We have the following, L, of the beam varies as the product of the width and the square of the height:
[tex]L\propto w\cdot h^2[/tex]And varies inversely as the lenght of the wooden beam:
[tex]L\propto\frac{w\cdot h^2}{l}[/tex]therefore:
[tex]L=k\cdot\frac{w\cdot h^2}{l}[/tex]where k is the proportionality constant
w = 4, h=8, l = 216 and L = 5050
[tex]\begin{gathered} 5050=k\cdot\frac{4\cdot8^2}{216} \\ k=\frac{5050\cdot216}{256} \\ k=4260.93 \end{gathered}[/tex]now, if w = 2, h = 5, l = 144:
[tex]\begin{gathered} L=4260.93\cdot\frac{2\cdot5^2}{144} \\ L=1479.5 \end{gathered}[/tex]Here are the ages (in years) of 10 professors at a college. , 44,38,45,34,28,56,54,28,61,48.what is the percentage of these professors who is younger than 47
Solution:
Given:
The ages in years of the 10 professors at a college to be;
44,38,45,34,28,56,54,28,61,48
Professors who are younger than 47 = 44,38,45,34,28,28
Number of Professors who are younger than 47 = 6
The percentage of these professors who is younger than 47 =
[tex]\begin{gathered} =\frac{6}{10}\text{ x 100} \\ =60\text{ \%} \end{gathered}[/tex]Therefore, the percentage of professors who is younger than 47 is 60%
Farmer Ed has 2,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
500,000cm²
Explanations:
The formula for calculating the perimeter of the fence is expressed as:
[tex]P=2(l+w)[/tex]where:
• L is the ,length, of the fencing
,• W is the ,width ,of the fencing
If Farmer Ed does not fence the side along the river, the perimeter of the river will become;
[tex]\begin{gathered} P=l+2w \\ 2000=l+2w \\ l=2000-2w \end{gathered}[/tex]The area of the rectangular plot will be expressed as:
[tex]A=lw[/tex]Substitute the expression for the length into the area to have:
[tex]\begin{gathered} A=w(2000-2w) \\ A=2000w-2w^2 \end{gathered}[/tex]If the area of the plot is maximized, then dA/dw = 0. Taking the derivative will give:
[tex]\begin{gathered} \frac{dA}{dw}=0 \\ 2000-4w=0 \\ 4w=2000 \\ w=\frac{2000}{4} \\ w=500m \end{gathered}[/tex]Calculate the length of the plot. Recall that:
[tex]\begin{gathered} l=2000-2w \\ l=2000-2(500) \\ l=2000-1000 \\ l=1000m \end{gathered}[/tex]Determine the largest area that can be enclosed
[tex]\begin{gathered} A=lw \\ A=500m\times1000m \\ A=500,000m^2 \end{gathered}[/tex]Hence the largest area that can be enclosed is 500,000cm²
Can you please help me answer the question?
We have the equation:
[tex]48h-6=426[/tex]Then solve for h:
[tex]\begin{gathered} 48h-6+6=426+6 \\ 48h=432 \\ \frac{48h}{48}=\frac{432}{48} \\ h=9 \end{gathered}[/tex]Answer: B. 9 feet
Simplify the expression. (W6) (w^8)^3=
We must simplify the following expression:
[tex](w^8)^3.[/tex]To simplify this expression, we must take into account the following property:
[tex](x^a)^b=x^{a\cdot b}.[/tex]Using the property above, we have:
[tex](w^8)^3=w^{8\cdot3}=w^{24}\text{.}[/tex]Answer
[tex](w^8)^3=w^{24}[/tex]1/2×-8=9 and ×-8=18 are not equivalent because
By definition, you know that two equations are equivalent when they have the same solution. So, solving the first equation you have
[tex]\begin{gathered} \frac{1}{2}x-8=9 \\ \text{ Add 8 }to\text{ both sides of the equation} \\ \frac{1}{2}x-8+8=9+8 \\ \frac{1}{2}x=17 \\ \text{Multiply by 2 }on\text{ both sides of the equation} \\ 2\cdot\frac{1}{2}x=17\cdot2 \\ x=34 \end{gathered}[/tex]Now, solving the second equation you have
[tex]\begin{gathered} x-8=18 \\ \text{ Add 8 to both sides of the equation} \\ x-8+8=18+8 \\ x=26 \end{gathered}[/tex]Since the equations do not have the same solution then these equations are not equivalent.
Hi , can you help me please , I did the run and ride the results is y=-4/3x + 4/3. what would the graph look like with ours results?
Given the equation of a straight line below
[tex]y=-\frac{4}{3}x+\frac{4}{3}[/tex]The general equation of a line,
[tex]y=mx+c_{}[/tex]Where
[tex]\begin{gathered} m\text{ is the slope of the line} \\ c\text{ is the y-intercept} \end{gathered}[/tex]The slope, m, of the given line is
[tex]m=-\frac{4}{3}[/tex]The graph of the equation of the line given is shown below
Hence, the slope of the given equation of a line is, m = -4/3
Reason that y=f(x+a) is a horizontal translation by -a and not +a
Solution:
Given:
[tex]y=f(x+a)[/tex]y = f(x + a) is a horizontal translation left by a units.
Hence, the coordinate is transformed as shown;
[tex](x,y)\rightarrow(x-a,y)[/tex]Hence, since it is a horizontal translation to the left, it is translated by -a units from the original x-coordinate given.
A car that originally cost $3,668 in 1955 is valued at $62,125 if in excellent condition, which is1 times as much as a car in very nice condition—if you can find an owner willing to part with one for any price.What would be the value of the car in very nice condition? (Do not round intermediate calculations.)Value of the car
Let
x ----> value of the car in very nice condition
we know that
1 3/4 x=62,125 ----> linear equation that represent this situation
Solve for x
but first
Convert mixed number to an improper fraction or decimal number
1 3/4=1+3/4=1+0.75=1.75
substitute
1.75x=62,125
x=62,125/1.75
x=35,500
therefore
the answer is $35,500Simplify the expression, if possible. Write the answer without negative exponents. (If the solution is not a real number, enter NOT REAL.)(-216) 1/3
The simplified expression without using negative exponents is -6 .
The given expression is of the form [tex](-216)^{\frac{1}{3}}[/tex] .
this can be written using the radical sign as ∛(-216)
Now we know that the cube root of a negative number is always a negative number .
using the properties of exponents we can write
∛(-216) = ∛(-1) × ∛216
now we know that ∛(-1) = -1 as -1³ = -1 and ∛216 = 6
Exponents are a way to show sudden increases in power. So to speak, the exponent is the amount of times a number has been multiplied by itself.
The exponent determines how many times a number is multiplied by itself, as was shown above. The mathematical notion known as the power serves as an example of the recurring multiple of the same integer or factor.
Therefore the simplified expression is -6.
To learn more about exponents visit:
https://brainly.com/question/15993626
#SPJ9
What is the major axis for the equation+= 1? Type h for horizontal or v for vertical.
Consider the given equation,
[tex]\begin{gathered} \frac{x^2}{49}+\frac{y^2}{7}=1 \\ \frac{x^2}{(7)^2}+\frac{y^2}{(\sqrt{7})^2}=1 \end{gathered}[/tex]This is a standard equation of a horizontal ellipse, whose semi-major axisis given as,
[tex]a=7[/tex]So the length of major axis will be,
[tex]2a=2(7)=14[/tex]Thus, the length of major axis of the given equation is 14 units.
Demonstrate your understanding of segment edition postulate by writing an example of a using the picture below.
hello
segment addition postulate implies given two points and a third point between them, the sum of the first two point equals the distance of ot the third point.
i'll explain better using the question given
[tex]\begin{gathered} DN=DO+OW+WN \\ we\text{ can also say} \\ DW=DO+OW \\ ON=OW+WN \end{gathered}[/tex]given a line DN with segment O and W, the sum of DO + OW + WN = DN
Which graph shows a function with a range of all real numbers greater than or equal to -1?55444-3+3+3+2-2-2+14 4-5-4-3-2-1₁ 1 2 3 4 5 x-5-4-3-111 2 3 4 5 x--5--3-2-11 1 2 3 4 5 x-2+-24-3+-3-3--4<-4O-5-4-3-2-1₁. 12-2-11-4 5 X543214+3YO
Answer:
The graph that has a range of all real numbers greater than or equal to -1 is the graph below (top middle graph).
Explanation:
Since the range or the y-values of the graph must be greater than or equal to -1, then the graph must be increasing starting from y = -1.
Out of the 4 graphs, only the two graphs in the middle shows a graph that is increasing.
The graph at the top part is increasing starting from y = -1 while the graph at the bottom part is increasing starting from y = 1 hence, the answer is the graph at the top middle part.
Keisha and her friends visit the concession stand at a football game. The stand charges $2 for a hot dog and $1 for a drink. The friends buy a total of 8 items for $11. Tell how many hot dogs and how many drinks they bought. $2.00 HOT DDLC 6100 STEP
EXPLANATION
Let's see the facts:
x= number of hot dogs they buy
y= number of drinks they buy
They buy 8 items, so
x + y = 8
Cost of a hot dog = $2
Cost of x hot dogs = 2x
Cost of a drink = $1
Cost of y drinks = 1y
The total amount they spent is:
2x + y
They spent $11, so
2x + y = 11
Now, we have a system of equations:
(1) x + y = 8
(2) 2x + y = 11
Subtracting (2) from (1):
2x + y = 11
- ( x + y = 8)
------------------
x = 3
Then, to find the number of drinks they bought, substitute x=3 into x + y = 8 and the solve for y:
3 + y = 8
Subtracting -3 to both sides:
3 - 3 + y = 8 -3
Simplifying:
y = 5
Answer:
They bought 3 hot dogs and 5 drinks.
Suppose some government bonds are paying 5.8% simple interest. How much should you invest in the bonds if you want them to be worth $5,000 in 9 years? Round your final answer to two decimal places.
The simple interest formula is given by:
[tex]FV=PV(1+in)[/tex]FV: future value
PV: present value
i: interest rate
n: interest periods
We have from the question:
FV: $5000
PV: ?
i: 5.8%
n: 9.
Then:
[tex]5000=PV(1+(0.058\cdot9))[/tex]Thus
[tex]PV=\frac{5000}{1.522}\Rightarrow PV=3285.15[/tex]Then, we should invest in $3285.15 to have $5000 in 9 years.
Need help with #3, also might not respond very quick. Please don’t end session if I don’t!!
from the question,
if it takes the rate of 2 seats in 11 minutes
then we will we will set up a proportion to show how many minutes it will take at the rate of 1 seat.
so if,
so lets make the munites to make 1 seat be x
2 seats = 11 minutes
1 seat = x
lets cross multiply
2 X x = 11 X 1
2x = 11
divide both sides by 2
2x/2 = 11/2
x = 5.5 minutes
so i will take 5.5 minutes to make 1 seat.
Nathan is taking an SAT prep class at the community center in Princeton. The community center is 4 centimeters away from Nathan's house on a city map. The scale of the map is 1 centimeter : 1 kilometer. In real life, what is the distance between Nathan's house and the community center?
we know that
The scale of the map is 1 centimeter: 1 kilometer
Applying proportion
1/1=x/4
x=4*1
x=4 km
the answer is 4 kilometers1 Х 15 8 sin-1 8 =mZT 15 T 17 U
Given:
In a right angled traingle with hypotenuse 17.
The other two length of the sides are 15 and 8.
The objective is to find the correct way of finding the angle T.
While solving a trigonometric ratio, the hypotenuse always present opposite to angle. 90 degree.
The opposite side of the triangle depends on the angle which we have to find out.
In this case, the objective is to find the measure of angle T.
So, the side opposite to angle T will be named as opposite side of right angled triangle and the reminig side will be named as adjacent side of the right angled triangle.
Since, the formula of sin is,
[tex]\sin \theta=\frac{opposite\text{ }}{hypotenuse}[/tex]If T is the angle, then opposite side is 8 and the hypotenuse is 17.
So the correct formula will be,
[tex]\begin{gathered} \sin \angle T=\frac{8}{17} \\ \angle T=\sin ^{-1}\frac{8}{17} \\ \angle T=\sin ^{-1}0.47058 \\ \angle T=28.07 \end{gathered}[/tex]Hence, the correct correct value is sin^-1 (8/17) and the measure of angle T is 28.07.
What polynomial must be added to x² - 2x + 6 so that the sum is 3x^2 + 7x ? A. 4x^2 + 5x + 6 B. 3x² + 9x + 6 C. 3x² + 9x - 6 D. 2x² + 9x - 6 E. 2x^2 – 5x + 6
Answer:
The polynomial that must be added is;
[tex]2x^2+9x-6[/tex]Explanation:
Given the polynomial;
[tex]x^2-2x+6[/tex]We want to find the polynomial that must be added to it to give the polynomial;
[tex]3x^2+7x[/tex]To get that we will subtract the polynomial from the sum;
[tex]\begin{gathered} 3x^2+7x-(x^2-2x+6) \\ =3x^2+7x-x^2+2x-6) \\ \text{rearranging;} \\ =3x^2-x^2+7x+2x-6 \\ \text{simplifying;} \\ =2x^2+9x-6 \end{gathered}[/tex]Therefore, the polynomial that must be added is;
[tex]2x^2+9x-6[/tex]Can someone please help me understand algebra.I just want to learn how to understand it because I can not understand it at all.
Algebra
Algebra is a branch of mathematics that uses not only numbers and signs, but also letters to solve operations.
Algebraic term
The algebraic term is a simple expression where letters and numbers are combined, and variables are not added or subtracted. For example:
[tex]-7x^4[/tex]In the previous algebraic term we can identify its parts:
Sign: It can be positive or negative, as in the example.
Coefficient: The number that accompanies the variable, which in this case would be 5.
Variable: It is the unknown represented by the letter x.
Exponent: The power to which the variable is raised, which in the example would be 3. If no exponent appears, it is understood that it is 1.
Algebraic expression
The algebraic expression is a set of variables and numbers that can be combined with different mathematical operations, including addition and subtraction, unlike algebraic terms. An example can be the following:
[tex]-5x^2+4y[/tex]Expressions can be expressed as a function of the number of terms that contain them as
Monomial: Has a term:
[tex]15z[/tex]Binomial: It has two terms:
[tex]2x^2-7y[/tex]Trinomial: It has three terms:
[tex]3x^2+8y+2z[/tex]Polynomial: It has more than three terms:
[tex]5x^3-3y+6z-9[/tex]Algebraic equations
An equation is the association between two algebraic expressions through the equal sign. They can be mainly of two types:
First degree equation: When the variable is raised to the maximum power 1. It is known as an equation.
5x + 5y = 9
Second degree equation: When the variable is raised to the maximum power 2. It is also called a quadratic equation.
5x2-3y + 6z-9 = 3x
The accompanying data give the heights of 18 male college students and their fathers, in inches. Use these data to complete parts (a) through (e) below.R Click the icon to view the father and son height data.
Given:
The set of data of Capital of prisons.
1, 126, 8, 2, 746, 2, 82, 9, 33, 0 ,0.
Aim:
We need to find the median of the given data set.
Explanation:
Rewrite the given data set in terms from least to greatest numbers.
0,0, 1, 2,2,8,9,33, 82, 126, 746.
There are 11 terms in this data set.
The middle term is the 6th term.
We know that median = the middle term.
[tex]Median\text{ = 6th term.}[/tex]6 th term is 8.
[tex]Median\text{ =8.}[/tex]Median is middle term so some wedern states must have fewer than 8.
For example, Wyoming has 1 capital prisoner.
The first option is wrong.
50 % of western states have fewer than 8 capital prisoners is true since 8 is the middle of the data set.
Final answer:
D. The median is 8 capital prisoners. This means that 50% of these western states have fewer than this many capital prisoners.
1.y = 6xSolve:(4x + y = 72.y = 3xsolve: { x + 2y + 703Which equation, together with y = -1.5x + 3, makes a system with one solution?Ay = -1.5x + 6B.y = -1.5xC.2y = -3x + 6D.2y + 3x = 6IE.y = -2x + 34.The system x - 6y = 4, 3x - 18y = 4 has no solution.a.Change one constant or coefficient to make a new system with one solution.b.Change one constant or coefficient to make a new system with an infinite number ofsolutions5.Match each graph to its equation.Im
The system of equations:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]This comes from the fact that if we multiply the first equation by 3 then we have:
[tex]3x-18y=12[/tex]But this clearly contradicts the second one. Then the system has no solutions.
a.
To find a system with one solution we only have to change one of the coefficients of the equation. If we change the first x coefficient from 1 to 2. then we have the system:
[tex]\begin{gathered} 2x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]which has one solution.
b.
To find a system with an infinite number of solutions we can change the constant of the second equation to 12, then:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=12 \end{gathered}[/tex]then if we multiply the first by 3 then we have the second one, therefore the equations are the same and the system will have and infinite number os solutions.
The probability of being dealt a club and a diamond is
There are a total of 52 cards in a standard deck.
There are 13 club cards and 13 diamond cards.
The probability of getting a club card is given by
[tex]P(club)=\frac{\text{number of club cards}}{\text{total number of cards}}=\frac{13}{52}[/tex]The probability of getting a diamond card is given by
[tex]P(diamond)=\frac{\text{number of diamond cards}}{\text{total number of cards}}=\frac{13}{52}[/tex]The probability of getting a club and diamond is given by
"And" means to multiply the probabilites
[tex]\begin{gathered} P(club\; \; and\; \; diamond)=P(club)\times P(diamond) \\ P(club\; \; and\; \; diamond)=\frac{13}{52}\times\frac{13}{52} \\ P(club\; \; and\; \; diamond)=\frac{169}{2704}=\frac{1}{16} \end{gathered}[/tex]Therefore, the probability of getting a club and diamond is 1/16
Please look at the picture for accurate description thank you in advance
Given:
Height of person 5.3 ft.
Distance between person and tree is 34 feet
In triangle ABC
BC=34
Angle = 71
[tex]\begin{gathered} \tan \theta=\frac{\text{ perpendicular}}{\text{ base}} \\ \tan \theta=\frac{AB}{BC} \\ \tan 71=\frac{AB}{34} \\ AB=34\times\tan 71 \\ AB=98.7431 \end{gathered}[/tex]So height of tree is person height + AB
[tex]\begin{gathered} =98.7431+5.3 \\ =104.0431 \end{gathered}[/tex]So height of tree is 104
spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute.Find the rates of change of the radius when r=30 centimeters and r=85 centimeters.Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant.
Answer
Explanation
Given:
A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute means
[tex]\frac{dV}{dt}=800\text{ }cm^3\text{/}min[/tex](a) The rates of change of the radius when r = 30 centimeters and r = 85 centimeters is calculated as follows:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ \frac{dV}{dr}=\frac{4}{3}\times3\pi r^{3-1} \\ \\ \frac{dV}{dr}=4\pi r^2 \\ \\ But\frac{\text{ }dV}{dr}=\frac{dV}{dt}\div\frac{dr}{dt} \end{gathered}[/tex]So when r = 30, we have
[tex]\begin{gathered} \frac{dV}{dr}=4\pi(30)^2 \\ \\ \frac{dV}{dr}=4\times\pi\times900 \\ \\ \frac{dV}{dr}=3600\pi \\ \\ From\text{ }\frac{dV}{dr}=\frac{dV}{dt}\div\frac{dr}{dt} \\ \\ Putting\text{ }\frac{dV}{dt}=800,\text{ }we\text{ }have \\ \\ 3600\pi=800\div\frac{dr}{dt} \\ \\ \frac{dr}{dt}=\frac{800}{3600\pi}=\frac{800}{3600\times3.14} \\ \\ \frac{dr}{dt}=0.071\text{ }cm\text{/}min \end{gathered}[/tex]Therefore, the rate of change of the radius when r = 30 is dr/dt = 0.071 cm/min.
For when r = 25 cm, the rate of change is:
[tex][/tex](1 point) Rework problem 4 from section 2.2 of your text, involving the choice of officers for acommittee. For this problem, assume that you have a committee of 10 members, and that youmust choose a parliamentarian, and secretary.msIn how many ways can these selections be made?
There are 90 possible ways the selection can be made
Here, we want to know the number of ways the choice can be made from 10 members
Firstly, we want to select 1 parliamentarian from 10 members; then after the selection we will select a secretary from the remaining nine
As pertaining selections, selecting r items from a total n , can be calculated by the use of the combinatorial formula as follows;
[tex]\begin{gathered} ^nC_r\text{ = }\frac{n!}{(n-r)!r!_{}} \\ \\ \text{Also, we have;} \\ ^nC_1\text{ = n} \end{gathered}[/tex]So, we have 10 ways to select an item from 10 items, we also have 9 ways to select an item from 9 items
So, the total possible number of ways would be;
[tex]10\times\text{ 9 = 90 ways}[/tex]Identify the property that justifies each step asked about in the answer area below.Line 1:(xz)yLine 2:x(zy)Line 3:x(yz)Line 1 to Line 2:Line 2 to Line 3:
Line 1 to line 2) This property,
[tex](xz)y=x(zy)[/tex]is called associativity.
Line 2 to line 3) The property used here is this:
[tex]xy=yx[/tex]It is called commutativity.
Identify the diameter of⊙Q, given that A=169π2please help
Solution:
Given that the area of circle Q is;
[tex]A=169\pi in^2[/tex]Also, the general formula is;
[tex]\begin{gathered} A=\pi r^2 \\ \\ \text{ Where }r=radius \end{gathered}[/tex]Thus, the radius, r, of the circle is;
[tex]\begin{gathered} 169\pi=\pi r^2 \\ \\ r^2=169 \\ \\ r=\sqrt{169} \\ \\ r=13in \end{gathered}[/tex]Thus, the diameter, d, is;
[tex]\begin{gathered} d=2r \\ \\ d=2(13in) \\ \\ d=26in \end{gathered}[/tex]ANSWER: The diameter of the circle is 26in
1f $300 is invested at a rate of 6% per year and is compounded quarterly, how much will the investment be worth in 12 years?Use the compound interest formula A-P(1+r/n)^ntO $145.23O $358.69O $613.04O $618.41
$613.04
Explanation:Amount invested is the principal
Principal, P = $300
Interest rate, r = 6% = 6/100
r = 0.06
Number of times the interest is compounded per year, n = 4
Time, t = 12
Amount after 12 years, A(12) = ?
Amount formula for compound interest is:
[tex]\begin{gathered} A(t)=P(1+\frac{r}{n})^{nt} \\ \\ A(12)=300(1+\frac{0.06}{4})^{4(12)} \\ \\ A(12)=300(1.015)^{48} \\ \\ A(12)=613.04 \end{gathered}[/tex]In 12 years, the investment will be worth $613.04
The table shows coffee preference from a survey. …If a person is chosen at random in the survey what is P (regular or creamer)?
The formula we will use to calculate the probability is given to be:
[tex]P(A\text{ or }B)=P(A)+P(B)-P(A\cap B)[/tex]Let A represent regular and B represent creamer.
We have the following parameters:
[tex]\begin{gathered} P(A)=0.78 \\ P(B)=0.41 \\ P(A\cap B)=0.32 \end{gathered}[/tex]Therefore, we can calculate the probability to be:
[tex]\begin{gathered} P(A\text{ or }B)=0.78+0.41-0.32 \\ P(A\text{ or }B)=0.87 \end{gathered}[/tex]The FOURTH OPTION is correct.
Bev got six dollars from her mom and four from her dad. she wants to buy a game that cost 18 dollars how many more she needs
Answer
Bev needs 8 dollars more to buy her game.
Explanation
Let the amount of dollars that Bev needs be x dollars
She needs 18 dollars
She gets 6 dollars from her mom
And 4 dollars from her dad
Mathematically,
(Amount that she has currently) + (Amount that she needs) = 18
Amount that she has currently = 6 + 4 = 10 dollars
Amount that she needs = x dollars
(Amount that she has currently) + (Amount that she needs) = 18
10 + x = 18
Subtract 10 from both sides
10 + x - 10 = 18 - 10
x = 8 dollars
Hope this Helps!!!