The surface area of the exterior of the building rounded to the nearest hundred square feet is 40700 feet².
What is surface area ?Surface area is the amount of space covering the outside of a three-dimensional shape.
Given, base of prism = 60 feet, height of the prism h₁= 150 feet, and height of the pyramid h₂ = 1/6 (150)
= 25 feet.
The surface area of the exterior of the building = lateral surface area of prism + pyramid.
SA = ( 4ah₁ ) +(a√(a² + 4h₂²) )
SA = ( 4(60)150 ) + ( 60(√60² + 4(25)² )
= ( 240* 150 ) + 60(√3600 +2500 )
= 36000 + 60(√6100)
= 36000 + 60(78.1024)
= 36000 + 4686.15
= 40686.15
≈ 40700 feet².
Therefore, the surface area of the exterior of the building rounded to the nearest hundred square feet is 40700 feet².
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Answer:
The surface area of the exterior of the building is approximately 40700 feet
What is the value of 6¹?
6° = 1
6 = 6
6 = 36
6 = 216
A.220
B.240
C.864
D.1,296
Answer: D
Step-by-step explanation:
6^4 = 6 x 6 x 6 x 6 = 1,296
6^4 = 1,296
Task
On April 15, 1912, the Titanic struck an iceberg and rapidly sank with
only 710 of her 2,204 passengers and crew surviving. Data on survival
of passengers are summarized in the table below. (Data source:
http://www.encyclopedia-titanica.org/titanic-statistics.html)
a.
First class passengers
Second class passengers
Third class passengers
Total passengers
Survived
201
118
181
500
Did not survive
123
166
528
817
Total
324
284
709
1317
a. Calculate the following probabilities round your answers to three decimal points
i. If one of the passengers is randomly selected what is the probability that this passenger survived
iii. If one of the passengers is randomly selected what is the probability that this passenger was in first class and survived
iv. If one of the passengers is randomly selected from the first class passengers what is the probability that this passenger survived
v. If one of the passengers who survived is randomly selected what is the probability that this passenger was in first class
vi. If one of the passengers who survived is randomly selected what is the probability that this passenger was in third class?
The probability that a random passenger survived is 0.38
The probability that this passenger was in first class and survived is 0.153
The probability that the passenger in the first class survived is 0.620
The probability that the passenger that survived was in first class is 0.402
The probability that the passenger that survived was in third class is 0.362
What are the probabilities ?The probability that a random passenger survived is 500 / 1317 = 0.38
The probability that this passenger was in first class and survived is 201 / 1317 = 0.153
The probability that the passenger in the first class survived is: 201 /324 = 0.620
The probability that the passenger that survived was in first class: 201/500 = 0.402
The probability that the passenger that survived was in third class is: 181 / 500 = 0.362
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A baby weighed only 8.7 ounces at birth. How much lighter was she than an average baby, who weighs about 7 lb 8 ounces?
The baby is 111.3 ounces or 6.96 pounds lighter than an average baby.
What is weight ?Weight is the measurement of Gravitational force on an object.
It can be zero as in the space.
It is given in the question that
A baby weighed only 8.7 ounces at birth
weight of an average baby is 7lb 8 ounces
1 lb = 16 ounce
an average baby weight = 7 * 16 +8 = 120 ounces
The baby weight is just 8.7 ounces
so the baby is 120-8.7 = 111.3 ounces lighter than an average baby.
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write an exponential expression that shows (10 to the power of 4) to the power of 4 simplified
Answer: it could be
[tex](10^{4} ) ^{4}[/tex]
Step-by-step explanation:
(h+k)(1) is
(k-h)(4) is
(k/h)(3) is
(h•k)(0) is
(k •h)(0) is
(h•k)(3) is
h(k(-2))
Answer:
Step-by-step explanation:
(h+k)(1)=h(1)+k(1)=2+(-1)=2-1=1
(k-h)(4)=k(4)-h(4)=0-(-1)=1
(k/h)(3)[tex]=\frac{k(3)}{h(3)} =\frac{-1}{0} =- \infty[/tex]
(h.k)(0)=h(0).k(0)=3(-2)=-6
(k.h)(0)=k(0).h(0)=-2(3)=-6
(h.k)(3)=h(3).k(3)=0(-1)=0
h(k(-2))=h(-3)=0
A hose fills a hot tub at a rate of 5.2 gallons per minute. How many minutes will it take to fill a 600 gallon hot tub? (nearest tenth)
Answer:
115.38 is what I got when I tryed to work it out
Which of the following sets represents the range of the diagram below?
The set that represents the range of the diagram below is given as follows:
B. {3, 5, 7}.
What is the range of a data-set?It is the set that contains all possible output values.
In the diagram, we have that:
The input values are: {1,2,3,4,5}.The output values are: {3,5,7}.Hence the set that represents the range of the diagram below is given as follows:
B. {3, 5, 7}.
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Determine whether it is a function
Answer:
Relation 3 is not a function, as s has two outputs: tree and desk. Relation 4 is not a function for the same reason. -1 has three outputs: -2, -4, and -7.
A line has slope Four-thirds. Through which two points could this line pass?
Answer:
Two points this line can pass through (1, 4/3) and (2, 8/3)
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given:
slope = 4 / 3equation: y = 4/3xwe can plug in a number for x to find y
when x = 0,
y = 4/3(0)
y = 0
point: (0,0)
when x = 1,
y = 4/3(1)
y = 4/3
point: (1, 4/3)
when x = 2,
y = 4/3(2)
y = 8/3
point: (2, 8/3)
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Which statement is true about the end behavior of the graphed function?
Step-by-step explanation:
both ends are going to the same direction so the degree is even. the right side is going up so the leading coefficient is positive.
10 points need help finding area
Answer:
8 un^2
Step-by-step explanation:
to find this answer you must find the area of the rectangle and then the triangle
the rectangles area is
2 * 3 = 6 un^2
the traingle is
2 * 2 * 1/2 = 2 un^2
now you add them
6 + 2 = 8 un^2
A manufacturer of pacemakers wants the standard deviation of the lifetimes of the batteries to be less than 1.8 months. A sample of 20 batteries had a standard deviation of 1.6 months. Assume the variable is normally distributed. Find the 95% confidence interval of the standard deviation of the batteries. Based on this answer, do you feel that 1.8 months is a reasonable estimate?
Answer:
Look down my answer↓:
Step-by-step explanation:
The fox population in a certain region has a continuous growth rate of 7 percent per year. It is estimated that the population in the year 2000 was 15000.
(a) Find a function that models the population
t
years after 2000 (
t
=
0
for 2000).
Your answer is
P
(
t
)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)
There are 25773 foxes in the region in the year 2008
How to determine the function?The given parameters are:
Initial value, a = 15000Rate, r = 7% or 0.07Let the number of years after 2000 be x.
So, the function is
f(x) = a * (1 + r)^x
This gives
f(x) = 15000 * (1 + 0.07)^x
In 2008, we have:
x = 8
So, the equation becomes
f(8) = 15000 * (1 + 0.07)^8
Evaluate
f(8) = 25773
Hence, there are 25773 foxes in the region in the year 2008
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Use the calculator to graph the function y = 2x2 25x + 3. What are the coordinates of the turning point of the graph to the nearest hundredth?
Vertex = (
,
)
The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]In this problem, the function is given by:
y = 2x² + 25x + 3.
Hence the coefficients are a = 2, b = 25, c = 3, then the coordinates of the vertex are given as follows:
[tex]x_v = -\frac{25}{2(2)} = -6.25[/tex][tex]y_v = -\frac{25^2 - 4(2)(3)}{4(2)} = -75.13[/tex]The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).
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Answer:
6.25, -75.13
Step-by-step explanation:
it just is
Separable differential equation
y’ln^2y+ysqrtx=0 y(0)=e
By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].
How to solve separable differential equation
In this question we must separate each variable on each side of the equivalence, integrate each side of the expression and find an explicit expression (y = f(x)) if possible.
[tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex]
[tex](\ln y)^{2}\,dy = -y \cdot \sqrt{x}\, dx[/tex]
[tex]-\frac{(\ln y)^{2}}{y}\, dy = \sqrt{x} \,dx[/tex]
[tex]-\int {\frac{(\ln y)^{2}}{y} } \, dy = \int {\sqrt{x}} \, dx[/tex]
If u = ㏑ y and du = dy/y, then:
[tex]-\int {u^{2}\,du } = \int {x^{\frac{1}{2} }} \, dx[/tex]
[tex]-\frac{1}{3}\cdot u^{3} = \frac{2\cdot x^{\frac{3}{2} }}{3} + C[/tex]
[tex]u^{3} = -2\cdot x^{\frac{3}{2} } + C[/tex]
[tex](\ln y)^{3} = - 2\cdot x^{\frac{3}{2} } + C[/tex]
[tex]C = (\ln e)^{3}[/tex]
[tex]C = 1[/tex]
And finally we get the explicit expression:
[tex]\ln y = \sqrt [3]{-2\cdot x^{\frac{3}{2} }+ 1}[/tex]
[tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex]
By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].
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Need help anyone please!!!
Identifying Proportional Relationships
Which graph represents a proportional relationship?
Answer:
I can't answer this if you don't have the answer choices
I'm sorry
4 Pencils and 2 rulers cost $8. 2 pencils and 4 rulers cost $10. Find the cost of 3 rulers and 3 pencils
Answer:
$9
Step-by-step explanation:
Let, the price of pencils is x, and the price of rulers is y.
4x+2y=8.....(i)
2x+4y=10......(ii)
From eq(i),
2(2x+y)=8
2x+y=4
y=4-2x eq(iii) .....put in eq(ii)
2x+4(4-2x)=10
2x+16-8x=10
-6x=10-16
x=-6/-6
x=1 put in eq (iii)
y=4-2(1)
y=2
Now, the price of 3 rulers and 3 pencils = 3x+3y=3(1)+3(2)
=9
Please give me brainlist.
Analyze the conditional statement below and complete the instructions that follow.
If an angle measures 90°, then it is a right angle.
Identify ~q.
O An angle does not have measure 90°.
OIt is not a right angle.
An angle measures 90°.
OIt is a right angle.
Answer: It is not a right angle.
1. EL precio a la venta de una impresora de inyección de tinta es de $285.000 incluida una Ganancia del 35%. ¿cuánto le cuesta a la tienda cada impresora?
Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.
¿Cómo encontrar el precio de una impresora sin ganancia?
En el enunciado tenemos el precio de una impresora para el consumidor, el cual comprende el dinero invertido por vendedor más la ganancia esperada. Este indicador observa la siguiente fórmula:
C' = C · (1 + r/100) (1)
Donde:
C - Coste asumido por el vendedor, en unidades monetarias.C' - Coste para el consumidor, en unidades monetarias.r - Tasa de ganancia, en porcentaje.Si sabemos que C' = $ 285.000 y r = 35 %, entonces el coste asumido por el vendedor es:
285.000 = 1,35 · C'
C' ≈ 211.111,11
Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.
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Identify the category to which the following statement belongs: Brandon has two weeks to decide on the topic of his research paper.
O Not important - Not Urgent
O Not Important - Urgent
O Important - Not Urgent
O Important-Urgent
Answer:
Important- not urgent
Step-by-step explanation:
The research paper is important but since Brandon has two weeks to decide it is not urgent.
What is the present value of a cash inflow of 1250 four years from now if the required rate of
return is 8% (Rounded to 2 decimal places)?
Using simple interest, it is found that the present value of the cash inflow is of 947.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = A(0)(1 + rt)
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.In this problem, the parameters are given as follows:
r = 0.08, t = 4, A(t) = 1250.
We have to solve for A(0) to find the present value, hence:
A(t) = A(0)(1 + rt)
1250 = A(0)(1 + 0.08 x 4)
A(0) = 1250/1.32
A(0) = 947.
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find the roots of x^4-1=0
Answer:
x = +1
x = -1
Step-by-step explanation:
x^4-1=0
x^4=+1
fourth root of x^4= fourth root of +1
x = +1
x = -1
What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .
Answer:
All its side lengths are equal
(and all the agle of 60°)
Step-by-step explanation:
What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .
Solve the system of equations by graphing.
y = x − 6
3x − 3y = 18
X = 6
Y = (-6)
P(-4, 6), Q(2, 5), R(3, -1), S(-3, 0)
Use slope to determine whether the following is a parallelogram. Explain why or why not.
Find the slope of PQ
Find the slope of QR
Find the slope of RS
Find the slope of SP
Use this information to determine if the quadrilateral a parallelogram.
From the slopes it is confirmed that PQ || RS OR|| SP and therefore it is a parallelogram .
What is a Parallelogram ?A parallelogram is a quadrilateral in which the opposite sides are parallel.
The coordinates of a quadrilateral is given
To prove that it is a parallelogram
PQ || RS
OR|| SP
The slope of a straight line is given by
[tex]\rm m = \dfrac{y_2 -y_1}{x_2- x_1}[/tex]
For PQ
m = (-1/6) = -1/6
For QR
m = -6/1 = -6
For RS
m = 1/(-6) = -1/6
For SP
m = -6
From the slopes it is confirmed that
PQ || RS
OR|| SP
and therefore it is a parallelogram
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What is the length of BC¯¯¯¯¯?
Answer:
meight you gotta do better then that
Step-by-step explanation:
a picture is probably necessary
what is π x 5
please tell me the answer as quick
Help please I need asap
Answer: -120
Step-by-step explanation:
[tex]2\sum^{4}_{p=1} (p^{2}-9p)=2[(1^{2}-9(1))+(2^{2}-9(2))+(3^{2}-9(3))+(4^{2}-9(4))]=\boxed{-120}[/tex]
Line l passes through point (−2,37) and line p is the graph of y+3=−5(x+4) .
If l is parallel to p what is the equation of l ?
The slope of line p is -5, so substitute into point-slope form, we get
[tex]\boxed{y-37=-5(x+2)}[/tex]
