An isosceles triangle is a triangle which has two of its sides with the same length
The office floor is 250 ft. X 80 ft. The conference room floor is 50 ft. X 20 ft. , which covers __?__ of the office
The percentage of area covered by the conference room is 5%.
What is area?
A region's size on a flat or curved surface is expressed in terms of area, a unit of measurement. A surface region or plane area is the area of an open surface or the boundary of a three-dimensional object, whereas a plane region or area refers to the area of a form or planar lamina.
The quantity of unit squares necessary to completely encompass a form is its area. In order to express and measure it, square units are used.
Given, the dimension of office as
Length= 250 ft and breadth is 80 ft
Area of office = length ×breadth = 250 ×80 = 20,000
Length of conference room = 50 ft
Breadth of conference room = 20 ft
Area = 50 (20) = 1000
Percentage of office covered by conference room is given as:
1000/20000×100=5
Hence, 5% is occupied
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The domain of a function f(x) is x< 4, and the range is y≤ 0. What are the
domain and range of its inverse function, f-¹ (x)?
A. Domain: x≤0
Range: y< 4
B. Domain: x<0
Range: y≤ 4
C. Domain: x24
Range: y> 0
D. Domain: x < 4
Range: y≤ 0
Answer:
Step-by-step explanation:
d
Selwyn wanted to place point V on the same number line to represent the opposite number of point W . Which instruction should he follow to place point V
Move ten units to the left of point W.
1) Counting the marks on the number line, we can tell that Selwyn placed point V 5 units to the right of zero.
2) Since we need to find the opposite number, we need to find the negative 5 ( -5). Hence, we need to:
Move ten units to the left of point W.
Because we need to remember that the reference is not zero but W.
The measures of the angles of a triangle are shown in the figure below. Solve for x.
50°
(6x-18)°
70°
Answer:
x=13
Step-by-step explanation:
We add all the numbers together, and all the variables
6x-78
We move all terms containing x to the left, and all other terms to the right
6x=78
x=78/6
which should equal 13
In a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle. find the measure of all 3 angles. Hint: the angles of a triangle add up to 180.
The three angles of the triangle are 22.5, 67.5 and 90 degrees.
How to find the angles of a triangle?A triangle is a polygon with three sides.
The sum of angles in a triangle is 180 degrees.
Therefore, the angles of the triangle can be found as follows;
In the triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle.
Therefore,
let the smallest angle = x
Therefore, the three angles are as follows;
x3x45 + 2xTherefore,
x + 3x + 45 + 2x = 180
6x + 45 = 180
6x = 180 - 45
6x = 135
divide both sides by 6
x = 135 / 6
x = 22.5
Therefore, the three angles are as follows;
22.5 degrees22.5 × 3 = 67.5 degrees45 + 22.5(2) = 90 degreeslearn more on triangle here: https://brainly.com/question/15386380
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Use the point-slope formula to write an equation of the line that passes through (0,6) and (-2,0) write answer in slope intercept form
Equation using slope intercept form is 3y = x + 18
What is slope intercept form?An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx + b, where m denotes slope and c denotes the y-intercept. Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.
Given Data
Points(0,6) and (-2,0)
The slope formula = [tex]\frac{y_{2}-y_{1 } }{x_{2}-x_{1} }[/tex]
y₂= 0
y₁=6
x₂=-2
x₁=0
Slope = (-2-0)/(0-6)
Slope = -2/ -6
Slope = 1/3
Slope intercept form
y = mx + b
y = (1/3)x + 6
y = (x+18)/3
3y = x + 18
Equation using slope intercept form is 3y = x + 18
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What’s the correct answer answer asap i need help can somebody answer this question?
il give you brainlist
Answer: A
Step-by-step explanation:
What is the measure of ZABD? What is the reason?60° , isosceles triangle theorem48°, equilateral triangle theoremCO 48°, isosceles triangle theorem60° , equilateral triangle theoremB66°DA
Consider the traingle ABD,
The side AB and A are equal means that angle A is equal to angle D.
Determine the angle B of traingle ABD by using angle sum property of triangle.
[tex]\begin{gathered} \angle A+\angle B+\angle D=180^{\circ} \\ 66^{\circ}+66^{\circ}+\angle B=180^{\circ} \\ \angle D=48^{\circ} \end{gathered}[/tex]So angle D is of 48 degree and two sides are equal so isoceles traingle theorem is used for angle measurement. Option C is correct.
Sue used 4 ounces of dark chocolate chips for every 3 ounces of white chocolate chips if she uses 21 ounces of chips altogether how many ounces of dark chocolate chips did she use
Answer: 12 oz
Step-by-step explanation:
Answer: 12
Step-by-step explanation:
Suppose a hospital would like to estimate the proportion of patients who feel that physicians who care for them always communicated effectively when discussing their medical care. A pilot sample of 40 patients found that 28 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 90% confidence interval with a margin of error equal to 2% to estimate this proportion.
Part 1
The additional number of patients that need to be sampled is
(Round up to the nearest integer.)
174 more patients need to have their samples taken than were originally anticipated. This is further explained below.
What is a Marginal error?Generally, the equation for the margin of error is mathematically given as
[tex]{Margin\ of \ error } & \ amp;=Z_{o \text { it }} \text { at } 5 \% \text { lo.s } \times S E(p)[/tex]
Where
Z is the distributionSE is the standard deviationGiven that the margin of error should be 7%, or 0.07, the total number of extra patients is denoted by n.
sample proportion = 11/20 = 0.55
q =0.45
Margin of error = Zo at 5% lo.s * S E(p)
To solve for the 0.07amp
[tex]\\\\0.07 =1.96 \times \sqrt{\frac{p q}{n}}[/tex]
[tex]\\\\&0.07=1.96 \sqrt{\frac{0.55 \times 0.45}{20+n}} \\\\0.07 =\frac{0.97508}{\sqrt{20+n}} \\\\\sqrt{20+n} =\frac{0.97508}{0.07} \\\\\end{aligned}[/tex]
20+n =194.04
n =174.04
n=174
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f(x)=x^2+6x+7
f(x+h)=?
f(x+h)-f(x)=?
f(x+h)-f(x)/h=?
The values are;
f (x + h) = x² + 2xh + h² + 6x + 6h + 7
f (x + h) - f (x) = h² + 2xh + 6h
f (x + h) - f (x) / h = h + 2x + 6
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The value of the function is;
f (x) = x² + 6x + 7
Now, Find the given values of f (x + h) , f (x + h) - f (x) and f (x + h) - f (x) / h by substitution method.
The value of the function is;
f (x) = x² + 6x + 7
Substitute x = x + h;
The value of the function is;
f (x + h) = (x + h)² + 6(x + h) + 7
= x² + 2xh + h² + 6x + 6h + 7
Thus, The value of f (x + h) = x² + 2xh + h² + 6x + 6h + 7.
Now,
f (x + h) - f (x) = (x² + 2xh + h² + 6x + 6h + 7) - (x² + 6x + 7)
= x² + 2xh + h² + 6x + 6h + 7 - x² - 6x - 7
= h² + 2xh + 6h
Thus, The value of f (x + h) - f (x) = h² + 2xh + 6h.
Now,
f (x + h) - f (x) / h = h² + 2xh + 6h / h
= h (h + 2x + 6) / h
= h + 2x + 6
Thus, The value of f (x + h) - f (x) / h = h + 2x + 6.
Therefore, The values are;
f (x + h) = x² + 2xh + h² + 6x + 6h + 7
f (x + h) - f (x) = h² + 2xh + 6h
f (x + h) - f (x) / h = h + 2x + 6
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If a 1/3 cup serving of cheese provides your fully daily value of calcium, then what percentage of your daily value of calcium is provided by 3/4 cup of the cheese?
If a 1/3 cup serving of cheese provides your full daily value of calcium, then 225% of your daily value of calcium is provided by ¾ cup of the cheese.
What are the ratios rules?Between amounts of the same sort, the ratio should exist. The units used to compare two items should be comparable.
Terms should be in a meaningful sequence. If two ratios are comparable to one another like fractions, they may be compared.
An easy ratio Is what?When both sides are whole numbers and cannot be split by another
whole number, a ratio is considered to be in its simplest form.
Think about full number ratios, such as 6:4. The fraction 64 can be used to represent it.
What proportion of your daily intake of calcium is delivered by 3/4 cup of the food if a serving of cheese that is 1/3 cup in size delivers your whole daily value of calcium?Daily value of calcium= (3/4)/(1/3) = 9/4
3/4 cup gives you 9/4 of your daily value of calcium.
We can convert fractions to percentages, we will get
9/4= 2.25
2.25*100=225%
Then the percentage of your daily value of calcium is 225%.
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How could you correctly rewrite the equation 6(11-3) = 4(7 + 5) using the distributive property?
66-3 = 28 +35
Answer:
The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c );
Step-by-step explanation:
6(11-3) = 4(7 + 5)
(6×11)-(6×3)=(4×7)+(4×5)
66 - 18 = 28 + 20
Find 98.6% of 343.7. Round to the nearest thousandth.
Percentage, a relative value indicating hundredth parts of any quantity.
98.6% of 343.7 is in nearest thousandth 338.888
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
We need to find 98.6% of 343.7.
Ninty eight point six percentage of three hundred forty three point seven.
Ninty eight point six percentage we need to convert into decimal number this can be achieved by dividing with 100.
98.6% =98.6/100
When ninty eight point six is divided by hundred we get zero point nine eight six.
=0.986
We need to find what is 98.6% of 343.7.
To find ninty eight point six percentage of three hundred forty three point seven. we are required to multiply the converted value of 98.6% with three hundred forty three point seven.
Simply we need to multiply 0.986 with 343.7.
=0.986×343.7
=338.888
Hence 98.6% of 343.7 is 338.888
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Show all work for full credit.
Sketch the following curves, indicating all relative extreme points and inflection points. (10 pts)
a. y= x^3-6x^2+9x+3
For the given function, it is found that:
The extreme points are given by: (3,3) and (1,7).The inflection point is: (1,7).What are the extreme points of a function?The extreme points of a function happen at the values for x for which the first derivative is zero, that is:
y' = 0.
In this problem, the function is:
y = x³ - 6x² + 9x.
Hence the first derivative is:
3x² - 12x + 9.
The extreme values of x are:
3x² - 12x + 9 = 0.
3(x² - 4x + 3) = 0
x² - 4x + 3 = 0
(x - 3)(x - 1) = 0.
Then:
x - 3 = 0 -> x = 3.x - 1 = 0 -> x = 1.The numeric value of the function at these points is:
x = 3: y = 3³ - 6(3)² + 9(3) + 3 = 3.x = 1: y = 1³ - 6(1)² + 9(1) + 3 = 7.Hence the points are:
(3,3) and (1,7).
What are the inflection points of a function?The extreme points of a function happen at the values for x for which the second derivative is zero, that is:
y'' = 0.
For this problem, the second derivative is given by:
y'' = 6x - 12.
Hence the x-coordinate of the inflection point is:
6x - 12 = 0
6x = 12
x = 2.
The numeric value at x = 2 is:
2³ - 6(2)² + 9(2) + 3 = 5.
Then the inflection point is:
(2,5).
The graph with these points labeled is given at the end of the answer.
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The probability that an adult is actively looking for a job is 0.18. The probability of an adult being unemployed and actively looking for a job is 0.04. What is the probability of an adult being unemployed given that they are actively looking for a job?
The probability of an adult being unemployed given that they are actively looking for a job is 0.22.
How to calculate the probability?It should be noted that probability gas to do with the likelihood that something will occur.
Remember the multiplication rule for conditional probability:
P(B AND A)=P(B|A)P(A)
Rearranging, we see thatP(B|A)=P(B AND A)P(A)
So if we think of A as being the event that an adult is actively looking for a job and B as the event that an adult is unemployed, then we can plug in the known information to find
P(B|A)=0.04 + 0.18
≈0.22
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PLEASEE I NEED HELP!!
Figure 3 can also be created by transforming figure 1 with a sequence of two transformations. Which statement describes a possible sequence of transformations that transforms figure 1 into figure 3?
A. a rotation 180 degrees clockwise about the origin, followed by translation 2 units to the left.
B. a rotation 90 degrees clockwise about the origin, followed by a reflection across the x-axis.
C. a rotation 180 degrees clockwise about the origin, followed by a reflection across the y-axis.
D. a rotation 90 degrees clockwise about the origin, followed by a translation 3 units to the right.
the correct answer is A. Option A describes a rotation of 180 degrees clockwise, which would result in figure 1 being upside down, and then a translation of 2 units to the left.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To transform figure 1 into figure 3, we need to apply two transformations. We can eliminate option B because a rotation of 90 degrees followed by a reflection across the x-axis would transform figure 1 into a mirror image of figure 2, not figure 3.
Option A describes a rotation of 180 degrees clockwise, which would result in figure 1 being upside down, and then a translation of 2 units to the left. This would transform figure 1 into figure 3, so option A is a possible sequence of transformations.
Option C describes a rotation of 180 degrees clockwise followed by a reflection across the y-axis. This would transform figure 1 into a mirror image of figure 2, not figure 3.
Option D describes a rotation of 90 degrees clockwise followed by a translation of 3 units to the right. This would transform figure 1 into a position that is similar to figure 3, but the orientation of the triangle would be different.
Therefore, the correct answer is A.
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In desperate need of help with my college algebra problem
To find the nth degree of polynomial function f(x) = x^4 - 4x^3 + 27x^2 -46x +60
What is Function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
For polynomial with real coefficients, the complex zeros come with conjugates so 2+4i must come with 2-4i , then for 4th degree polynomial
f(x) =a (x+1)(x-3)(x-2-4i)(x-2+4i). With given f(1)=-68
a(1+1)(1-3)(1-2-4i)(1-2+4i)= -68.
By this we can find a
a (2)(-2)(-1-4i)(-1+4i) = -68
a(-4)(1+4i-4i-16i^2) = -68
a(-4)(1+16) = -68
a(-4)(17) = -68
a(-68) = -68
a = 1
Now, solving
f(x) =(x+1)(x-3)(x-2-4i)(x-2+4i)
f(x) = (x+1)(x-3)(x^2 - 2x + 20)
f(x) = (x^2 - 2x - 3)(x^2 - 2x + 20)
f(x) = x^4 - 2x^3 + 20x^2 - 2x^3 + 4x^2 - 40x + 3x - 6x + 60
f(x) = x^4 - 4x^3 + 27x^2 -46x +60
Hence, the for 4th degree polynomial is f(x) = x^4 - 4x^3 + 27x^2 -46x +60
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Evaluate : limx→ tan2-sin2x x3
Given:
[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]Solve:
[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]Use l'hopital's rule:
[tex]\begin{gathered} =\lim _{x\to0}\frac{\frac{d}{dx}(-\sin 2x+\tan 2x)}{\frac{d}{dx}(x^3)} \\ =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \end{gathered}[/tex]Simplify:
[tex]\begin{gathered} =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \\ =\lim _{x\to0}\frac{2(-\cos (2x)+\tan ^2(2x)+1)}{3x^2} \end{gathered}[/tex]Apply the constant multiple rule:
[tex]\begin{gathered} \lim _{x\to0}cf(x)=c\lim _{x\to0}f(x) \\ \text{With c=}\frac{2}{3} \\ f(x)=\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2} \end{gathered}[/tex][tex]\begin{gathered} =\frac{2\lim _{x\to0}\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2}}{3} \\ =\frac{2\lim _{x\rightarrow0}\frac{(4\tan ^2(2x)+4)\tan (2x)+2\sin (2x)}{2x}}{3} \end{gathered}[/tex]Similary :
[tex]\begin{gathered} =\frac{2\lim _{x\to0}(2\cos (2x)+12\tan ^4(2x)+16\tan ^2(2x)+4)}{3} \\ =\frac{2(6)}{3} \\ =4 \end{gathered}[/tex]Mr. Connor's physics class has 105 students, classified by academic year and gender, as illustrated in the table. Mr. Connor randomly chooses one student to collect yesterday's work
Academic Year male female
Junior 8 11
senior 19 19
freshman 9 12
sophomore 19 8
The probability that he selects a Mel given that he chooses randomly from only the Juniors is 0.076.
How to calculate the probability?It should be noted that the probability is the likelihood that something will happen. The table shows that Connor's physics class has 105 students, classified by academic year and gender.
The probability will be:
Fraction of males that are junior / Fraction if Junior
= 8/105 / 19/105
= 0.076
The probability is 0.076.
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What is the probability that he selects a Mel given that he chooses randomly from only the Juniors.
help
fast 20 point
please
Answer:
A. 2
Step-by-step explanation:
Hope this helps
HELP!
Do units affect significant figures? For example, I know that the number 5600 has two significant figures. But if I wrote it as 5600 L, would the unit "L" count as a sig fig? Please help me!!
Gourmet in Italy has a policy of automatically adding an 18% tip to a restaurant bill. How much would a restaurant bill be if it had a tip of $3.20 added to it?
The restaurant charger a tip of the 18% of the bill
So the total amount charged is the money spent + 18%
The bill had a tip of $3.20 this is the 18% of the amount spent.
Using cross multiplication you can calculate the amount of the bill as:
Bill without tip: 100%
Tip: 18%
Total amount (bill + tip): 118%
If 18% ____ $3.20
Then 118%___$x
[tex]undefined[/tex]Round 18,792 to the nearest thousand is the answer 18,790 or 00019 or 00018 or 18800 please due today please give brainiest.
Answer:
The answer is 19,000
Step-by-step explanation:
18,792 you round to the thousand which is 8 and the number after is 7 which is above 5 so the 8 turns into a 9
Answer:
19000
Step-by-step explanation:
18,792
Rounding to the nearest thousand
The 8 is in the thousands place
We look at the number in the hundreds place, 7
It is 5 or higher so we will round the 8 up to 9 and everything else to the right will become zeros
18,792 becomes 19000
please quick I need this
Answer:
The remainder is [tex]4[/tex].
The quotient is [tex]3x^{2}+6x+1[/tex]
Step-by-step explanation:
Step 1: Do long division
To divide these expressions, we will have to make use of long division, which is shown in the picture.
Step 2: Identifying the remainder and quotient
The remainder is [tex]4[/tex].
The quotient is [tex]3x^{2}+6x+1[/tex]
A DVD is available at a store for $16.99. The list price of this DVD was $18.75. What was the percent discount? % (Round to the nearest tenth as needed.)
The cost of DVD = $16.99
The list price of this DVD was $18.75
So, the discount =
[tex]18.75-16.99=1.76[/tex]And the percent discount =
[tex]\frac{1.76}{18.75}\cdot100=9.3866\%[/tex]Rounding the answer to the nearest tenth
So, the answer will be : the percent discount = 9.4%
What is the answer to m
the sum of the internal angles of a quadrilateral is 360, therefore:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C+m\angle D=360 \\ \text{and} \\ m\angle A+m\angle C=180 \\ m\angle B+m\angle D=180 \end{gathered}[/tex]so
[tex]\begin{gathered} a+5+a-25=180 \\ 2a-20=180 \\ 2a-20+20=180+20 \\ 2a=200 \\ \frac{2a}{2}=\frac{200}{2} \\ a=100 \end{gathered}[/tex]mm
mm
Borrowed $30000 four year loan at 7% what’s monthly payment? And what’s the intrest I will pay on loan?
given:
There are given that the Borrowed is $30000.
Explanation:
To find the monthly amount, we need to use the formula:
[tex]R=\frac{P}{1-(i+1)^{-n}}[/tex]Where,
[tex]\begin{gathered} P=30000 \\ r=0.07 \\ m=12\text{ Thenn} \end{gathered}[/tex][tex]\begin{gathered} i=\frac{r}{m}=\frac{0.07}{12} \\ =0.0058 \end{gathered}[/tex]Ans,
[tex]\begin{gathered} n=mt=12(4) \\ =48 \end{gathered}[/tex]Then,
From the formula:
[tex]\begin{gathered} R=\frac{Pi}{1-(1+i)^{-n}} \\ R=\frac{30000(0.0058)}{1-(1+0.0058)^{-48}} \\ R=\frac{30,000(0.0058)}{1-(1.0058)^{-48}} \\ R=\frac{30000(0.0058)}{0.24} \\ R=725 \end{gathered}[/tex][tex]\begin{gathered} S.I=\frac{P\times r\times t}{100} \\ =\frac{30000\times7\times4}{100} \\ =4800 \end{gathered}[/tex]Final answer:
Hence, the monthly payment is $725 and the interest will be: $4800
A test was given to a group of students. The grades and gender are summarized below A B C TotalMale4192043Female1116532Total15352575If one student is chosen at random from those who took the test,Find the probability that the student got a 'B' GIVEN they are male.
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