Answer:144
Step-by-step explanation:
A flag pole and a building stand on the same horizontal level. From the point p at the bottom of a building the angle of the top T of the flagpole is 65°. From the point Q of the building the angle of elevation of the point T is 25°. If the building is 20m high. calvulate the distance PT, The heigt of the flagpole,The distance QT
Answer:
PT is approximately 28.2 m
The height of the flagpole is approximately 25.56 m
QT is approximately 13.15 m
Step-by-step explanation:
Part A
From the attached drawing of the building and the flagpole, we have;
∠TQP = 25° + 90° = 115°
∠TPQ = 90° - 65° = 25°
∴ ∠QTP = 180° - (115° + 25°) = 40°
By sine rule, we have;
[tex]\dfrac{\overline {QT}}{sin(\angle TPQ)} = \dfrac{\overline {PT}}{sin(\angle TQP)} = \dfrac{\overline {QP}}{sin(\angle QTP)}[/tex]
[tex]\therefore \overline {PT} = sin(\angle TQP) \times \dfrac{\overline {QP}}{sin(\angle QTP)}[/tex]
∴ PT = sin(115°) × 20 m/(sin(40°)) = 28.1992924 ≈ 28.2
PT ≈ 28.2 m
Part B
The height of the flagpole, Ta = PT × sin(∠TPa)
∴ Ta ≈ 28.2 × sin(65°) ≈ 25.56
The height of the flagpole, Ta ≈ 25.56 m
Part C
[tex]\overline {QT} = sin(\angle TPQ) \times \dfrac{\overline {QP}}{sin(\angle QTP)}[/tex]
The distance QT= sin(25°) × 20 m/(sin(40°)) ≈ 13.15
QT ≈ 13.15 m
The diameter of a circular pond 63 m. Find the cost of fencing the edge of the pond if the fence costs $12 per meter.
Answer:
$2,373.84
Step-by-step explanation:
The formula for circumference is C = (pi)(diameter)
C = (3.14)(63)
C = 197.82 m
then multiply that by the cost of fence/m
197.82 x 12 = $2,373.84
An ordered pair tells us what about a system of equations ?
Answer:
Step-by-step explanation:
It may not tell you anything. You have to be careful how you think about the answer to this. An ordered pair is just that: it describes an x and y value and that is really all that it does.
However it may also be used to describe the solution to a system of equations which cross in one place. For example, if you plot
y = x + 1
y = -3x + 2
The ordered pair that gives the point where both equations equal the same thing is (0.25,1.25) The graph is shown below, and the ordered pair marks the solution.
A farmer plants corn and wheat on a 180-acre farm
The farmer needs to sow 135 acres of corn and wheat, and 45 acres of wheat.
What is linear equation ?A linear equation is the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "linear equation in two variables" is the term used to describe the previous sentence, where y and x are variables. Two variables make up bivariate linear equations. Examples include the linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
180 acres total land area
The corn acres should be C.
The wheat acres should be W.
A 180-acre property is planted with wheat and corn by a farmer.
Equation 1: C + W = 180
Corn is grown on three times as many acres as wheat:
Equation 2 is created by substituting C = 3W into Equation 1. The result is:
45 acres is W.
For corn, 135 acres equals C.
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X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter λ = 0. 1342. (a) What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m? (Round your answers to four decimal places. ) at most 100 m at most 200 m between 100 and 200 m (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places. ) (c) What is the value of the median distance? Hint: Find a such that P(X≤a)= 0. 50 (Round your answer to two decimal places. ) m
The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979
What is Probability ?
probability can be defined as the ratio of the number of favourable outcomes and the total number of outcomes.
We are given with an exponential distribution with
λ=0.01386.
The probability distribution function is:
F(x)=λ * e power (−λx)
Cumulative distribution function is
F(x) = 1- e power (−λx)
The mean of the exponential distribution function
E(X) = 1 / λ
= 1/0.01386
= 72.15
Hence, E(X) = 72.15
The variance of the exponential distribution function
V(X) = 1 / λ ^{2}
= 1/0.01386*0.01386
= 5205.63
V(X) = 5205.63
Probability that the distance is at most 100m
P(X <= 100 ) = F (100)
= 1- e power (−λx)
= 1 - e power (-0.01386*100)
= 1- e power (-1.386)
= 1-0.25007
= 0.749926
Therefore, P(X<=100) = 0.749926
probability that the distance is at most 200m
P ( X<= 200) = F(200)
=1-e power (−λx)
=1-e power (-0.01386*200)
= 1 - e power (-2.772)
= 1-0.06253
= 0.9375
P(X<= 200) = 0.9375
Probability that the distance is between 100 and 200m
P(100<= X <= 200) = F(200) - F(100)
= 0.9375-0.7499
=01876
P(100 <= X <= 200) = 0.1876
Probability that the distance exceeds the mean distance by more than 2 standard deviation.
P( X + P>μ+2σ) = P(X>72.15+2√5205.63)
= P(X > 72.15 +144.3)
P(X>216.45)
= 1-P(X<= 216.45)
1 - (1- e power (-0.01386*216.45)
= e power (-2.9999)
= 0.04979
P( X + P>μ+2σ) = 0.04979
Hence , The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979
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Predict the approximate GPA of a student who watches television for 8 hourson average, per day
Answer:
2
Step-by-step explanation:
When Tobey was born, his parents invested $2,000 in a fund that paid an annual interest of 6%. How old will Tobey be when the investment is worth at least $5,000?
So, a 72-month loan with a 2 annual simple interest rate is the loan choice that would need her to repay the least amount of money.
What is interest rate ?An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.
According to the information provided, a 72-month loan with a 2 annual simple interest rate is the loan choice that would require her to repay the least amount of money. This is because the amount she would have to pay will be the least compared to other loan options.
[tex]Loan = 72 months (2per cent of $6,000)\\Loan = 120 for 72 months\\Loan =$8,640\\[/tex]
a 72-month loan with a 2 yearly simple interest rate.
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20 points, pls help, its angles
A single pump can add only 0.35 pound of air into a bicycle tire. The bicycle tire will hold a maximum of 640 ounces of air per square inch. How many pumps are required to inflate the bicycle tire to maximum pressure?
A.15 pumps
B. 115 pumps
C. 225 pumps
D. 1,829 pumps
The bicycle tire needs an amount of 115 pumps to be fully inflated. (Correct choice: B)
How many pumps are required to inflate the bicycle tire to maximum pressure
In this problem we need to determine the number of pumps needed to inflate the bicycle tire at maximum pressure, this number (n) is equal to the maximum capacity of the tire (V), in ounces, and the mass added by a single pump (p), in ounces:
n = V / p
If we know that V = 640 oz and p = 5.6 oz (1 lb = 16 oz), then the number of pumps is:
n = 640 oz / 5.6 oz
n = 114.286
n = 115
An amount of 115 pumps are needed to inflate the bicycle tire to maximum pressure.
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Find the next three terms in each geometric sequences
2500, 500, 100, ...
2, 6, 18, ...
-4, 24, -144, ...
4/5, 2/5, 1/5....
-3, -12, -48 ...
72, 12, 2 ...
Answer:
20
54
864
-192
I haven't figured out the last yet and the fraction one
What is a coordinate plane example?
A coordinate plane is a two-dimensional surface formed by two number lines
What is coordinate system?In a plane, a Cartesian coordinate system is a system of coordinates that designates each point uniquely by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length. Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. The coordinate plane allows us to graph points, lines, and more. The plane that houses the x- and y-axes is known as the xy-plane, while the y- and z-axes are housed in the yz-plane and the x- and z-axes are housed in the xz-plane.To learn more about coordinate system refer to:
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A.SSE.A Carlos borrowed $26,000 for a car for 5 years at an APR of 5.25%. What will his monthly payment be? *
Answer:
$568.75
Step-by-step explanation:
Monthly payment = annual payment / 12
Annual payment = amount borrowed x time x APR
$26,000 X 0.0525 X 5 = $6825
Monthly payment = $6825 / 12 = $568.75
The monthly payment is $568.75 for 5 years at an Annual Percentage Rate (APR) of 5.25%.
The amount borrowed for a car is $26,000.
The time period is 5 years.
The Annual Percentage Rate (APR) is 5.25%.
What is APR?The Annual Percentage Rate (APR) is the cost you pay each year to borrow money, including fees, expressed as a percentage.
Monthly payment = annual payment / 12
Annual payment = amount borrowed x time x APR
Annual payment =$26,000 X 0.0525 X 5
Annual payment = $6825
Monthly payment = $6825 / 12
= $568.75
Hence, the monthly payment is $568.75.
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what is the value of z?
420
60
440
240
Angle W measures 36°. What is the angle measure of angle y? (Angle Includes x, y, w, z and is in the shape of an X?) SO confused.
Answer:
The angle measure of angle y is 36°. [ Because vertically opposite angles are equal]
The area of a square is given by x?, where x is the length
of one side. Mary's original garden was in the shape of a
square. She has decided to double the area of her
garden.
Part 1 out of 2
Enter an expression that represents the area of Mary's
new garden.
An expression that represents the area is
✓ Check
Next
Answer:
Step-by-step explanation:
If she doubles the area of her lot, it should be 2x^2.
But how do you get that?
The answer is that the sides have now increased to √2x
How did I get that, and why did I choose it?
The formula for a square's area is s^2If you want to double the area, it will be 2 s^2. Now what?Take the square root of 2s^2 which is √(2s^2).What that means is the side is now √2 sIll mark brainly if its correct. :) a,b,c, or d. answer quick please
Answer:
d.
Step-by-step explanation:
What word is used to remember the 3 trigonometric ratios?
The word used to remember the 3 trigonometric ratios sine, cosine, and tangent is SOH-CAH-TOA
We know that in right triangle for an angle θ, the trigonmetric ratios are:
sin(θ) = opposite side of θ/ hypotenuse
cos(θ) = adjacent side of θ / hypotenuse
tan(θ) = opposide side of θ / adjacent side of θ
cot(θ) = 1/tan(θ)
sec(θ) = 1/cos(θ)
cosec(θ) = 1/sin(θ)
The word 'SOH-CAH-TOA' is used to remember the sine, cosine, and tangent ratios in a right triangle.
SOH means, Sine = Opposite side / Hypotenuse.
CAH means, Cosine = Adjacent side / Hypotenuse.
TOA means, Tangent = Opposite side / Adjacent side
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The following table displays the number of sofas sold in a furniture store during certain months of the year.
Furniture Store Sofa Sales
January 255
February 234
March 263
April 229
May 248
Based on these data, which statement is correct?
A. There are outliers.
B. The mean best describes the data.
C. The median best describes the data.
D. The measure of variability that best describes the data is the IQR, 27.5.
mary and max are playing a game with complex numbers. mary has a score of 3+2i. Wat must Max's score be so that the product of their score is one?
Since Mary and Max are playing a game with complex numbers, Max's score must be equal to 1/(3 + 2i), so that the product of their score is one.
What is a reciprocal function?A reciprocal function simply refers to a type of function which comprises a constant on its numerator and an algebraic expression or complex number in its denominator such as: f(x) = 2/3 + 7i.
In Mathematics, a reciprocal function is typically used when describing relationships that are inversely proportional to one other.
Let the variable n represent Max's score. Therefore, a mathematical expression which models the product of both Mary and Max's score is given by the following:
Product = 3 + 2i × n = 1
Making n the subject of formula, we have the following as Max's score;
n = 1/(3 + 2i)
Check:
3 + 2i × 1/(3 + 2i) = 1
(3 + 2i)/(3 + 2i) = 1
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A sample of fish from a river showed
that of the fish were less than one
year old. If there are an estimated
8,000 fish in the river, about how
many of them are less than one year
old?
Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown. If he used the
same amount concrete to construct a spherical barrier, how tall would it be? Express your answer in terms of π?
Is it:
A)1 2/3 π
B)3 2/3 π
C)4 1/3 π
D)5 π
The volume of the cone is (2/3)π cubic feet. And the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft. The correct option is A.
What is volume?Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.
Given:
Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown.
He used the same amount of concrete to construct a spherical barrier.
According to the information given in the exercise, the height and the radius of the pylons are the following:
Height h = 2 ft
Radius r = 1 ft
So, the volume of the cone,
= (1/3)πr²h
= (1/3)π(1)²(2)
= (2/3)π cubic feet.
And the volume of the sphere is twice the volume of the cone.
So, the volume of the sphere,
4πr³/3 = 2π/3
2r³ = 1
r³ = 1/2 = 0.5
r = ∛0.5 = 0.8 ft.
Therefore, the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.
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I suck at angles, if someone can answer this I’ll give Brainliest when I can. I’m going to post other questions as well so this is not the only chance I’ll give brainliest
4th option
Step-by-step explanation:
Corresponding angles are congruent, so x = 43! I hope this helps, have a good day!
Ali found out the number of rooms in each of 40 houses in a town. He used the information to complete the frequency table. Number of Rooms Frequency 4 4 5. 7 6 10 7 12 8 5 9 2 Calculate the mean number of rooms.
The mean number of rooms = 6
We know that the formula for the mean.
mean = sum of all observations / total number of observations
First we find thr total number of rooms, from given frequency table.
Number of Rooms Frequency Total number of rooms
4 4 16
5 7 35
6 10 60
7 12 84
8 5 40
9 2 18
So, the total number of rooms of 40 houses in a town would be,
16 + 35 + 60 + 84 + 40 + 18 = 253
And the total number of houses = 40
Using above formula of mean, the mean number of rooms would be,
x = 253/40
x = 6.325
Therefore, on an average there are 6 rooms in each house.
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Is 5 a polynomial or not?
Because 5 is represented by the polynomial 5x0, the answer is yes.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An example of a polynomial of a single indeterminate x is x² − 4x + 7.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.
For instance, the polynomial 3x+2x-5.
By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.
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whats the slope and y intercept of y-2x=5
I have a set of numbers: 7, 3, 9, 5, 2. What number do I have to add to get the mean to be 6?
Answer:
10
Step-by-step explanation:
(7+3+9+5+2+x)/6=6
26+x/6=6
26+x=36
x=10
Answer:
you need to add 10
Step-by-step explanation:
7+3+9+5+2=26
26+10= 36
total 6 numbers so you divide it by 6
36/6= 6
Find the value of x.
Answer:
x = 25
Step-by-step explanation:
The top angle is the supplement of 3x - 10
180 - (3x - 10) = -3x + 190
The sum of the angles in a triangle is 180
(-3x + 190) + (25) + (x + 15) = 180
Combine like terms
-2x + 230 = 180
Subtract 230 from both sides
-2x = -50
Divide both sides by -2
x = 25
Tomas wanted to buy a computer priced at $950. He waited for the store's annual clearnace sale and bought the computer for $712.50. What percent was the discount at the clearnace sale?
Answer:
25%
Step-by-step explanation:
Discount is given by x(1-r) = y, where x is the original price and r is the percentage (made into a decimal) that was discounted, while y is the price after the discount.
So, plugging the numbers given in, we have 950(1-r) = 712.50, as we don't know r. This is hard to find, so we replace (1-r) with m (just a random letter).
Therefore, we have 950m = 712.50. To find m, we divide 712.50 by 950, getting m = 0.75.
That is not our answer. Earlier, we subsituted (1-r) for m. Now, we subsitutite it back. m = 0.75 so 1-r = 0.75. Therefore, we get that r, the discount rate, is equal to 0.25, or 25%.
At her birthday party, Sam is serving a slice of cake to each attendee. Of each attendee receives 2 slices, there will be 20 slices left. If 5 attendees do not receive any slices and the rest receive 5 slices each, there will be no cake left. How many attendees were at the party
On solving the provided question, we can say that by having the equation 15 attendees were at the party
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
let x = number of attendees
[tex]2x[/tex] + 20 = number of slices 5(x-5) = [tex]2x[/tex] - 20
[tex]5x[/tex] - 25 = [tex]2x[/tex] + 20
[tex]3x[/tex] = 45
[tex]x[/tex] = 15
[tex]2x[/tex] + 20 = 50 slices
15 attendees
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work out the areas of these compound shapes ? Pls step by step
Answer:
Step-by-step explanation:
7+5+2=14