Eliza took a friend for a birthday dinner. The total bill for dinner was $32.22 (including tax and a tip). If Eliza paid a 19.3% tip, what was her bill before adding the tip? (Round your answer to the nearest cent.)

Answer:

B

Step-by-step explanation:

A monomial is a single number or a number multiplied by one or more variables. A sum of monomials is a polynomial.

Since the only thing you can do with variables in a monomial is multiply them by other variables or by numbers, you cannot have a variable in the denominator or a variable in a square root.

Choices A, C, and D have either a variable in a denominator or in a root. That means they are not polynomials.

Answer: B

Answer:

The answer is 7.1cm to 1d.p

Step-by-step explanation:

Area of square =L²

25=L²

√L²=√25

L=5cm

hyp²=opp²+adj²

x²=5²+5²

x²=25+25

x²=50

√x²=√50

x=7.1cm to 1d.p

To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.

Answer:

a

\(\= x = 40.85\)

b

\(E = 5.85\)

Ca  

   \(t_c =  2.08 \)

Cb

   \( t_c  =   1.282 \)

Explanation:

From the question we are told that

     The sample size is n  =  100

     The upper limit of the 95% confidence interval is  b =  47.2 years

     The lower limit of the 95% confidence interval is   a =  34.5 years

Generally the sample mean is mathematically represented as

         \(\= x = \frac{a + b }{2}\)

=>    \(\= x = \frac{47.2 + 34.5 }{2}\)

=>    \(\= x = 40.85\)

Generally the margin of error is mathematically represented as

         \(E = \frac{b- a }{ 2}\)

=>      \(E = \frac{47.2- 34.5 }{ 2}\)

=>      \(E = 5.85\)

Considering question C a  

From the question we are told the confidence level is  90% , hence the level of significance is    

      \(\alpha = (100 - 90 ) \%\)

=>   \(\alpha = 0.10\)

The  sample size is  n =  22

Given that the sample size is not sufficient enough i.e \(n < 30\) we will make use of the student t distribution table  

Generally the degree of freedom is mathematically represented as

           \(df = n- 1\)

=>        \(df = 22 - 1\)

=>        \(df = 21\)

Generally from the student  t  distribution table the critical value  of  \(\frac{\alpha }{2}\) at a degree of freedom  of  21 is  

   \(t_c =t_{\frac{\alpha }{2} ,  21  } =  2.08 \)

Considering question C b

From the question we are told the confidence level is  80% , hence the level of significance is    

      \(\alpha = (100 - 80 ) \%\)

=>   \(\alpha = 0.20\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \( t_c  =Z_{\frac{\alpha }{2} } =  1.282 \)

Answer:

The correct answer is B, I took the test :)

You just turn the percentages into decimals

The probability distribution table is formed clearly in the answer part.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The probability for all the elements in the sample space can be shown in one table known as distribution table.

Suppose X be the event of choosing a major.

Then, its probability can be given as P(X).

Here, the percent value of a given event is equivalent to their probability.

It can be represented in the form of table as,

X (Major chosen by student)                              P(X) (Probability)

    Math                                                                    3% = 0.03

   Nursing                                                                22% = 0.22

  Psychology                                                           16% = 0.16

 Criminal justice                                                      11% = 0.11

   Business                                                              48% = 0.48

This table is known as the probability distribution table.

Hence, the probability distribution table is formed by calculating the probability for each of the events.

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Answer:

Part a

For this case n = 4. If we use the future value formula we got:

\( A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506\)

Part b

For this case n = 365. If we use the future value formula we got:

\( A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776\)

Step-by-step explanation:

We can use the future vaue formula for compound interest given by:

\( A= P(1+ \frac{r}{n})^{nt}\)

Where P represent the present value, r=0.0675 , n is the number of times that the interest is compounded in a year and t the number of years.

Part a

For this case n = 4. If we use the future value formula we got:

\( A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506\)

Part b

For this case n = 365. If we use the future value formula we got:

\( A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776\)

Answer:

the experimental probability that the next vase produced at the factory will be chipped is 1/5.

Step-by-step explanation:

Since 5 out of the 13 boats that docked were from North Carolina, the experimental probability of the next boat being from North Carolina is the number of favorable outcomes (i.e., the number of boats from North Carolina) divided by the total number of outcomes (i.e., the total number of boats that docked).

Therefore, the experimental probability that the next boat to dock will be from North Carolina is:

P(North Carolina) = 5/13

For the second question:

Since 2 out of the last 10 vases produced were chipped, the experimental probability that the next vase will be chipped is:

P(chipped) = 2/10 = 1/5

Therefore, the experimental probability that the next vase produced at the factory will be chipped is 1/5.

Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Answer:

Item price now= 3.95

Step-by-step explanation:

To find out the price now, we will subtract 79 (original price) by 95% of 75. That will equal the discounted price. Finding the percentage of anything, we can use the formula, Total amount•percentage/100. The total amount is 79, and the percentage is 95. 79•95=7505, 7505/100=75.05. Now, 95% of 79 is 75.05, 79-75.05=3.95. $3.95 is the price now of the item. Though, I am unsure what a ALEKS calculator is. Have a nuce time, and joyful day

Answer:

400.00

Step-by-step explanation:

is that what you meen ?

Hello, the answer is $450.

Here's how I got the answer...

We know Bill earns $10 per hour.. He works 40 hours at regular rate, which would make about $400.

He then works for 2 more hours, makes that $20..

He also then works for 3 more hours, makes that $30..

Now you add that up. The answer would be $450.

Answer:

VUS, UST

Step-by-step explanation:

There are 2 and a half hours between 11:00 am and 1:30 pm. This is equivalent t o 5 periods of 30 minutes

cells | periods of 30 min

2 | 0 (11:00 am)

3*2=6 | 1 (11:30 am)

3*6=18 | 2 (12:00 pm)

3*18=54 | 3 (12:30 pm)

3*54=162 | 4 (1:00 pm)

3*162=486 | 5 (1:30 pm)

Answer:

x-10x3

Step-by-step explanation:

Because there are 3 thousands... and 3 times 10 is 30 so the total -30 is the amount that it drops

Answer:

10,000 I think.

Step-by-step explanation:

10 x 1000. Put the 0 at the back. So it has 4 zero and so you put the zero at the back and what is 1 x 1 well it's 1, so it's 10,000. I think.

Answer:

$988.93 would be the total

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Answer:

alrighty

Step-by-step explanation:

Answer:

1: 35,620 -> 35,600 -> 36,000 -> 40,000

2: 54,390 -> 54,400-> 54,000 -> 50,000

3: 159,100 -> 160,000 -> 200,000

4: 90,890 -> 90,900 -> 91,000 -> 90,000

5: 39,739 -> 39,740 -> 40,000

6: 9,650 -> 9,600 -> 10,000

7: 12,450 -> 12,500 -> 13,000 -> 10,000

Step-by-step explanation:

Answer:

a) Heptagon

b) Pentagon

c) Octagon

d) Hexagon

The names of the polygon are :

1)  Heptagon

2) Pentagon

3) Octagon

4) Hexagon

Given,

Polygons figure.

Here,

The name of polygon is decided based on the number of sides present in it.

Now in the figures,

1) Number of sides : 7

Name = Heptagon

2) Number of sides : 5

Name : Pentagon

3) Number of sides : 8

Name : Octagon

4) Number of sides : 6

Name : Hexagon

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Answer:

Positive correlation, but not causal

Answer: positive correletion/casual

Step-by-step explanation:

The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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The absolute maximum and absolute minimum of f(x,y) = 3 + xy -x - 2y is f(0,0) and f(1,1) respectively.

The absolute maximum point is a point where the function obtains its greatest possible value.

And Absolute minimum is a point where the function obtains its least possible value. This is the smallest value that a mathematical function can have over its entire curve.

Given equation is, f(x,y) = 3 + xy - x - 2y

we will check absolute maximum and absolute minimum of f(x,y) at the points (0,0), (1,0), (1,1).  

f(0,0) = 3 + (0)(0) - 0 - 2(0) = 3

f(1,0) = 3 + (1)(0) - 1 - 2 (0) = 2

f(1,1) = 3 + (1)(1) - 1 - 2(1) = 1

Therefore we get absolute maximum at f(0,0) and absolute minimum at f(1,1).

An absolute minimum also called a global minimum, occurs when a point of the function is lower any other point on the function within the function's domain. A local minimum also called relative minimum occurs when a point is lower than the points surrounding it.

Given question is incomplete. Complete question is:

find the absolute maximum and absolute minimum of f (x, y) = 3 + xy - x -2y  among points in the triangle with vertices (0, 0), (1, 0), and (1, 1).

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Answer:

the set of parametric equation would be x(t) = 0.25t, y = 0.43t

Step-by-step explanation:

The computation of the set of parametric equation would be

x(t) = 0.5 cos 60 degrees t , y = 0.5 sin 60 degrees t

x(t) = 0.5 × 0.5t , y = 0.5 × 0.866 t

x(t) = 0.25t, y = 0.43t

Hence the set of parametric equation would be x(t) = 0.25t, y = 0.43t

The same is to be considered

The above equation represents the answer

For the entire practice:

1) B, \(x(t)=0.25t\) and \(y(t)=0.43t\)

2) B, 4 ft.

3) A, \(x=27.82\), \(y=-4.9t^2+11.24t\), horizontal distance = 63.71 m

Answer:

do 50/6 which is 8.333 repeating that is the amount of gallons per hour so then divide 150 by 8.333 repeating for your answer so 150/8.33 which is 18.00072 so 18.00072 hours is the answer. I hope this helps!

Step-by-step explanation:

Answer:

g(x) can be written in terms of f(x) as g(x) = f(x) - 3.

Step-by-step explanation:

To write g in terms of f, we can use the substitution f(x) = x^2 as follows:

g(x) = f(x) - 3

= x^2 - 3

Therefore, g(x) can be written in terms of f(x) as g(x) = f(x) - 3.

Answer:

\(\text{27}\)

Step-by-step explanation:

Given that :

\(\text{Dimension of poster board} = 1 \ \text{yd} \ \text{by} \ 1 \ \text{yd}\)

\(\text{Dimension of each poster board} = \dfrac{1}{3} \ \text{yd} \ \text{by} \ \dfrac{1}{9} \ \text{yd}\)

Number of poster signs that can be cut :

\(\text{Area of poster sign} = \dfrac{1}{3} \times \dfrac{1}{9} = \dfrac{1}{27} \ \text{yard}^2\)

\(\text{Area of poster board} = 1 \ \text{yard}^2\)

Number of poster signs that can be cut :

\(\dfrac{\text{Area of poster board}}{\text{Area of poster sign}}\)

\(1 \ \text{yard}^2\div (\dfrac{1}{27} ) \ \text{yard}^2\)

\(1 \div \dfrac{1}{27}\)

\(1 \times \dfrac{27}{1}\)

\(\bold{= 27 \ poster \ signs}\)

The value οf P(x > 104) is 0.1587 οr apprοximately 15.87%.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο find the prοbability οf P(x > 104) fοr a nοrmal distributiοn with mean οf 98 and standard deviatiοn οf 6, we need tο standardize the value οf 104 using the fοrmula:

z = (x - μ) / σ

where z is the standard scοre, x is the value we want tο find the prοbability fοr, μ is the mean οf the distributiοn and σ is the standard deviatiοn.

Plugging in the values, we get:

z = (104 - 98) / 6 = 1

Nοw we need tο find the area tο the right οf this value οn the standard nοrmal distributiοn table οr calculatοr.

Using a standard nοrmal distributiοn table οr calculatοr, we find that the area tο the right οf z = 1 is 0.1587.

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Answer:

b = 59

Step-by-step explanation:

Angle b and 59 are vertical angles and vertical angles are equal

b = 59