Answer:
Volume of paint required is 3.125 litres.
Step-by-step explanation:
It would be noted that each side walls would have the shape of a trapezium. So that the areas of each wall can be determined as:
wall 1 = [tex]\frac{1}{2}[/tex](a + b) h
= [tex]\frac{1}{2}[/tex](0.5 + 1.5)2
= 2 [tex]m^{2}[/tex]
wall 2 = [tex]\frac{1}{2}[/tex](a + b) h
= [tex]\frac{1}{2}[/tex](1 + 3)2
= 4 [tex]m^{2}[/tex]
wall 3 = [tex]\frac{1}{2}[/tex](a + b) h
= [tex]\frac{1}{2}[/tex](0.5 + 1.5)2
= 2 [tex]m^{2}[/tex]
wall 4 = [tex]\frac{1}{2}[/tex](a + b) h
= [tex]\frac{1}{2}[/tex](1 + 3)2
= 4 [tex]m^{2}[/tex]
Total area of the walls = 2 + 2 + 4 + 4
= 12 [tex]m^{2}[/tex]
Area of the bottom base = l x b
= 1 x 0.5
= 0.5 [tex]m^{2}[/tex]
Total area to be painted = 12 + 0.5
= 12.5 [tex]m^{2}[/tex]
But to paint one square meter of a gap surface, we need 0.25 litres of a green paint color. Thus, to paint 12.5 [tex]m^{2}[/tex] of the gap surface:
12.5 x 0.25 = 3.125
The litres of paint required is 3.125.
A radar station located at ground level picks up a plane flying at a direct distance of 47,440 feet
away. If the angle of elevation from the station to the plane is 29°, what is the altitude of the plane?
Answer:
22,999 feets
Step-by-step explanation:
Given the solution diagram attached,
The altitude, h of the plane can be solved using trigonometry :
Using :
Sin θ = opposite / hypotenus
Opposite = h
Hypotenus = 47440
Sin 29 = h / 47440
h = 47440 * sin29
h = 22999.368
h = 22,999 feets
Kelly has $25 in her purse, and Dante has d dollars in his wallet
Which algebraic expression represents the total amount that Kelly and dante have?
The equation will be:
25 + d = t
where t is total money
can someone please help me..
Answer:
A. It acts perpendicular to an object
What percent of 45 is 27
Answer:
60%
Step-by-step explanation:
27/45 = .6
.6 = 60%
12 times 12 divided by 6
Answer:
24 , 12x12 = 144. , 144/6 =24
let's write the whole numbers from 90 to 100 . Select the appropriate number to form the following sets . Then , write the type of sets .
A={ even number}
B={ odd number}
C={ X:X is a prime numbers}
D={ y:y is a composite number}
E={z:z is a square number}
F={ cube number}
G={ multiples of 7}
H={ X:X is divisible by 11}
A={ even number}
B={ odd number}
C={ X:X is a prime numbers}
D={ y:y is a composite number}
E={z:z is a square number}
F={ cube number}
G={ multiples of 7}
H={ X:X is divisible by 11}
꧁Aɴsᴡᴇʀ꧂AThe even numbers between 90 and 100 are: 90, 92, 94, 96, 98, 100B The odd numbers between 90 and 100 are: 91, 93, 95, 97, 99C The prime number between 90 and 100 is: 97DThe composite numbers between 90 and 100 are: 91, 92, 93, 94, 95, 96, 98 and 99.EThe square numbers between 90 and 100 are:90 = 8100
91 = 8281
92 = 8464
93 = 8649
94 = 8836
95 = 9025
96 = 9216
97 = 9409
98 = 9604
99 = 9801
100 = 10000
F The answer for this is on the attached picture above. Kindly look at it. The cube numbers between 90 and 100. GThe multiples of 7 between 90 and 100 are: 91 and 98HDivisible by 11 (between 90 and 100) is: 99
✩ ⁱ ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ ✩
Answer:
A
The even numbers between 90 and 100 are: 90, 92, 94, 96, 98, 100
B
The odd numbers between 90 and 100 are: 91, 93, 95, 97, 99
C
The prime number between 90 and 100 is: 97
D
The composite numbers between 90 and 100 are: 91, 92, 93, 94, 95, 96, 98 and 99.
E
The square numbers between 90 and 100 are:
90 = 8100
91 = 8281
92 = 8464
93 = 8649
94 = 8836
95 = 9025
96 = 9216
97 = 9409
98 = 9604
99 = 9801
100 = 10000
F
The answer for this is on the attached picture above. Kindly look at it. The cube numbers between 90 and 100.
G
The multiples of 7 between 90 and 100 are: 91 and 98
H
Divisible by 11 (between 90 and 100) is: 99
What is the simplified value of the expression below?
1/3 divided by 2/3
0
1/3
1/2
1
Answer:
option C : 1/2
Step-by-step explanation:
[tex]\frac{1}{3} \div \frac{2}{3} \\\\\frac{\frac{1}{3}}{\frac{2}{3}}\\\\\frac{1}{3} \times \frac{3}{2} \\\\\frac{1}{2}[/tex]
Solve -x/3>5 i don't know what to do
Answer:
It's D, x≤-15
Find the prime factorization on 168
Answer:
The prime factors of 168 are 2, 3, and 7.
Step-by-step explanation:
Function A and Function B are linear functions. Function A x y – 10 – 14 – 1 – 5 9 5 Function B y=2x+4 Which statement is true?
Answer:
See explanation
Step-by-step explanation:
Function A is not clear; I will use the following in place of function A
Function A:
[tex]x \to\ 1 |\ 3 |\ 4 |\ 6[/tex]
[tex]y \to -1|\ 3|\ 5|\ 9[/tex]
Function B:
[tex]y = 2x + 4[/tex]
Required
Compare both functions
For linear functions, we often compare the slope and the y intercepts only.
Calculating the slope of function A, we have:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (1,-1)[/tex]
[tex](x_2,y_2) = (3,3)[/tex]
So, we have:
[tex]m = \frac{3 - -1}{3 - 1}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m = 2[/tex]
To calculate the y intercept, we set [tex]x = 0[/tex], then solve for y
i.e.[tex](x,y) = (0,y)[/tex]
Using the slope formula, we have:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex]m = 2[/tex]
[tex](x_1,y_1) = (0,y)[/tex]
[tex](x_2,y_2) = (3,3)[/tex]
So, we have:
[tex]2 = \frac{3 - y}{3 - 0}[/tex]
[tex]2 = \frac{3 - y}{3}[/tex]
Multiply by 3
[tex]6 = 3 - y[/tex]
Collect like terms
[tex]y = 3 - 6[/tex]
[tex]y = -3[/tex]
So, for function A:
[tex]m = 2[/tex] -- slope
[tex]y = -3[/tex] --- y intercept
For function B
[tex]y = 2x + 4[/tex]
A linear function is represented as:
[tex]y = mx + b[/tex]
By comparison
[tex]m = 2[/tex] --- slope
[tex]b = 4[/tex] --- y intercept
By comparing the results of both functions, we have the following conclusion:
Functions A and B have the same slope (i.e. 2)
Function B has a greater y intercept (i.e. 4)
Find the area of the region between the curve x^3+2x^2-3x and the x-axis over the interval [-3,1]
Answer:
[tex]\displaystyle A = \frac{32}{3}[/tex]
General Formulas and Concepts:
Calculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
Curve: x³ + 2x² - 3x
Interval: [-3, 1]
Step 2: Find Area
Set up: [tex]\displaystyle A = \int\limits^1_{-3} {(x^3 + 2x^2 - 3x)} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle A = \int\limits^1_{-3} {x^3} \, dx + \int\limits^1_{-3} {2x^2} \, dx - \int\limits^1_{-3} {3x} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle A = \int\limits^1_{-3} {x^3} \, dx + 2\int\limits^1_{-3} {x^2} \, dx - 3\int\limits^1_{-3} {x} \, dx[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = (\frac{x^4}{4}) \bigg| \limits^1_{-3} + 2(\frac{x^3}{3}) \bigg| \limits^1_{-3} - 3(\frac{x^2}{2}) \bigg| \limits^1_{-3}[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle A = -20 + 2(\frac{28}{3}) - 3(-4)[/tex]Evaluate: [tex]\displaystyle A = \frac{32}{3}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
pls hurry!! helpppp i wil give brainliest..
he sum of the first two terms of a G.P is 27 whereas the sum of the second and third term is 54. Find the first term and the common ratio.
Answer:
[tex]{ \tt{sum = \frac{a(r {}^{n - 1} )}{n - 1} }} \\ 27 = \frac{a(r {}^{2 - 1} )}{2 - 1} \\ { \bf{27 = ar - - - (i)}} \\ \\ 54 = \frac{a( {r}^{3 - 1} )}{3 - 1} \\ { \bf{108 = a {r}^{2} - - - (ii) }} \\ { \tt{(ii) \div (i) : }} \\ r = \frac{108}{27} \\ { \bf{common \: ratio = 4}} \\ { \bf{first \: term = \frac{27}{4} }}[/tex]
HELP!!!!!!!!!!!!!!!! pls
Answer: y = 25 - 2x
Step-by-step explanation:
y = mx + b
m = slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{23-25}{1-0} =\frac{-2}{1} =-2[/tex]b = y-intercept = when x = 0 = 25y = -2x + 25
Suppose that X1 and X2 are independent random variables each with a mean μ and a variance σ^2. Compute the mean and variance of Y = 3X1 + X2.
Mean:
E[Y] = E[3X₁ + X₂]
E[Y] = 3 E[X₁] + E[X₂]
E[Y] = 3µ + µ
E[Y] = 4µ
Variance:
Var[Y] = Var[3X₁ + X₂]
Var[Y] = 3² Var[X₁] + 2 Covar[X₁, X₂] + 1² Var[X₂]
(the covariance is 0 since X₁ and X₂ are independent)
Var[Y] = 9 Var[X₁] + Var[X₂]
Var[Y] = 9σ² + σ²
Var[Y] = 10σ²
3x + y = 10 x - y = 2 2
In ∆ABC if AB = 6 cm , BC = 8cm, AC = 10 cm then value of ∠B is ________
Answer:
90 degrees
Step-by-step explanation:
B is the corner and angle opposite of the side AC.
so, AC is becoming side c, and the other two are a and b (it does not matter which is which).
we use the enhanced Pythagoras formula for general triangles
c² = a² + b² - 2ab×cos(C)
in our example the angle C is named B.
but other than that we simply calculate
10² = 6² + 8² - 2×6×8×cos(B)
100 = 36 + 64 - 96×cos(B)
100 = 100 - 96×cos(B)
0 = -96×cos(B)
cos(B) = 0
=>
B = 90 degrees
The measurement of the angle K is 3x - 42, and it is obtuse. Find the restriction(s) on the values of x.
Answer:
x = 44° and 74°: x cannot be less than 44°, x cannot be greater than 74°.
Step-by-step explanation:
Obtuse angles are greater than 90° but less than 180°.
We can first solve for the lower bound of x.
[tex]3x-42=90[/tex][tex]3x=132\\[/tex][tex]x=44[/tex]°Thus the lower bound restriction of x is 44°
We can now solve for the upper bound of x.
[tex]3x-42=180[/tex][tex]3x=222[/tex][tex]x=74[/tex]°Thus the upper bound restriction of x is 74°
Cathy ran 10 meters in 2 seconds. How much time did she take to complete 100 meters?
Answer:
If Cathy ran at a constant speed of 10 meters in 2 seconds, it took Cathy 20 seconds to run 100 meters.
Step-by-step explanation:
Hope this helps.
Answer:
If Cathy run at constant speed of 10 meters in 2 seconds, it took Cathy 20 second to run 100 meters.
6 foxes catch 6 hens in 6 minutes, how many foxes will it take to catch 60 hens in 60 min. AND NO ITS NOT 60 I ALREADY TRIED. WHOEVER ANSWERS GETS 50 POINTS!
Answer:
It is 6 foxes
Step-by-step explanation:
Because if 6 foxes can catch 6 hens in 6 minuets then 6 foxs can can 60 hens in 60 minutes because you just multiply 6 minutes by 10 and get 60 minutes which is also the same for hens.
Answer:
6 foxes
Step-by-step explanation:
For 6 foxes to catch 60 hens (10 x 6 or 10 times more than 6 hens) they will need 10 times more time than they had to catch 6 hens, or 10 x 6 = 60 minutes.
Write a function rule for the table.
Answer:
A
Step-by-step explanation:
slope=(1-0)/(5-4)=1
eq. of line through (4,0) with slope 1 is
y-0=1(x-4)
put y=f(x)
f(x)=x-4
Help me ASAP please
Step-by-step explanation:
similar triangles are simply like a linear protection, a "zoom" without distortion from one triangle to the other.
so, all linear distances and connections change by the same scaling factor.
therefore also the height EF of the smaller triangle colors the same scaling factor as the other lines. and EF is half the length of CG.
the area of a triangle is defined as baseline × height /2.
so, 2 linear distances are multiplied.
each one now contains the same scaling factor. so, the formula for the similar triangle multiplies the original distances and fire each also the scaling factor leading to the square of the scaling factor.
so, area new = area old × scaling²
in our example the scaling factor is 2, and 2² = 4.
so the area of ABC is 4 times as large as the area of ADE.
Find the area of circle x that has a radius at coordinates X = (0, 3) and Y = (-3, -1). Round to the nearest tenth.
Answer:
78.5 units²Step-by-step explanation:
Area of circle:
A = πr²Distance between x and y is same as r, so:
r² = (0 + 3)² + (3 + 1)² = 9 + 16 = 25Then the area is:
A = π*25 = 78.5 units² (rounded)at the farmers market 8 apple cost $5.20 if each apple cost the samw amount what is the price per apple
[tex]\displaystyle\bf Solve:8\times p=5,2 \$ => p=\frac{5,2}{8} =\frac{5,2:\boxed{8}}{8:\boxed{8}} =0,65\$\quad She \:unit\: cost\:is\:\underline{ 0,65} \\\\Check :\:8\times\underline{0,65} =5,2\$ \\\\0,65=0,65 \\\\\rightarrow The\: price\:per \:apple \:is \: 0,65 \$[/tex]
Emmy just bought a new laptop! She used a student discount code that took $50.75 off the original price. The discounted price of the laptop was $349.24. Let p represent the original price of the laptop. Which equation models the problem?
Answer:
can you show the equations?
A jewellery shop is having a sale. A bracelet is now reduced to £420. This is 70% of the original price. Work out the original price of the bracelet.
Answer:
Step-by-step explanation:
x is the original price.
420/x = 70% = 0.7
x = 420/0.7 = 600
Original price of bracelet was £600
Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the situation can be modeled by the equation, where t is the number of hours it would take to clear the field together.
How long will it take Ted and Jacob to clear the field together?
Answer:
[tex]\frac{6}{5}[/tex] of an hour = 1 1/5 hour = 72 minutes
Step-by-step explanation:
[tex]\frac{1}{3} h + \frac{1}{2}h = 1\\\\\frac{2}{6} h + \frac{3}{6}h = 1\\\\\\\frac{5 }{6} h =1\\\\h=\frac{6}{5}[/tex]
It would take Ted and Jacob 6/5 or 1.2 hours to clear the field together.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Let's use the formula for the work rate:
Ted's work rate = 1/3 of the field per hour
Jacob's work rate = 1/2 of the field per hour
Together, their work rate.
= (1/3 + 1/2) of the field per hour
Now,
We can simplify the equation for the combined work rate by finding a common denominator:
(1/3 + 1/2)
= (2/6 + 3/6)
= 5/6 of the field per hour
Now we can use the formula for the work rate to solve the time it would take them to clear the field together:
(5/6)t = 1
(where t is the time in hours)
Solving for t:
(5/6)t = 1
t = 6/5
Therefore,
It would take Ted and Jacob 6/5 or 1.2 hours to clear the field together.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ7
The coordinates of the point that is a reflection of Y(-4, -2) across the x-axis are (_,_)
The coordinates of the point that is a reflection of Y across the y-axis are (_,_) also anwser the top u know
Answer:
(-4,2)
Step-by-step explanation:
A bakery offers 4 different flavors of cake, 3 types of icing, 6 toppings, and 3 different sizes. If one option is chosen from each list, how many different cakes are possible? *
Answer:
216 different cakes are possible.
Step-by-step explanation:
Given that a bakery offers 4 different flavors of cake, 3 types of icing, 6 toppings, and 3 different sizes, if one option is chosen from each list, to determine how many different cakes are possible the following calculation must be performed:
4 x 3 x 6 x 3 = X
12 x 18 = X
216 = X
Therefore, 216 different cakes are possible.
The lines r: x+3=0 and s: y-2=0 intersect at a point P.
a) Determine the coordinates of point P.
b)What is the distance of P from the origin?
Answer:
(-3,2)
Step-by-step explanation:
The given Equations of lines are ,
[tex]\implies x + 3 = 0 [/tex]
[tex]\implies y -2 = 0 [/tex]
On plotting the graph of the given two equations we will get that the two lines will intersect each other at a point and that point will be the solution of the system of equation. On drawing a graph ,
On looking at graph , Point P will be ,
[tex]\implies Solution = P(-3,2) [/tex]