The total cost to tile a rectangular floor measuring 231 feet by 37 feet, with tile costing $14 per square foot, will be $119,658.
Explanation:To find the cost of tiling a rectangular floor, first, calculate the area of the floor which is the length times the width. In this case, the rectangle is 231 feet by 37 feet so its area is 231 x 37 = 8,547 square feet.
With the tile costing $14 per square foot, the total cost will be the area of the floor times the cost per square foot. This can be calculated by multiplying 8,547 square feet x $14 per square foot = $119,658.
Therefore, the total cost to tile the rectangular floor will be $119,658.
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Express the complex number in trigonometric form. -2 + 2square root of three i
Answer:
The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]
Step-by-step explanation:
Given : Complex number [tex]-2+2\sqrt{3}i[/tex]
To find : Express the complex number in trigonometric form?
Solution :
The complex number [tex]a+ib[/tex] trigonometric form is [tex]r(\cos\theta+i\sin\theta)[/tex]
Where, [tex]r=\sqrt{a^2+b^2}[/tex]
and [tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]
On comparing with given complex number [tex]-2+2\sqrt{3}i[/tex]
a=-2 and [tex]b=2\sqrt{3}[/tex]
Substitute the value,
[tex]r=\sqrt{a^2+b^2}[/tex]
[tex]r=\sqrt{(-2)^2+(2\sqrt{3})^2}[/tex]
[tex]r=\sqrt{4+12}[/tex]
[tex]r=\sqrt{16}[/tex]
[tex]r=4[/tex]
[tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]
[tex]\theta=\tan^{-1}(\frac{2\sqrt3}{-2})[/tex]
[tex]\theta=\tan^{-1}(-sqrt3)[/tex]
[tex]\theta=\tan^{-1}(\tan(-60))[/tex]
[tex]\theta=-60[/tex]
Substituting all values in the formula,
[tex]r(\cos\theta+i\sin\theta)[/tex]
[tex]4(\cos(-60)+i\sin(-60))[/tex]
[tex]4(\cos(60)-i\sin(60))[/tex]
Therefore, The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]
Write an equation of a line containing (2, 1) and (3, 4) in point-slope form.
A box contains 16 transistors, 5 of which are defective. if 5 are selected at random, find the probability that
a. all are defective. and. none are defective.
A - all defective
B - none defective
[tex] \displaystyle
|\Omega|=\binom{16}{5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{2\cdot3\cdot4\cdot5}=4368\\
|A|=1\\
|B|=\binom{11}{5}=\dfrac{11!}{5!6!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\\\
P(A)=\dfrac{1}{4368}\approx0.02\%\\
P(B)=\dfrac{462}{480480}=\dfrac{1}{1040}\approx0.1\% [/tex]
A 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours. Assuming the variables are directly related, how many hours would a 9-ounce candle be expected to burn?
18
27
33
45
Answer:
B. 27.
Step-by-step explanation:
We have been given that a 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours.
We know that a direct proportional equation is in form [tex]y=kx[/tex], where k represents constant of proportionality.
Let is find value of k by substituting [tex]x=20[/tex] and [tex]y=60[/tex] in above equation as:
[tex]60=k*20[/tex]
[tex]\frac{60}{20}=\frac{k*20}{20}[/tex]
[tex]3=k[/tex]
The equation [tex]y=3x[/tex] represents our given direct proportional relation.
Now, we will substitute [tex]x=9[/tex] to solve for y as:
[tex]y=3*9[/tex]
[tex]y=27[/tex]
Therefore, a 9-ounce candle would be expected to burn for 27 hours and option B is the correct choice.
Which sequence is modeled by the graph below? coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8)
a. an = 1(2)n − 1
b. an = 2(1)n − 1
c. an = 1 + (2)n − 1
d. an = (2)(n − 1)
Answer: The correct option is d.
Explanation:
From the given information it is noticed that the coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8).
The coordinates are in the form of (x,y), it means the value of xth term of the sequence is y.
The point (1,1) represents that the first term is 1. Similarly from (2, 2) (3, 4) and (4, 8) points we can say that the second term is 2, third term is 4 and fourth term is 8.
The sequence is 1,2,4,8.
It can be written as,
[tex]2^0,2^1,2^2,2^3[/tex]
Since the base is common that is 2 and the power is one less than the position of term. So the sequence is in the form of,
[tex]a_n=2^{n-1}[/tex]
Therefore, the correct option is d.
An integer greater than 1 that is not prime is called composite. if the two-digit integer n is greater than 20, is n composite?
If the person can't accommodate and the glasses is + 2.50d, at which distance will the person see clearly
Answer:
40 cm or 2/5 of a meter.
Step-by-step explanation:
A short-sighted person, at a positive diopter, will take an estimation of about 2.5 and make it the denominator by 1 as the numerator to find out the distance (in meters) that they can see clearly.
We can find the value of f, given the value for P:
P = +2.50
f = 1 / p = 1 / 2.50
(changing the units, it will be) ---> 100 / 2.50 which is equal to 40 cm.
Therefore, 40 cm which is 2/5 of a meter is the distance a person with glasses +2.5d can see clearly.
If a single die is rolled twice there are how many possible outcomes
You plan on financing a new road bike for $2,500. The bike shop offers a 13.5% APR for a 24 month loan. Use this information, and the table above, to determine the monthly payments. Round your answer to the nearest cent.
A pretzel maker was interested in knowing the number of pretzels in each bag it sold. The results of their research are shown in the box-and-whisker plot. What is the median number of pretzels?
The median number of pretzels is 54.
What is Box and whisker plot?The lower and upper quartiles are represented by the left and right sides of the box in a box and whisker plot. The box encompasses the interquartile interval, which contains 50% of the data. The median is the vertical line that divides the box in half. On the box plot, the mean is sometimes shown by a dot or a cross.
From the given box plot we can have the following information:
Minimum = 45
Lower Quartile = 47
Median= 54
Upper Quartile= 61
Maximum = 68
Thus, the Required median is 54.
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Find the area of the surface of the part of y=4x+z^2 that lies between the planes
What did the prince do whenever he found a girl who might be cinderella
Final answer:
When a prince in fairy tales finds a potential Cinderella, he typically engages in a quest to determine if she is the one, reflecting the theme of male heroism and romantic pursuit found in traditional literature and films.
Explanation:
The passage raises the theme of romantic endeavors and the traditional role of women in classical literature and film, typically anchored within the context of royalty and fairy tales. When the prince in such stories finds a girl that could potentially be Cinderella, typically he would engage in a quest to discover if she truly is the one - often symbolized by a glass slipper fitting or other identifying item. This quest underscores the narrative of countless romantic tales where the male lead seeks to find and often rescue his female counterpart, a concept reflected in various Disney princess movies.
In the greater realm of literature and films, the prince often represents the chivalrous savior. This tradition is evident in the series of princess-centric stories produced by Disney, where a common girl becomes royalty by marriage or starts as a princess whose ultimate happiness is achieved through romance. Although contemporary stories may showcase more agency in their female protagonists, the motif of the male hero remains prevalent.
can someone please explain the steps to solve these questions.
WZ and XR are diameters of circle C. The diagram is not drawn to scale.
What is the measure of convex arc upper ZWX?
The measure of convex arc upper ZWX is 180 degrees.
Explanation:The measure of convex arc upper ZWX can be found by considering the angles formed by the diameters WZ and XR. Since WZ and XR are diameters of the circle, they intersect at the center of the circle. The angle formed by the diameters at the center is a right angle, which means that arc upper ZWX is a semicircle. A semicircle has a measure of 180 degrees. Therefore, the measure of convex arc upper ZWX is 180 degrees.
What is the value of y in the equation 2(3y + 6 + 3) = 196 − 16?
The spoke of a wheel reaches from the center of the wheel to its room if the circumference of the rim of the wheel is 42 inches how long is each spoke
Look at the figure rectangle PQRS, find m angel P
Answer: [tex]144^{\circ}[/tex]
Step-by-step explanation:
In the given figure , we have given a parallelogram .
We know that the opposite sides and angles of a parallelogram are equal.
Thus from the given parallelogram PORS we have
[tex]\angle {Q}=\angle {S}\\\\\Rightarrow\ (4\alpha-12)^{\circ}=3\alpha^{\circ}\\\\\Rightarrow\ 4\alpha-12=3\alpha\\\\\Rightarrow 4\alpha-3\alpha=12\\\\\Rightarrow\ \alpha=12[/tex]
Also, the value of angle p is given by :-
[tex]\angle {P}=12\alpha^{\circ}\\\\\Riightarrow\ \angle {P}=12(12)^{\circ}\\\\\Riightarrow\ \angle {P}=144^{\circ}[/tex]
Slips of paper numbered 1 through 14 are placed in a hat. in how many ways can two numbers be drawn so that the sum of numbers is 12
A multiple choice test has 9 questions each of which has 5 possible answers
WILL MARK BRAINLIEST
There are 50 red beans and 50 white beans in a bag. The first bean selected is red. The red bean is returned to the bag. What are the chances of the second bean selected being red?
Recently, the texas junior college teachers association annual conference was held in austin. at the time a taxi ride in austin was $ 1.75 $1.75 for the first 1 5 15 of a mile and $ 0.25 $0.25 for each additional 1 5 15 of a mile. if the distance from one of the convention hotels to the airport is 5.8 5.8 miles, how much will it cost to take a taxi from that hotel to the airport?
To calculate the total taxi fare in Austin, first calculate the initial fee for the first 1/15 mile and then the cost for each additional 1/15 mile. For 5.8 miles, the total cost amounts to $23.25, comprising a $1.75 initial fare and $21.50 for the subsequent distance.
Let's break down the cost of a taxi ride based on the given pricing structure. To find the total cost of a taxi ride for a given distance, we need to calculate the cost for the first 1/5 mile and the additional cost for the remaining distance.
The initial cost for the first 1/5 mile is given as $1.75.
We know the total distance is 5.8 miles. Since the first 1/5 mile is included in the initial cost, the distance to be charged in increments of 1/5 mile is:
[tex]\[ 5.8 - \frac{1}{5} = 5.8 - 0.2 = 5.6 \, \text{miles} \][/tex]
To find the number of 1/5 mile increments in 5.6 miles, divide by 0.2:
[tex]\[ \frac{5.6}{0.2} = 28 \][/tex]
Thus, there are 28 additional 1/5 mile increments.
Each additional 1/5 mile increment costs $0.25. Thus, the total cost for the additional distance is:
[tex]\[ 28 \times 0.25 = 7.00 \][/tex]
The total cost is the initial cost plus the cost for the additional distance:
[tex]\[ 1.75 + 7.00 = 8.75 \][/tex]
Thus, the total cost to take a taxi from the hotel to the airport, given a distance of 5.8 miles, is $8.75.
How many questions can i miss on a 28 question test to get a 70%?
please help...
The radius of the planet is 4100 miles. Find the distance d to the horizon that a person can see on a clear day from a height of 1298 feet above the planet. (hint: use the conversion 1 mile = 5280 ft) Round your answer to the nearest 10th, and don't forget to convert feet to miles.
HELP ! I've been stuck on this for over 15 mins. :(
What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5?
an = 8 − 5(n − 1); all integers where n ≥ 1
an = 8 − 5(n − 1); all integers where n ≥ 0
an = 8 − 3(n − 1); all integers where n ≥ 1
an = 8 − 3(n − 1); all integers where n ≥ 0
what are solutions to the equation sinx cosx = square root 3 over4
Center c of the circle above has coordinates of (4, 3). what is the circumference of the circle?
Norma stopped to get gas for her car before beginning a trip. her odometer read 2587 miles, and she filled up her tank with 26 gallons. at the end of her trip, her odometer read 3295 miles. what is her car's miles per gallon?(round to the closest gallon)
Please help i'm really confused.
0! = 0
True
False
What is log base 5(4*7 )+log base 5 of 2 written as a single log?
A.log base 5 of 21
B.log base 5 of 26
C.log base 5 of 30
D.log base 5 of 56
Answer:
D. log base 5 of 56
Step-by-step explanation:
Since, by the multiplication law of logarithm,
[tex]log_a(m)+log_a(n) = log_a(mn)[/tex]
Given expression is,
log base 5(4*7 )+log base 5 of 2
[tex]=log_5(4\times 7)+log_5(2)[/tex]
[tex]=log_5(28)+log_5(2)[/tex]
By the above property,
[tex]=log_5(28\times 2)[/tex]
[tex]=log_5(56)[/tex]
= log base 5 of 56
Hence, Option D is correct.
able below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often? Male Female Total Blue Car 0.04 0.12 0.17 Black Car 0.08 0.06 0.13 White Car 0.11 0.20 0.31 Gray Car 0.02 0.09 0.11 Red Car 0.17 0.10 0.27 Total 0.43 0.57 1.00
Answer:
31%
Step-by-step explanation:
Answer:
31%
Step-by-step explanation: