Find the area the sector.arc circle 7A. 1083π4 in²B. 1083π8 in²C. 57π4 in²D. 38π in²
Answers
Solution:
Given:
A circle with the sector details;
[tex]\begin{gathered} r=19\text{ }in \\ \theta=135^0 \end{gathered}[/tex]The area of a sector is given by;
[tex]\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ A=\frac{135}{360}\times\pi\times19^2 \\ A=\frac{1083\pi}{8}\text{ }in^2 \end{gathered}[/tex]Therefore, the area of the sector is;
[tex]\frac{1083\pi}{8}\text{ }in^2[/tex]Related Questions
f(x) = x + 6f(x) = x - 6What’s the answers
Answers
Question:
Solution:
Consider the following function:
[tex]f(x)\text{ = x+6}[/tex]this is equivalent to:
[tex]y\text{ = x+6}[/tex]solving for x, we get:
[tex]x\text{ = y - 6}[/tex]exchanging the notation we get:
[tex]f(x)\text{ = x- 6}[/tex]The same procedure is applied analogously for the function f(x) = x-6.
We can conclude that the correct answer is:
YES
Use inductive reasoning to find the next number in the pattern: 1 / 3 , 2 / 4, 3 / 5, ____.
Answers
..
SOLUTION
[tex]\frac{1}{3},\frac{2}{4},\frac{3}{5},...[/tex]The sequence progresses by the addition of 1 to both numberator and denominator.
[tex]\frac{3+1}{5+1}=\frac{4}{6}[/tex]The next number is 4/6.
help!!! thanks :))))))
Answers
The length of given sides BC = 38 and EF = 38.
Given:
ΔABC ≅ ΔDEF
BC = x + 30 , EF = 4x + 6
we know that
BC = EF
x + 30 = 4x + 6
30 - 6 = 4x - x
24 = 3x
divide by 3 on both sides
3x/3 = 24/3
x = 8
BC = x + 30
= 8 + 30
= 38
EF = 4x + 6
= 4*8 + 6
= 32+6
= 38
Therefore the length of given sides BC = 38 and EF = 38.
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What are the next 4 terms of the sequence 1, 6, 11...?
Answers
The formula to find the sequence is given by:
[tex]a_n=a_1+(n-1)d[/tex]Where a1 is the first term of the sequence, n is the number of terms and d is the common difference. We can find the common difference by the following formula:
[tex]d=a_n-a_{n-1}[/tex]With the given terms of the sequence we can find d:
[tex]\begin{gathered} d=11-6=5 \\ or \\ d=6-1=5 \end{gathered}[/tex]The common difference is d=5.
Now, apply the formual to find the next 4 terms of the sequence:
[tex]\begin{gathered} a_4=1+(4-1)\cdot5=1+3\cdot5=1+15=16 \\ a_5=1+(5-1)\cdot5=1+4\cdot5=1+20=21 \\ a_6=1+(6-1)\cdot5=1+5\cdot5=1+25=26 \\ a_7=1+(7-1)\cdot5=1+6\cdot5=1+30=31 \end{gathered}[/tex]The next 4 terms are: A. 16,21,26,31
x²+25factor and find gcf first
Answers
First, write out the binomial expression.
[tex]x^2\text{ + 25}[/tex]The binomial expression is a prime mathematical express meaning it has two factors, 1 and x^2 + 25.
Therefore,
[tex]\begin{gathered} \text{The factors of x}^2+25 \\ \text{are 1 and (x}^2\text{ + 25).} \end{gathered}[/tex]Emma has money into savings accounts. One rate is 8% and the other is 12%. If she has $450 more in the 12% account and the total interest is $220, how much is invested in each savings account?
Answers
A account 8% B account 12%
A+$450 = B (1)
Ax8% +Bx12%= $220
Ax0.08 + Bx0.12 = 220
Now we replace (1) on B:
Ax0.08 + (A+450)x0.12 = 220
Ax0.08 + Ax0.12 + 54 = 220
Ax0.2 = 166
A= 830.
Now we replace the value of A on equation (1):
830 + 450 = B
B = 1280
-3x+5y=-8 solve for x and y
Answers
ANSWER
The set of equations has no solution
EXPLANATION
-3x + 5y = -8 ------ equation 1
6x - 10y = 16 -------- equation 2
These two equations can be solve simultaneously either by substitution method or elimination method
To solve for the value of x and y, we will be using the elimination method
-3x + 5y = -8
6x - 10y = 16
Let us eliminate x first.
We need to make the coefficient of x in both equation equal
Hence, multiply equation 1 by 2 and equation 2 by 1
-3x*2 + 5y*2 = -8 x 2
6x * 1 - 10y * 1 = 16 x 1
-6x + 10y = -16 ------------ equation 3
6x - 10y = 16 -------------- equation 4
To eliminate x , add equation 3 and 4 together
-6x + 6x + 10y + (-10y) = -16 + 16
-6x + 6x + 10y - 10y = -16 + 16
0 + 0 = 0
0 = 0
Hence, the set of equations has no solution
Question #2Several points are plotted on the graph. Which of the plotted points on the graph represent the zeros of the function:f (x) = (x^2+ 2x- 8) (x – 6)
Answers
Given function is:
[tex]f(x)=(x^2+2x-8)(x-6)[/tex]Now put f(x)=0
[tex]\begin{gathered} (x^2+2x-8)(x-6)=0 \\ (x^2+2x-8)=0,(x-6)=0 \\ x-6=0 \\ x=6 \end{gathered}[/tex]so the first point is (6,0) now for another points:
[tex]\begin{gathered} (x^2+2x-8)=0 \\ (x^2+4x-2x-8)=0 \\ x(x+4)-2(x+4)=0 \\ (x+4)(x-2)=0 \\ x=-4,2 \end{gathered}[/tex]So the points are (-4,0) and (2,0) and(6,0)
Hence the correct options are 1,2 and 4.
This table shows how many sophomores and juniors attended two school events.What is the probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert?Round your answer to two decimal places.
Answers
Given:
Number of sophomores attended jazz band concert = 35
Total number of students = 137
Required: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert.
Explanation:
The formula to find probability is
[tex]p=\frac{\text{Number of favorable outcomes}}{\text{ Total number of outcomes}}[/tex]Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert
[tex]\begin{gathered} =\frac{\text{Number of sophomores attended jazz band concert}}{\text{ Total number of students in this group}} \\ =\frac{35}{137} \\ =0.26 \end{gathered}[/tex]Option D is correct.
Final Answer: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert is 0.26.
8Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true.p=(-c ≤ Z ≤ c ) =0.9127Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Answers
The value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
It is given to us that -
[tex]P(-c\leq Z\leq c)=0.9127[/tex] is true
It is also given that Z follows the standard normal distribution.
We have to find out the value of c.
Since Z follows the standard normal distribution, so we can say that
Z ∼ N(0,1)
To find out c,
[tex]P(-c\leq Z\leq c)=0.9127\\= > P(Z\leq c)-P(Z\leq -c)=0.9127\\[/tex]
Since there is a symmetric z-distribution, the above equation can be represented as -
[tex][1-P(Z\leq -c)]-P(Z\leq -c) = 0.9127\\= > 1-P(Z\leq -c) - P(Z\leq -c) = 0.9127\\= > 1-2P(Z\leq -c)=0.9127\\= > 2P(Z\leq -c)=0.0873\\= > P(Z\leq -c)=0.04365[/tex]
=> -c ≈ 0.0873 (Using online calculator)
Therefore, the value of c such that [tex]P(-c\leq Z\leq c)=0.9127[/tex] is true is 0.0873 where Z follows the standard normal distribution.
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Answer:
The value of c such that is true is 0.0873 where Z follows the standard normal distribution.
Step-by-step explanation:
bailey buys new winter clothes for $136 she has to pay 8.25% sales tax on her purchase. how much is the sales tax for her new clothes?
Answers
Given :
The cost of the new winter clothes = $136
The sales tax = 8.25%
So, the sales tax = 8.25% of 136 =
[tex]\frac{8.25}{100}\cdot136=11.22[/tex]So, the answer is : the sales tax = $11.22
Sally's wallet contains• 5 quarters• 3 dimes• 8 nickels• 4 penniesSally will randomly choose a coin, replace it, and randomly choose another coin. What is teh probability thatshe will choose a dime and then a quater?
Answers
Sally's wallet contains the following coins
Quarters = 5
Dimes = 3
Nickels = 8
Pennies = 4
What is the probability that she will choose a dime and then a quarter?
Recall that the probability of an event is given by
[tex]P=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}[/tex]The probability that she will choose a dime is given by
[tex]P(dime)=\frac{3}{5+3+8+4}=\frac{3}{20}[/tex]The probability that she will choose a quarter is given by
(note that replacement is allowed so the total number of coins remains the same)
[tex]P(quarter)=\frac{5}{5+3+8+4}=\frac{5}{20}=\frac{1}{4}[/tex]So, the probability that she will choose a dime and then a quarter is
[tex]\begin{gathered} P(dime\: and\: quarter)=P(dime)\times P(quarter) \\ P(dime\: and\: quarter)=\frac{3}{20}\times\frac{1}{4} \\ P(dime\: and\: quarter)=\frac{3}{80} \end{gathered}[/tex]Therefore, the probability that she will choose a dime and then a quarter is 3/80
Liam placed 24 patio pavers as shown below.
A rectangular array shows four patio pavers wide by six patio pavers long. The total length of the side of the rectangle that has four patio pavers is sixty-three and two-tenths inches.
What is the length of a single patio paver?
A.
18.2 in.
B.
15.8 in.
C.
10.53 in.
D.
2.63 in.
Answers
4 patio pavers = 63.2 inches
1 patio pavers = 15.8 inches.
The length of one patio paver is 15.8 inches.
What is a rectangle?
A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The total length of the side of the rectangle that has four patio pavers is sixty-three and two-tenths inches.
This means,
Length of the side with 4 patio pavers.
= 63(2/10) inches
= 632/10
= 63.2 inches
Now,
The length of one patio paver.
4 patio pavers = 63.2 inches
Divide both sides by 4.
1 patio pavers = 63.2/4
1 patio pavers = 15.8 inches.
Thus,
The length of one patio paver is 15.8 inches.
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A shipping container will be used to transport several 40-kilogram crated across the country by rail. The greatest weight that can be loaded into the container is 24500 kg.other shipments waiting 11300 kilograms have already been loaded into the container. right and solved an inequality which can be used to determine x, the number of 40 kg crates that can be loaded into the shipping container.
Answers
The greatest load that fits in the container is 24500kg
There are already 11300Kg loaded
Let x indicate the number of 40Kg crates, then 40x symbolized the total weight of the crates loaded.
You can express the inequality as
[tex]11300+40x\leq24500[/tex]From this expression we can calculate the number of crates that can be loaded as follows:
[tex]\begin{gathered} 11300+40x\leq24500 \\ 40x\leq24500-11300 \\ 40x\leq=13200 \\ \frac{40x}{40}\leq\frac{13200}{40} \\ x\leq330 \end{gathered}[/tex]You can load up to 330 crates into the container.
Clean Machine is Middletown's premier house cleaning service. The company used 2,920 gallons of soap last year, and 35% less this year. How many gallons of soap did the company use this year?
Answers
Answer:
Step-by-step explanation:)
A standard die is rolled. Find the probability that the number rolled is less than 3. Express your answer as a fraction
Answers
Once a die has the numbers 1,2,3,4,5 and 6, it means the numbers that are less than 3 are just the numbers 1 and 2. Now the probability can be built as follows:
As we can see above, once there are just two possibilities of numbers that are less than 3, the probability that the number rolled is less than 3 is equal to 2/6.
What is 4.73 x 3.4?
Please answer
Answers
Answer:
Explanation:
The product of 4.73 and 3.4 is calculated below:
Solve the system of equations.y = x2 - 2y = -2x + 1A. (-3,7) and (-1,3)B. (-3,7) and (1, -1)C. (1.-1) and (3,-5)D. (-1,3) and (3, -5)
Answers
Answer
Option B is correct.
the solutions to the system of equations include
(-3, 7) and (1, -1)
Step-by-step Explanation
The question is to solve the system of equations
y = x² - 2 ..... equation 1
y = -2x + 1 ..... equation 2
To solve this, we can just equate the expression given for y in equation 1 to the expression given for y in equation 2.
y = x² - 2
y = -2x + 1
Since
y = y
x² - 2 = -2x + 1
x² + 2x - 2 - 1 = 0
x² + 2x - 3 = 0
This gives a quadratic equation which we will now solve
x² + 2x - 3 = 0
x² + 3x - x - 3 = 0
x (x + 3) - 1 (x + 3) = 0
(x - 1) (x + 3) = 0
So,
x - 1 = 0 or x + 3 = 0
x = 1 or x = -3
If x = 1,
y = x² - 2
= 1² - 2
= 1 - 2
= -1
x = 1, y = -1
If x = -3
y = x² - 2
= (-3)² - 2
= 9 - 2
= 7
x = -3, y = 7
So, the solutions to the system of equations include
x = -3, y = 7, that is, (-3, 7)
And
x = 1, y = -1, that is, (1, -1)
Hope this Helps!!!
In 1960, the world record for the men's mile was 3.91 minutes. In 1980, the record time was 3.81 minutes. a, write the linear model that represents the world record (in minutes) for the men's mile as a function of the number of years, t , since 1960. y=___b, use the model to estimate the record time in 2000 and predict the record time in 2020.2000:___ minutes2020:___ minutes
Answers
To first answer this question, we need to find the slope of the linear equation. We have the following information:
x1 = 1960, y1 = 3.91
x2 = 1980, y2 = 3.81
Then
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3.81-3.91}{1980-1960}=-0.005[/tex]Then, we have that the linear model will be:
[tex]y-y1=m\cdot(x-x1)\Rightarrow y-3.91=-0.005\cdot(x-1960)_{}[/tex]Or
[tex]y=-0.005\cdot(x-1960)+3.91\Rightarrow y=-0.005x+13.71[/tex]This is the linear model.
Then, to use the model to estimate the record time in 2000 and in 2020, we have:
[tex]y=-0.005\cdot(2000)+13.71\Rightarrow y=3.71[/tex]And
[tex]y=-0.005\cdot(2020)+13.71\Rightarrow y=3.61[/tex]Therefore, the linear model is y = -0.005x + 13.71.
The estimation for the record time in 2000 is 3.71 minutes.
The estimation for the record time in 2020 is 3.61 minutes.
This is a linear model.
How can we tell when every point on the graph is a solution to the problem?
Answers
One way to verify that if a point exist on both lines is to substitute the x- and y-values of the ordered pair into the equation of each line. If the substitution results in a true statement, then you have the correct solution!
A rectangular piece of metal has an area of 112 square centimeters. Its perimeter is 46 centimeters. What are the dimensions of the piece?
Answers
Let the length of rectabgle be l and width of rectangle be b.
The equation for the area of rectangle is,
[tex]l\cdot b=112[/tex]The equation for perimeter of rectangle is,
[tex]\begin{gathered} 2(l+b)=46 \\ l+b=23 \\ l=23-b \end{gathered}[/tex]Substitute 23 - b for l in the equation lb
Which of the following statements are true for the image of a triangle after a dilation that has a scale factor of 5/6
Answers
EXPLANATION
Since we have a dilation with a scale factor of 5/6, the appropriate statement is the following:
1st) Each angle has the same measure as its corresponding angle in the preimage. This is true because the dilations don't change the shape.
II. Each has a measure 5/6 the length of its corresponding side in the pre-image.
Part a: How many pieces are in the step functionpart b: how many intervals make up the step function? What are the interval valuespart c: why do we use open circles in some situations and closed in otherspart e are the pieces of this piecewise function linear or non linear?part f what is the range of this piecewise function?
Answers
a) The step function seen in the figure has 6 pieces, one for each step
b) There are 6 intervals, one for each piece. Their values are:
(0, 1]
(1, 2]
(2, 3]
(3, 4]
(4, 5]
(5, 6]
c) The open circles indicate that the endpoint is not included in the interval. The closed circles indicate the endpoint is included in the interval.
For example, in the second interval, 1 is not included (open circle) and 2 is included (closed circle).
d) This is a function because for eac value of x there iss one and only one of y. If the open circles were closed circles, then thi wouldnot be a function.
e) All the pieces are linear because their graph is a line (flat horizontal line)
f) The range of the function is the set of output values:
Range = {46, 48, 50, 32, 54, 56}
Find the inverse of 1/4x^3+2x-1=y
Answers
Choose all of the options below that are expressions.
5t +1
9+4t
16=t
2-17t
6-t
3t=0
Answers
Answer:
here are the answers
Step-by-step explanation:
5t +1 2-17 3t=0 so yeah those are the answers
I think?
Debra has ridden 6 miles of a bike course. The course is 15miles long. What percentage of the course has Debra ridden so far
Answers
From the question
Miles covered for bike course = 6 miles
Total miles of course = 15 miles
In percentage, this becomes
Let z = percentage of miles covered
Hence
[tex]z=\frac{\text{miles covered}}{Total\text{ miles}}\times100\text{\%}[/tex]Substitute in the values to get
[tex]z=\frac{6}{15}\times100\text{\%}[/tex]Simplify:
[tex]\begin{gathered} z=\frac{2}{5}\times100\text{\%} \\ z=2\times20\text{\%} \\ z=40\text{\%} \end{gathered}[/tex]Therefore, the percentage of the course Debra has ridden so far is 40%
Will a truck that is 14 feet wide carrying a load that reaches 12 feet above the ground clear the semielliptical arch on the one-way road that passes under the bridge shown in the figure on the right?
Answers
Given the equation of an elipse
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]from the question,
[tex]\begin{gathered} \text{major axis}\Rightarrow2a \\ \therefore2a=52 \\ a=\frac{52}{2}=26ft \\ b=13ft \end{gathered}[/tex]Given that
[tex]x=14ft[/tex]Substitute, for a,b, and x in the elipse formula to find y
[tex]\begin{gathered} \frac{14^2}{26^2}+\frac{y^2}{13^2}=1 \\ \frac{196}{676}+\frac{y^2}{169}=1 \end{gathered}[/tex]Multiply through by 169
[tex]\begin{gathered} 49+y^2=169 \\ y^2=169-49 \\ y^2=120 \\ y=\sqrt[]{120}=10.95ft \end{gathered}[/tex]Hence, it clear the arch because the height of the archway of the bridge 7 feet from the center is approximatelyfeet
Could you help walk me through this problem? I keep getting the problem wrong and I don't know why.
Answers
to solve this we can get the equation in the form
F(x)=a(x-X1)(x-X2)
where X1 and X2 are the values of X where the line cross the axial X
in this case
X1= -1
X2= 2
so the function will be
F(x)=a*(x+1)*(x-2)
now we need to find the value of a
So for this we can replace with a random point of the curve, for example the point x= 0 y=-2
So if we replace
-2=a*(0+1)*(0-2)
-2=a*1*-2
-2=a*-2
-2/-2=a=1
So the answer is:
F(x)=1*(x+1)*(x-2)
A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measure the angle of depressionto the Groveburg soccer fields to be 20° 15'. To the right side of the balloon, the balloonist measures the angle ofdepression to the high school football field to be 62° 30'. The distance between the two athletic complexes is 4 miles.What is the distance from the balloon to the football field?a.b.>3.6 miC.~6.2 mi>2.2midy1.4 miPlease select the best answer from the choices providedOAOBOCOD
Answers
The distance from the balloon to the football field will be 1.4 miles.
Angle of depression to the Grove burg soccer fields = 20° 15'.
Use 1' = 1 / 60° :
15' = 1 / 4 ° = 0.25 °
20° 15' = 20.25°
Angle of depression to the high school football field = 62° 30'.
30' = 0.5°
62° 30' = 62.5°
the distance from the balloon to the football field will be:
Let the distance be a
a / sin a = c / sin c
a / sin (20.25) = 4 / sin (97.5)
a = 4 sin (20.25) / sin (97.5)
a = 1.4 miles.
Therefore, we get that, the distance from the balloon to the football field will be 1.4 miles.
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-x + 2y = 11 three points graphed please help !
Answers
We can see that we have the following equation:
[tex]-x+2y=11[/tex]And we can see that this is a linear equation in standard form:
[tex]Ax+By=C[/tex]And we need to graph the linear equation. To achieve that, we can proceed as follows:
1. We can find the intercepts of the linear function, and then we will have two points we can use to graph the line equation. We can find another point to graph it easier.
2. To find the x-intercept (the point where the line passes through the x-axis, and when y = 0) is as follows:
[tex]\begin{gathered} -x+2y=11\rightarrow y=0 \\ \\ -x+2(0)=11 \\ \\ -x=11\Rightarrow x=-11 \end{gathered}[/tex]Therefore, the x-intercept is (-11, 0).
3. To find the y-intercept (the point where the line passes through the y-axis, and when x = 0) is as follows:
[tex]\begin{gathered} -x+2y=11\rightarrow x=0 \\ \\ 2y=11 \\ \\ \frac{2y}{2}=\frac{11}{2} \\ \\ y=5.5 \end{gathered}[/tex]Therefore, the y-intercept is 5.5 (0, 5.5).
4. Since we have a decimal, and to be more precise, we can find another point. To do that, we can try with x = 5:
[tex]\begin{gathered} -x+2y=11 \\ \\ -5+2y=11 \\ \\ -5+5+2y=11+5 \\ \\ 2y=16\Rightarrow y=\frac{16}{2}=8 \\ \\ y=8 \\ \end{gathered}[/tex]Then we have another pair to graph the function: (5, 8).
5. We can find another point, using x = -5. Then we have:
[tex]\begin{gathered} -x+2y=11 \\ \\ -(-5)+2y=11 \\ \\ 5+2y=11\Rightarrow5-5+2y=11-5 \\ \\ 2y=6 \\ \\ \frac{2y}{2}=\frac{6}{2}\Rightarrow y=3 \end{gathered}[/tex]Therefore, another point is (-5, 3)
5. Now, with these values, we can sketch the graph of the line as follows (we will use (-5, 3) and (5, 8), and we will see that the line passes through the point (0, 5.5):
• (-11, 0),, (-5, 3),, (0, 5.5), ,(5, 8)
Therefore, we can see the points: (-5, 3), (0, 5.5), and (5, 8) are three points that solve the equation -x + 2y = 11, since they lie on that line:
[tex]\begin{gathered} -(-5)+2(3)=11 \\ \\ 5+6=11 \\ \\ 11=11\text{ \lparen It is true\rparen} \\ \\ \text{ And we can follow the same steps for the other two points:} \\ \\ -(0)+2(5.5)=11 \\ \\ 11=11 \\ \\ \text{ And} \\ \\ -5+2(8)=11 \\ \\ -5+16=11 \\ \\ 11=11 \end{gathered}[/tex]Therefore, in summary, we graphed the linear function as follows, and we found that the three points on the graph solve the equation -x + 2y = 11, that is, (-5, 3), (0, 5.5), and (5, 8):
