Answers
Step1: Write out the given parameter
Θ=114°,r= 6ft
Step2; Write out the formula
The area of a sector is given as
[tex]\frac{\theta}{360}\times\pi r^2[/tex]Step3: substitute the parameters into the formula
[tex]\frac{114}{360}\times\pi\times6^2[/tex][tex]\begin{gathered} \frac{114}{10}\pi \\ \frac{57}{5}\pi \end{gathered}[/tex]Hence the area of the sector is (57/5)π interms o
Related Questions
Add.(9s² - 3s) + (-6s - 9)
Answers
We have to add the expressions, grouping by similar terms:
[tex]\begin{gathered} \mleft(9s^2-3s\mright)+(-6s-9) \\ 9s^2-3s-6s-9 \\ 9s^2-9s-9 \end{gathered}[/tex]Answer: 9s²-9x-9
What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. How many grams of goo will remain after 68 minutes?
Answers
To solve this question on the half-life, we will use this expression:
[tex]\begin{gathered} G(t)=G_oe^{-kt} \\ \text{where G(t) is the remaining sample at time t.} \\ G_{o\text{ }}\text{ is the original sample} \\ K\text{ is a constant} \\ t\text{ is time} \end{gathered}[/tex]To proceed in solving, we will need to find the value of constant k
[tex]\begin{gathered} G(t)=G_oe^{-kt} \\ G(t)=17.25 \\ G_o=276 \\ t=255 \\ \text{Now substitute the parameters above into the formula:} \\ 17.25=276e^{-k(255)} \\ \frac{17.25}{276}=e^{-k(255)} \end{gathered}[/tex][tex]\begin{gathered} 0.0625=e^{-k255} \\ \ln 0.0625=-255k \\ \frac{\ln 0.0625}{-255}=k \\ 0.0109=k \end{gathered}[/tex]Now to get the half-life in minutes will be to get the time taken for the sample to go from 276g to 138g.
[tex]\begin{gathered} G(t)=G_oe^{-kt} \\ G(t)=138g \\ 138=276e^{-0.0109t} \\ \frac{138}{276}=e^{-0.0109t} \\ 0.5=e^{-0.0109t} \\ \ln 0.5=-0.0109t \\ \frac{\ln 0.5}{-0.0109}=t \\ 63.591\text{minutes = t} \end{gathered}[/tex]The half-life is 63.59 minutes.
The formula for G(t) at time t is:
[tex]G(t)=276e^{-0.0109t}[/tex]The amount of goo that will remain after 68 minutes is calculated using the formula above:
[tex]\begin{gathered} G(t)=276e^{-0.0109t} \\ t=68\text{ minutes} \\ G(t)=276e^{-0.0109(68)} \\ G(t)=276e^{-0.7412} \\ G(t)=131.5255\text{ grams} \\ G(t)\text{ = 131.53 grams (to 2 d.p)} \end{gathered}[/tex]The amount of goo remaining after 68 minutes is 131.53 grams.
log 2-log 5 can also be written as ?.
Answers
The formula for difference of two logarthimic terms are,
[tex]\log a-\log b=\log (\frac{a}{b})[/tex]Determine the expression for log 2 -log 5.
[tex]\log 2-\log 5=\log (\frac{2}{5})[/tex]Answer: log(2/5)
graph the line y=-4x
Answers
Solution
x=-2 , y = 8
x=-1, y= 4
x=0, y=0
x= 1, y= -4
x= 2, y=-8
Аis a solid consisting of two polygons which are parallel to each otherand all points between them.O A. cubeO B. prismO C. pyramidO D. triangle
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The prism is a type of polyhedron formed by two parallel faces that are identical polygons called bases. These figures are joined by the lateral faces that are parallelograms.
According to the previous definition we can conclude that the answer is:
B. Prism
Make Sense and persevere An office manageris selecting a water delivery service. AcmeH2O charges a $15 fee and $7.50 per 5-gallonjug. Best Water charges a $24 fee and$6.00 per 5-gallon jug. How many 5-gallonjugs will the office have to buy each monthfor the cost of Best Water to be less than thatof Acme H20?
Answers
You have that Acme H2O charges 15 fee and7.50 per 5-gallon. Furthermore, Best water charges 24 fee and 6.00 per 5-gallon.
In order to find the amount of five-gallons that the office have to buy, you can write, in an akgebraic form, the previous realtions, just as follow:
24 + 6x < 15 + 7.5x
That is, cost of Best water less than cost of Acme H20. x is the amount of five-gallons
You solve the previous inequality, as follow:
24 + 6x < 15 + 7.5x subtract 6x both sides and subtract 15 both sides
24 - 15 + 6x - 6x < 15 - 15 + 7.5x - 6x simplify
9 < 1.5x divide between 1.5 both sides
9/1.5 < 1.5x/1.5 simplify
6 < x
6 < x is the same as x > 6. Hence, Office would have to buy lower than 6 five-gallons.
while shopping at a 30% off sale, Robin was told that the sale price would saver her $6 on her purchase. Since the original price tag was missing, she had to calculate the price. what was the original price.
Answers
To do this, let x be the original price. Since the sale price would save you $ 6 on your purchase and this equates to 30% off, then using the rule of three you can find the original price, like this
[tex]\begin{gathered} \text{ \$6}\Rightarrow30\text{ \%} \\ x\Rightarrow100\text{ \%} \\ x=\frac{100\text{ \%}\cdot\text{ \$6}}{30\text{ \%}} \\ x=\text{ \$}\frac{600}{30} \\ x=\text{ \$20} \end{gathered}[/tex]Therefore, the original price was $20.
Verifying you have
[tex]\text{ \$20}\ast30\text{ \%= \$20}\cdot\frac{30}{100}=\text{ \$20}\cdot0.3=\text{ \$6}[/tex]Which was the $6 that Robin saved on his purchase.
NEED HELP ASAPP!!!!!!
Answers
Answer:
second line
Step-by-step explanation:
no more than :
x≤ 52 (the dot is full, 52 is a value)
Parabola in the form x^2=4pyIdentify Vertex, value of P, focus, and focal diameter.Identify endpoints of latus rectumWrite equations for the directrix and axis of symmetry X^2= -12y
Answers
Answer:
(a)
• The vertex of the parabola, (h,k)=(0,0)
,• The value of p = -3
• The focus is at (0,-3).
,• The focal diameter is 12
(b)The endpoints of latus rectum are (-1/12, -1/6) and (-1/12, 1/6).
(c)See Graph below
(d)
• I. The equation for the directrix is y=3.
,• II. The axis of symmetry is at x=0.
Explanation:
Given the equation of the parabola:
[tex]x^2=-12y[/tex]For an up-facing parabola with vertex at (h, k) and a focal length Ipl, the standard equation is:
[tex](x-h)^2=4p(y-k)[/tex]Rewrite the equation in the given format:
[tex]\begin{gathered} (x-0)^2=4(-3)(y-0) \\ \implies(h,k)=(0,0) \\ \implies p=-3 \end{gathered}[/tex]• The vertex of the parabola, (h,k)=(0,0)
,• The value of p = -3
The focus is calculated using the formula:
[tex]\begin{gathered} (h,k+p) \\ \implies Focus=(0,0-3)=(0-3) \end{gathered}[/tex]• The focus is at (0,-3).
Focal Diameter
Comparing the given equation with x²=4py, we have:
[tex]\begin{gathered} x^2=4ay \\ x^2=-12y \\ 4a=-12 \\ \implies a=-3 \\ \text{ Focal Diameter =4\mid a\mid=4\mid3\mid=12} \end{gathered}[/tex]The focal diameter is 12
Part B (The endpoints of the latus rectum).
First, rewrite the equation in the standard form:
[tex]\begin{gathered} y=-\frac{1}{12}x^2 \\ \implies a=-\frac{1}{12} \end{gathered}[/tex]The endpoints are:
[tex]\begin{gathered} (a,2a)=(-\frac{1}{12},-\frac{1}{6}) \\ (a,-2a)=(-\frac{1}{12},\frac{1}{6}) \end{gathered}[/tex]The endpoints of latus rectum are (-1/12, -1/6) and (-1/12, 1/6).
Part C
The graph of the parabola is given below:
Part D
I. The equation for the directrix is of the form y=k-p.
[tex]\begin{gathered} y=0-(-3) \\ y=3 \end{gathered}[/tex]The equation for the directrix is y=3.
II. The axis of symmetry is the x-value at the vertex.
The axis of symmetry is at x=0.
Stanley marked two points on the grid below to show the locations of the fiction section, point F, and the travel section, point T, in a bookstore.
Answers
EXPLANATION
We need to calculate the distance between the points (x₁,y₁)=(-8,-3) and (x₂,y₂)=(-3,8) applying the distance equation as shown as follows:
distance=
[tex]\text{Distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting terms:
[tex]\text{Distance = }\sqrt[]{(-3-(-8))^2+(8-(-3))^2}[/tex]Adding numbers:
[tex]\text{Distance}=\sqrt[]{(5)^2+(11)^2}=\sqrt[]{(25+121)}=\sqrt[]{146}[/tex]The shortest distance is sqrt(146)
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The population of Orange County is represented by the function f(x)=87,000(0.9)x, where x is the number of years since 2010.
The population of Greene County was 78,000 in 2010, and has decreased exponentially at a rate of 8% each year.
How do the populations of these counties compare in 2015?
Drag a value or word to the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
In 2015, the population of Orange County was approximately Response area and the population of Greene County was approximately Response area. In 2015, Response area County was more populous.
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The population of Greene County will be more than Orange County in 2015.
What is comparison?Comparing numbers, in maths, is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.
Given that, The population of Orange County is represented by the function f(x) = 87,000(0.9)x, where x is the number of years since 2010.
The population of Greene County was 78,000 in 2010, and has decreased exponentially at a rate of 8% each year.
Orange County population in 2015 = 87,000(0.9)^5 = 51372
Greene County population in 2015 = 78000(1+0.08)^5 = 51408
Hence, The population of Greene County will be more than Orange County in 2015.
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Help me please I don’t understand and I don’t get this
Answers
The solution:
Representing the given problem in a diagram, we have:
Rewrite the fraction (4/1)
Answers
Answer:
4
Explanation:
Given the fraction 4/1, this can be rewritten as 4 because any number divided by 1 can also be written as the number itself, both are equivalent.
Segment XY measures 5cm. How long is the image of XY after a dilation with: A scale factor of a?
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The image of the XY will be 5 times larger than the after dilation.
What is dilation?
resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.
The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.
Segment XY mesured as 5cm
It will undergo dilation.
If X(0,0) and Y(x,y)
XY = √x²+y²
The factor we need to multiply, a
X'(0,0), Y'(ax,ay)
So the X'Y'=√a²x²+a²y²
X'Y'=a√x²+y²
X'Y'=aXY = 5a
Hence the image of the XY will be 5 times larger than the after dilation.
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Solve the system by substitution. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter the general solution in terms of x, where x is any real number.)x − 0.2y = 2−10x + 2y = 10(x, y) =
Answers
Start multiplying the first equation for 10
[tex]\begin{gathered} 10(x-0.2y=2) \\ 10x-2y=20 \end{gathered}[/tex]add the resulting equation with the second equation
[tex]\begin{gathered} 10x-2y+(-10x+2y)=20+10 \\ 0=30\rightarrow false\text{ }0\ne30 \\ \end{gathered}[/tex]Answer:
There is no solution for the system
James bought a movie ticket for $4.05. Hepaid the movie ticket with quarters anddimes. If James used 18 coins in all, howmany quarters (q) and dimes (d) did he use?=q + d = 180.25q + 0.1d = 4.05+=ritorddia
Answers
q + d = 18
0.25q + 0.1d = 4.05
We will use substitution
Solving the first equation for q
q = 18 -d
Substituting this into the second equation
.25(18-d) + .1d = 4.05
Distribute
4.5 - .25d +.1d = 4.05
Combine like terms
4.5 - .15d = 4.05
Subtract 4.5 from each side
-.15d = -.45
Divide each side by -/15
-.15d/-.15 = -.45/-.15
d = 3
We have 3 dimes
Now we can find the number of quarters
q = 18-d
q = 18-3
q = 15
We have 15 quarters
11. The table shows the distance, y, a car can travel in feet in x seconds. Speed or Car Time, x (seconds) 5 10 Distance, y (feet) 700 1,400 2,100 2,800 3,500 15 20 25 Based on the information in the table, which equation can be used to model the relationship between x and y? A. y = 140x B.y = 5x C. y = x + 140 D. y = x + 5
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
y = distance
x = time
equation = ?
Step 02:
y = k x
if y = 700ft , x = 5 seconds
700 = k * 5
700 /5 = k
140 = k
y = 140 x
The answer is:
y = 140 x
Enter the equation in standard form.y = 4x - 9
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The general form of the standard line is:
[tex]Ax+By=C[/tex]So, we need to change the given equation to the standard form
the given equation is;
[tex]y=4x-9[/tex]Making x and y on the left side
So,
[tex]-4x+y=-9[/tex]And can be written as:
[tex]4x-y=9[/tex]A hotel swimming pool is made for semi circle and square. Find The perimeter of the swimming pool. Round your answer to the nearest tenth.
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Combining the 4 semi-circles of the pool, we can make 2 circles, with a diameter of 10 yd.
The perimeter of a circle is calculated as follows:
[tex]P=\pi\cdot D[/tex]where D is the diameter.
Then, the perimeter of the swimming pool is:
[tex]\begin{gathered} P=2\cdot\pi\cdot10 \\ P=62.8yd^{} \end{gathered}[/tex]Which of the following options results in a graph that shows exponentialdecay?5 pointsO f(x) 0.4(0.2)^xf(x) = 4(4)^xf(x) = 0.7(1.98)^xOf(x) = 5(1+.1)^x
Answers
Answer
Option A is the answer.
f(x) = 0.4(0.2)ˣ
The value carrying the power of x is less than 1, so, this expression represents exponential decay.
Explanation
The key to knowing which expression is represents an exponential decay or exponential growth is the value of the number carrying the power of x.
If that number is greater than 1, then it represents exponential growth.
But, if that number is lesser than 1 (but greater than 0), then it represents exponential decay.
(2)ˣ represents exponential growth.
(0.5)ˣ represents exponetial decay.
f(x) = 0.4(0.2)ˣ
The value carrying the power of x is less than 1, so, this expression represents exponential decay.
f(x) = 4(4)ˣ
The value carrying the power of x is greater than 1, so, this expression represents exponential growth.
f(x) = 0.7(1.98)ˣ
The value carrying the power of x is greater than 1, so, this expression represents exponential growth.
f(x) = 5(1 + .1)ˣ
The value carrying the power of x is greater than 1, so, this expression represents exponential growth.
Hope this Helps!!!
all of the Patron in part shade and rewrite (x × y)^nas a product of two single powers
Answers
we have
(2*3)^5
we know that
(2*3)^5=(2^5)(3^5)
Rewrite each term as product of two single powers
so
(2^5)(3^5)=(2^3)(2^2)(3^3)(3^2)
Part c
we have
10^2/10^0
when divide, subtract the exponents
so
10^(2-0)
10^2
another way
Any number elevated to zero is equal to 1
so
10^0=1
substitute
10^2/1=10^2
Part f
we have
(2/3)^5
we know that
(2/3)^5=2^5/3^5
The polynomial, 3x2 - x +1, can be classified as a 2nd degree trinomial.True or false?
Answers
The polynomial given is:
[tex]3x^2\text{ - x + 1}[/tex]A second degree polynomial is one in which the highest degree of powers is of the second degree.
Basically, a polynomial in which the highest power is 2.
By observing the given polynomial, it is a second degree polynomial.
So, the answer is True.
I need help please, it’s my math assignment also can you add simple answers
Answers
a)
Step 1:
Draw the scatter diagram from the table
x represents days and y represent set up time
Step 2:
b)
Draw the scatter diagram
Step 3:
c)
Pick two points from the graph to find the linear equation
Points (2 , 16 ) and (6, 11)
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \frac{y\text{ - 16}}{x\text{ - 2}}\text{ = }\frac{11\text{ - 16}}{6\text{ - 2}} \\ \frac{\text{y - 16}}{x\text{ - 2}}\text{ = }\frac{-5}{4} \\ \frac{y-16}{x-2}\text{ = -1.25} \\ y\text{ - 16 = -1.25x + 2.5} \\ y\text{ = -1}.25x\text{ + 18.5} \end{gathered}[/tex]The equation is y = -1.25x + 18.5
Select the conic section that represents the equation.4x2 - 25y2 = 100circleparabolaellipsehyperbola
Answers
We know that the equation of a circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]the equation a a parabola is:
[tex]y=ax^2+bx+c[/tex]the equation
Which ordered pair must be a solution in the graph of the linear inequalitybelow?(-2,2)(0, -2)
Answers
SOLUTION:
We want to determine which ordered pair must be a solution in the graph of the linear inequality. The point picked must be in the shaded region to be a solution.
Going through the options, we see that, the only ordered pair that is a solution there is;
[tex](-5,1)[/tex]
A woman invests $6300 in an account that pays 6% interest per year, compounded continuously.(a) What is the amount after 2 years? (Round your answer to the nearest cent.)$ (b) How long will it take for the amount to be $8000? (Round your answer to two decimal places.) yr
Answers
Given: A woman invests $6300 in an account that pays 6% interest per year, compounded continuously.
Required: a) To determine the amount after 2 years.
b) To determine how long it will take for the amount to be $8000.
Explanation: The amount, A after t years with an interest rate of r is given by-
[tex]A=Pe^{rt}[/tex]
Here,
[tex]\begin{gathered} P=6300 \\ r=\frac{6}{100} \\ =0.06 \\ t=2 \end{gathered}[/tex]Substituting the values, we get-
[tex]\begin{gathered} A=6300e^{0.06\times2} \\ =7103.23 \end{gathered}[/tex]Hence the amount after 2 years is $7103.23
Next, let t be the time it takes for the amount to be $8000-
[tex]\begin{gathered} 8000=6300e^{0.06t} \\ \frac{8000}{6300}=e^{0.06t} \\ \ln(1.2698)=0.06t \end{gathered}[/tex]Further solving for t as-
[tex]t=3.98\text{ years}[/tex]Hence, it takes 3.98 years for the amount to be $8000.
Final Answer: a) $7103.23
b) 3.98 years
Each expression represents the total number of dots in a pattern where n represents the step Select all the expressions that represent a quadratic relationship between the step number and the total number of dots. (If you get stuck, consider sketching the first few steps of each pattern as described by the expression.) A. I2 answer B. 2n C. non answer A D. nun E. n + 2 F.n=2 A &C • A, B, C B&C D. EF
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We have the following:
We have that an option is quadratic when the same value is being multiplied twice, that is,
[tex]n\cdot n=n^2[/tex]Therefore, among the answers the only quadratic options are A and C.
I paid $17.80 for 5 gallons of gas. using the unit rate. how much would you pay to fill all the way up if my car holds 14 gallons of gas ?
Answers
Answer: 67
Step-by-step explanation:
Stan stray kids. !!
Find the number of permutations of the letters in the word. APPLICATION
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SOLUTION:
We want to find the number of permutations of the letters in the word APPLICATION.
The word has 11 letters of which A,P,I are repeated two times.
Thus, the formula for the possible permutations of a word with repeated letters is;
[tex]=\frac{n!}{n_1!n_2!...n_k!}[/tex]Thus, we have;
[tex]\frac{11!}{2!2!2!}=4989600[/tex]I need help with this problem if anyone can help me please do Find the value of the variable
Answers
Answer:
u=11
Explanation:
The statement "The quotient of 44 and 4 is u" can be represented mathematically as:
[tex]u=44\div4[/tex]We can then solve the equation for u.
[tex]\begin{gathered} u=\frac{44}{4}=\frac{4\times11}{4} \\ \implies u=11 \end{gathered}[/tex]The value of u is 11.