ∠3 = ∠7

Alternate interior angles pairs.                     ∠4 = ∠5, ∠3 = ∠6

Alternate exterior angle pairs.                       ∠1 = ∠7, ∠2 = ∠8

Interior angle pairs that are on              ∠3 + ∠5 = 180°, ∠4 + ∠6 = 180°

same side of the transversal .

Vertically opposite angle pairs.         ∠7 = ∠6, ∠8 = ∠5, ∠1 = ∠3, ∠2 = ∠4,

Thus, total 8 angles are formed when parallel lines are cut by a transversal

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Refer to the attachment for graph:

What is rotation ?

The rotation of a point with regard to the origin is described by the rotation formula. To get the position of the point after rotation, apply the rotation formula. Rotation is a circular movement about the specific axis or point of rotation. In general, there are two common directions for rotation: clockwise and anti-clockwise or counter-clockwise.

An object moving in a circle around its center is said to as rotating. Rotation can occur in a variety of ways. Earth's rotative motion

During 180° rotation about origin,

the x and y coordinates changes to their negative values.

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The actual price an employee would pay for 1200 is 1050.

Given:

In a particular shop employee are given a 12. 5% discount on any item they purchase.

Let x be the actual price.

= 1200*12.5%

= 1200*12.5/100

= 1200*125/1000

= 12*125/10

= 12*25/2

= 6*25

= 150

Actual price x = 1200 - 150

= 1050

Therefore The actual price an employee would pay for 1200 is 1050.

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No, f (x) =9x^4+8x^3-6x^-2+2x is not a polynomial function.

We can define the polynomial function that are expressed in the form of polynomial. it must involves only non-negative integer powers or only positive integer exponents. The highest power of polynomial function is known as its degree. Domain of polynomial function is entire real numbers(R).

P(x) =[tex]a_{n}[/tex] [tex]x^{n}[/tex]  + [tex]a_{n-1}[/tex] [tex]x^{n-1}[/tex]+.……….…+[tex]a_{2}[/tex][tex]x^{2}[/tex] +[tex]a_{1}x[/tex] +[tex]a_{0}[/tex],

The function having power in the form of fraction, negative integer or having division in function will not be called as polynomial function.

From the question, we know that,

f (x) =9x^4+8x^3-6x^-2+2x

coefficient of 9 has power 4,

coefficient of 8 has power 3

coefficient of 6 has negative power -2

coefficient of 2 has power 1

but it is not a polynomial function because coefficient of 6 has negative power -2.

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