Mathematics College
Answers
Answer 1
The area of the sector to 3 significant figure is 221.108 square centimeter.
The quantity of space included inside the sector's perimeter is referred to as the sector's area in a circle. A sector always starts at the circle's center. The area of a circle encompassed by its two radii and the arc next to them is known as the sector of a circle. The area of sector is given by multiplying ratio of angle to 360° to area of circle. The formula is as follows,
[tex]A=\frac{\theta}{360^0} \pi r^2[/tex]
Where r is the radius and [tex]\theta[/tex] is angle of sector.
Finding the area of sector,
Here, the radius of the sector is 13 centimeter and the angle of the sector is [tex]\theta[/tex] = 150°.
Putting the values,
[tex]A=\frac{150^o}{360^0}\times 3.14\times 13^2\\\\=221.108 cm^2[/tex]
Therefore, the area of given sector upto three significant figures is 221.108 square centimeter.
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Related Questions
List two values that make -5x < 2 true and two values that make -5x < 2false
Answers
Ok, so
Here we have an inequality, so, we're going to solve it.
-5x<2. If we solve this inequality, we obtain x > (-2/5).
(Remember that sign change because of division by a negative number).
So, the interval of solution will be (-2/5, infinity).
Then, two values that make -5x<2 true would be:
- 1 and 2. for example.
And, two values that make -5x<2 false would be:
- -3 and -4, for example.
Just need you to answer the last question at the bottom of this problem
Answers
Solution
Since we already given
[tex]\begin{gathered} m=0 \\ b=-6 \end{gathered}[/tex]
Note: The equation for a line in slope-intercept is given as
[tex]y=mx+b[/tex]
Putting m and b
[tex]\begin{gathered} y=mx+b \\ y=0(x)-6 \\ y=-6 \end{gathered}[/tex]
Therefore,
[tex]y=-6[/tex]
John is painting parallel lines in the parking lot to create parking spaces. The measure of angle A is 60° What is the measure of angle B?A-60 °B-90 °C-120 °D-180 °
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Since these are parallel lines, the angles formed are congruent ( equal).
So, Angle B=A =60°
Correct option: A-60 °
how we do this one last tutor got it wrong
Answers
First, we have to find the derivative
[tex]\begin{gathered} h^(\theta)=3cos(\frac{\theta}{2}) \\ \\ h^{\prime}(\theta)=3\frac{d}{d\theta}(cos(\frac{\theta}{2})) \\ h^{\prime}(\theta)=3\text{ \lparen - }\sin(\frac{\theta}{2})\frac{d}{d\theta}(\frac{\theta}{2})) \\ \\ h^{\prime}(\theta)=3(\text{ -}sin(\frac{\theta}{2})(\frac{1}{2}) \\ \\ h^{\prime}(\theta)=\text{ -}\frac{3}{2}sin(\frac{\theta}{2}) \end{gathered}[/tex][tex]\begin{gathered} \text{ - }\frac{3}{2}sin(\frac{\theta}{2})=0 \\ sin(\frac{\theta}{2})=0 \\ \sin^{-1}(0( \\ sin0º=0 \\ andsin180º=0 \\ \\ \\ \end{gathered}[/tex]
now he solve for h(theta)
[tex]\begin{gathered} h(\theta)=3cos(\frac{\theta}{2}) \\ \\ h(\text{ -}2\pi)=3cos(\text{ -}\frac{2\pi}{2})=3cos(\text{ -}\pi)=3(\text{ -1\rparen= -3} \\ h(0)=3cos(\frac{0}{2})=3cos0=3(1)=3 \end{gathered}[/tex]
A room of a house is k meters wide and (k+5)meters long. A carpet is to be laid on the floor so that there will be a 1-meter border left all around the room. The uncovered area of the floor can be represented by the expression: k(k+5)−[(k+3)(k−2)] What does (k+3) represent? Athe width of the carpetBthe length of the carpetCthe width of the uncovered areaDthe length of the uncovered area
Answers
The length of the room is
[tex]=k+5[/tex]
The width of the room is
[tex]=k[/tex]
The image below illustrates the question
The side of the room should have a 1-meter border, this means that on both sides of the room,the length and breadth of the room will be reduced by 2 meter
Hence,
The length of the carpet will be
[tex]\begin{gathered} =\text{length of the room - 2} \\ =k+5-2 \\ =k+3 \end{gathered}[/tex]
The width of the carpet will be
[tex]\begin{gathered} =\text{width of the room}-2 \\ =k-2 \end{gathered}[/tex]
The area of the uncovered part will be
[tex]=\text{area of the room - area of the carpet}[/tex]
The area of the room is
[tex]\begin{gathered} =\text{length of room}\times\text{width of room} \\ =k(k+5) \end{gathered}[/tex]
The area of the carpet will be
[tex]\begin{gathered} =\text{length of carpet}\times width\text{ of carper} \\ =(k+3)(k-2) \end{gathered}[/tex]
Hence,
the area of the uncovered part will be
[tex]=k(k+5)-(k+3)(k-2)[/tex]
Therefore,
k+3 represents the length of the carpet
The final answer is OPTION B
Due to gravity, an object falls 16t2 feet in t seconds. You drop a rock from a bridge that is 64 feet above the water. Will the rock hit the water in 2 seconds?
Answers
It is given that the expression for the distance an object falls in t seconds is:
[tex]16t^2[/tex]
It is required to find out if a rock that is 64 feet above water will hit the water in 2 seconds.
To do this, equate the distance above water to the expression given for distance:
[tex]16t^2=64[/tex]
Next, solve the equation for t:
[tex]\begin{gathered} 16t^2=64 \\ \text{Divide both sides by 16:} \\ \Rightarrow\frac{16t^2}{16}=\frac{64}{16} \\ \Rightarrow t^2=4 \\ \Rightarrow t=\sqrt[]{4}=2 \end{gathered}[/tex]
The time it will take for the object to fall a distance of 64 feet, is calculated to be 2 seconds.
This implies that if the rock is 64 feet from the water, it will hit the water in 2 seconds.
Yes, the rock will hit the water in 2 seconds.
A bacteria colony starts with 3 bacteria at the beginning and doubles every hour. How wouldyou write an explicit equation to model this situation?A f(x) = 2-3%B. f(x) = 3x + 2C f(x) = 2x + 3D. f(x) = 3.24
Answers
In this problem we have a linear equatiion of the form
f(x)=mx+b
where
m=2 -----> slope or unit rate
b=3 -----> initial value or y-intercept
substitute
f(x)=2x+3
therefore
The answer is
Option C
Question 1When the inequality y < x is graphed on a coordinate plane, which quadrant will becompletely shaded? Write I, II, III, or IV.QuadrantThe solution is
Answers
To grap the given lineal inequality:
[tex]y
Find two points in the boundary line:
[tex]y=x[/tex]
As y=x the points have the same coordinate value for x and y
Points (5,5) and (-3,-3)
Put those points in the plane and link them with a dotted line (as the inequality sing is < the boundary line is a dotted line).
The shadow area is under the line (the inequality sing is < (less than), then the solution is the values that are less than the line (under the line).
As you can see above the quadrant that is completely shaded is IV.Solution is all the values in the shaded area.
Sam has a summer job at a new office building. He can paint 34 of a room in 23 of an hour. He gets paid $15 per hour.
How much money will he earn for painting 24 rooms?
Answers
The amount earned painting 24 rooms is 243.5 dollars.
How to find the amount he earns painting?
Sam has a summer job at a new office building. Sam can paint 34 of a room in 23 of an hour. He gets paid $15 per hour.
The amount of money he will earn painting 24 rooms can be calculated as follows:
Therefore,
34 rooms = 23 hours
24 rooms = ?
cross multiply
number of hours he will paint = 23 × 24 / 34
number of hours he will paint = 552 / 34
number of hours he will paint = 16.2352941176
He earns 15 dollars per hour.
Therefore,
amount earn painting 24 rooms = 16.2352941176 × 15
amount earned painting 24 rooms = 243.529411765
Therefore,
amount earned painting 24 rooms = 243.5 dollars
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a model house is 12 cm long if it was built with a scale factor of 3 cm equal to 7 feet then how long is the house in real life
Answers
ANSWER:
28 feet
STEP-BY-STEP EXPLANATION:
We can determine the actual size of the house, since we know the ratio between centimeters and feet, just like this:
[tex]12\text{ cm}\cdot\frac{7\text{ ft}}{3\text{ cm}}=28\text{ ft}[/tex]
The house is 28 feet in real life.
If the mean of five values is 41, find the sum of the values.The sum of the values is
Answers
The mean is determined by dividing the sum by the number of values. Let s be the sum, we can expressed it as
[tex]\frac{s}{5}=41[/tex]
Solve for s by multiplying both sides by 5
[tex]\begin{gathered} \frac{s}{5}\cdot5=41\cdot5 \\ \frac{s}{\cancel{5}}\cdot\cancel{5}=41\cdot5 \\ s=205 \end{gathered}[/tex]
Therefore, the sum of values is 205.
con_PRoPfoT66DjbRthZcZAiBIM2-Q/viewform?hr_submission=ChI2JiQ5uQGEHAIIMKcta4HEgclipmaqaYGEAE Jackie cut 3-yards of ribbon into 6 equal lengths of ribbon. What is the length of each ribbon in yards? B. C. A. 1 2 18 1 6 3 D.2
Answers
Explanation:
We have to divide the length of the ribbon by 6:
[tex]\frac{3}{6}=\frac{1}{2}[/tex]
Answer:
Each ribbon has a length of 1/2yd (option A)
What is the length of the line segment shown in the image?
Answers
Answer:
The length of the line segment is;
[tex]7.62\text{ units}[/tex]
Explanation:
Given the line segment in the attached image.
Drawing a right angled triangle to get the length of the line segment;
We can then use pythagoras theorem to calculate length of the line segment;
[tex]c=\sqrt[]{a^2+b^2}[/tex]
From the attached image;
[tex]\begin{gathered} a=3 \\ b=7 \end{gathered}[/tex]
substituting the given values;
[tex]\begin{gathered} c=\sqrt[]{3^2+7^2} \\ c=\sqrt[]{9+49} \\ c=\sqrt[]{58} \\ c=7.62\text{ units} \end{gathered}[/tex]
Therefore, the length of the line segment is;
[tex]7.62\text{ units}[/tex]
Use the protractor to find the measure of each angle. Then classify as acute, right, or obtuse.
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Answer:
∠CGE is a right angle and has a measure of 90.
∠BGD is an obtuse angle and has a measure of 93.
∠CGB is an acute angle and has a measure of 50.
Acute angles are angles that measure less than 90.
Right angles are angles that measure exactly 90.
Obtuse angles are angles that measure greater than 90.
∠CGE
As we can see, ray C is at 70, while ray E is at 160.
160 - 70 = 90, since it measures 90, it is a right angle.
∠BGD
Ray B is at 20 while Ray D is at 113
113 - 20 = 93, since it measures greater than 90, it is an obtuse angle.
∠CGB
Ray C is at 70, Ray B is at 20
70 - 20 = 50, since it measures less than 90, it is an acute angle.
The equation of a line of best fit relating the number of cats c at an animal shelter to thenumber of dogs dis c= 2.1d - 26. Predict the number of cats at a shelter where there are30 dogs.
Answers
In order to predict the number of cats at that shelter with 30 dogs, we can use the given equation
c = 2.1d - 26
and make d = 30:
c = 2.1 * 30 - 26
Now, we need to develop the calculations to find c (we first solve the multiplication, and then the subtraction):
c = 2.1 * 30 - 26
= 63 - 26
= 37
Therefore, the predicted number of cats at that shelter is 37.
The next model of a sports car will cost 6.2% more than the current model. The current model costs $39,000. How much will the price increase in dollars? Whatwill be the price of the next model?Increase in price:Price of next model:
Answers
We have to calculate the increase in price and the price of the new model.
The next model will cost 6.2% more than the current model.
We can calculate the increase in price by multiplying the price of the current model by the increase proportion (0.062, which is the decimal expression for 6.2%):
[tex]I=\frac{6.2}{100}\cdot39000=0.062\cdot39000=2418[/tex]
With the increase, we can calculate the price of the next model as:
[tex]N=P+I=39000+2418=41418[/tex]
Answer:
Increase in price: $2,418
Price of next model: $41,418
EXPRESSION1)A punch recipe requires 2 cups of cranberry juice to make 3 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 1 gallon of punch? Please show me how you got your answer.2)A HIGH-SPEED ELEVATOR CAN RISE 480 FT IN 30 SEC, WHICH EXPRESSION REPRESENTS THE RATE. IN FT PER MIN, OF THE ELEVATOR
Answers
Step 1
Given;
[tex]2\text{ cups of cranberry juice - 3 gallons of punch}[/tex]
Required; To find the amount of cranberry juice required for 1 gallon of punch juice.
Step 2
So basically, you can set this up in proportion.
For every gallon of punch, 2 cups of cranberry juice is needed. What you need to find is the amount of cranberry juice is needed for one gallon. So then you would have to set up your proportion like this:
[tex]\begin{gathered} \frac{2\text{ cups of cranberry juice}}{\text{3 gallons of punch}}=\frac{x\text{ cups of cranberry juice}}{1\text{ gallon of punch}} \\ or \\ \frac{2}{3}=\frac{x}{1} \end{gathered}[/tex]
We will now find the value of x by cross multiplying
[tex]\begin{gathered} 2\times1=3\times x \\ 2=3x \\ \frac{3x}{3}=\frac{2}{3} \\ x=\frac{2}{3} \end{gathered}[/tex]
So you will need 2/3 cups of cranberry juice for 1 gallon of punch
Answer;
[tex]\frac{2}{3}\text{ cups of cranberry juice}[/tex]
Step 3
2) The elevator rises 480ft in 30 seconds
One minute=60 seconds.
Therefore, we will have;
[tex]\begin{gathered} \frac{480ft}{\text{xft}}=\frac{30\sec onds}{1\text{ minute}} \\ 1\text{ minute=60 seconds} \\ \frac{480ft}{\text{xft}}=\frac{30\sec onds}{60\text{ seconds}} \\ or \\ \frac{480}{x}=\frac{30}{60} \\ \frac{480}{x}=\frac{1}{2} \\ \end{gathered}[/tex][tex]\begin{gathered} x=480\times2 \\ x=960ft\text{ per second} \end{gathered}[/tex]
1. June bought some books for $51. This was ⅗ of hermoney. How much money did she have to beginwith?
Answers
Since $51 was 3/5 of her money, then if we multiply 3/5 by the amount of money she had, x, we should obtain 51.
[tex]\frac{3}{5}x=51[/tex]
We can then solve the above equation for x.
[tex]\begin{gathered} 3\cdot x=51\cdot5 \\ 3\cdot x=255 \\ x=\frac{255}{3} \\ x=85 \end{gathered}[/tex]
She had $85.
Chester needs 2 feet of ribbon for an art project, but his ruler only measures in centimeters. There are 12 inches in I foot and 2.54 centimeters in 1 inch. Chester multiplied 12 by 2 and then divided the product by 2.54 to find that he needs about 9.4 centimeters of ribbon. This length is much shorter than 2 feet, so he knows he is incorrect. Which of these would give Chester the correct number of centimeters of ribbon he needs? Multiply 2.54 by 12, and then multiply this product by 2. Divide 12 by 2, and then multiply this quotient by 2.54 Divide 12 by 2.54, and then divide this quotient by 2. - Х Multiply 2 by 2.54, and then divide this product by 12. +
Answers
Answer
Option A is correct.
Multiply 2.54 by 12, and then multiply this product by 2.
2 feet = 60.96 centimeters
Explanation
The way forward for this is to convert the 2 feet into centimeters.
We've been told that
1 feet = 12 inches
1 inches = 2.54 centimeters
So, to convert the 2 feet into the centimeters, we need to first convert it to inches
1 feet = 12 inches
2 feet = 2 × 12 inches
2 feet = 24 inches
Then, to centimeters
1 inches = 2.54 centimeters
24 inches = 24 × 2.54 centimeters
24 inches = 60.96 centimeters.
So, we can see that option A is the correct answer.
Hope this Helps!!!
Write a function that transforms f(x) = 2x^3 in the following way:stretch vertically by a factor of 5 and shift 3 units left.
Answers
Given:
[tex]f(x)=2x^3[/tex]
To write:
The function when f(x) is stretched vertically by a factor of 5 and shifted 3 units left.
Explanation:
In general, a vertical stretch by a factor b and shift a units left is given by the equation
[tex]y=bf\left(x+a\right)[/tex]
So, the new function becomes,
[tex]\begin{gathered} y=5f(x+3) \\ y=g(x)=5\times2(x+3)^3 \\ g(x)=10(x+3)^3 \end{gathered}[/tex]
Final answer:
The new function is,
[tex]g(x)=10(x+3)^{3}[/tex]
6. The equation ft) = 13,000(1.024)^t models the annual tuition at a private school over time, t. By what percent does the tuition increase each year? a. 0.24% b. 2.4% C. 1.024% d. 24%
Answers
We have the expression:
[tex]f(t)=13000\cdot(1.024)^t[/tex]
We can find how much the annual tuition increases each year by calculating:
[tex]\begin{gathered} \Delta=\frac{f(t+1)-f(t)}{f(t)}=\frac{f(t+1)}{f(t)}-1=\frac{13000\cdot(1.024)^{t+1}}{13000\cdot(1.024)^t}-1 \\ \Delta=1.024^{\mleft\{t+1-t\mright\}}-1=1.024-1=0.024\cdot100\%=2.4\% \end{gathered}[/tex]
Answer: b. 2.4%
7 Find the selling price sofa: $225, discount 75%
Answers
Given
Price: $225
Discount: 75%
Procedure
Selling price sofa
[tex]225\cdot(1-0.75)=56.25[/tex]
The answer would be $56.25
You can insert Desmos graphs or hand-drawn graphs.Draw a normal curve representation for the area, then write thenumerical value of the area under the normal curve for each of thefollowingA) All values to the right of z=2.86B) All values Not between -1.09 and 0.16 standard deviations from themean. (hint: if you use Desmos, you will need to create two graphs)Edit View Insert Format Tools Table
Answers
SOLUTION:
We want to draw graphs showing the following:
A, All values to the right of z = 2.86
This is the plot, the area is marked in red;
The numerical value for this area is;
[tex]P\left(z>2.86\right)=0.0021182[/tex]
B. All values Not between -1.09 and 0.16 standard deviations from the mean.
The numerical value for this area which is the sum of the blue and red areas is;
[tex]P\left(z<-1.09\text{ }or\text{ }z>0.16\right)=0.5743[/tex]
What is the absolute value of Point A labelled on the number line?АBс+-101
Answers
For this case we can see that the point A is on the negative side of the line and we can see that the answer would be
[tex]-3\frac{1}{3}=-\frac{10}{3}[/tex]
But the absolute value would be:
[tex]\left|-3\frac{1}{3}\right|=\left|3\frac{1}{3}\right|[/tex]
And the best answer would be:
[tex]3\frac{1}{3}[/tex]
Use intercepts to graph the linear equation −12x+y=−4.
Answers
Answer:
x-intercept=-1/3
y-intercept=-4
Step-by-step explanation:
Find the x-intercept by setting y to zero:
-12x+0=4
-12x=4
x= 4/(-12)
x= -1/3
Find the y-intercept by setting x to 0
-12(0) + y=-4
y=-4
Draw a line through the intercepts
Za and Zbare complementary angles. Za measures 37°.What is the measure of Zb?
Answers
Complementary angles add up to 90°.
So:
Za+Zb=90°
Replacing with the value of Za = 37°
37°+Zb =90°
Solving for Zb:
Zb = 90°-37°
Zb= 53°
The first five terms of a pattern are given below.13, 19, 25, 31, 37, ...
Answers
Given:
13, 19, 25, 31, 37, ...
Required:
We need to find the expression to determine the nth term of the given pattern.
Explanation:
Consider the individual options.
1)
[tex]7+6n[/tex]
Substitute n=1 in the expression we get the first term.
[tex]7+6(1)=13[/tex]
Substitute n=2 in the expression we get the second term.
[tex]7+6(2)=7+12=19[/tex]
Substitute n=3 in the expression we get the third term.
[tex]7+6(3)=7+18=25[/tex]
Substitute n=4 in the expression we get the fourth term.
[tex]7+6(4)=7+24=31[/tex]
Substitute n=5 in the expression we get the fifth term.
[tex]7+6(5)=7+30=37[/tex]
All five terms of the given pattern satisfy the expression 7+6(n).
Hence the nth term of the given pattern is 7+6(n).
Final answer:
[tex]7+6(n)[/tex]
Question 4. QY W Which of the following numbers is irrational? A A. 2.1245 E B. 3.95 C. 0.231124. D. 6.5 10
Answers
Irrational numbers are all the real numbers which cannot be expressed as the ratio of two integers:
In this case, the elipsis (...) means that this number does not stop, so there is no repeating pattern of digits. Since the number does not stop and does not repeat, it is irrational.
ANSWER: 0.231124...
I'm so confused as to what this is asking please help
Answers
Given
Statements
Find
Which of the following can be used to estimate the instantaneous rate of change at a point on a continuous function.
Explanation
as we know that the slope of the tangent line through a point on the graph of a function gives the function's instantaneous rate of change at that point.
so , option b is correct .
Final Answer
Hence , the slope of the tangent line drawn at the point gives the instantaneous rate of change at a point.
Lamont builds a toy block tower 4 feet high. He then puts a toy antenna on the towerthat is 4 foot tall.What is the height of the block tower including the tower antenna?
Answers
Solution
Draw a diagramatic representation of the question
Step 2
Add both heights to determine the height of the block including the tower antenna
[tex]\begin{gathered} \frac{1}{4}+4\frac{2}{3} \\ =\frac{1}{4}+\frac{14}{3} \\ =\frac{59}{12}\text{feet} \\ =4\frac{11}{12}\text{ f}eet \end{gathered}[/tex]
Hence the total height required = 59/12 feet or 4 11/12 feet approximately