Area of Sector.
The area of a sector is given by the formula below:
[tex]\begin{gathered} \text{Area =}\frac{\theta}{360}\times\pi r^2 \\ \text{where }\theta=148\text{ ; r=6m ; }\pi=\frac{22}{7} \end{gathered}[/tex]Substituting these values into the formula above, we get
[tex]\begin{gathered} \text{Area of the shaded sector = }\frac{148}{360}\times\frac{22}{7}\times6^2 \\ \text{ } \\ \text{ = }\frac{148\times22}{70}\text{ = }46.514\text{ }\approx46.5m^2 \end{gathered}[/tex]Thus, the correct answer is 46.5 square meters.
The number of hours it takes for ice to melt varies inversely with the air temperature. A block of ice melts in 2.5 hours whenthe temperature is 54 degrees.How long would it take for the same block of ice to melt if the temperature was 45 degrees?
Let t be the time in hours it takes a block of ice to melt at T degrees.
Since both variables have an inverse relation, we can say that:
[tex]t=\alpha\cdot\frac{1}{T}[/tex]Where alpha is a constant value.
Since we know that a block of ice melts in 2.5 hours when the temperature is 54 degrees, we can plug in such data and find alpha as following:
[tex]\begin{gathered} 2.5=\alpha\cdot\frac{1}{54}\rightarrow2.5\cdot54=\alpha \\ \Rightarrow\alpha=135 \end{gathered}[/tex]Therefore, our expression would be:
[tex]t=\frac{135}{T}[/tex]For T = 45,
[tex]\begin{gathered} t=\frac{135}{45} \\ \\ \Rightarrow t=3 \end{gathered}[/tex]We can conclude that it would take 3 hours for the block of ice to melt.
convert these measurements to centimeters : (a)73.1 cm and (b) 0,0012km
Answer:
(a) 73.1 cm (b) 120 cm
Step-by-step explanation:
Step-by-step explanation:
Part (a)
73.1 cm [It remains the same as it is already given in cms]
Part (b)
To convert 0.0012km to cm we multiply x 100000
=> 0.0012 x 100000
=> 120 cm
To rent a certain meeting room, a college charges a reservation fee of $46 and an additional fee of $6.70 per hour. The math club wants to spend less than$106.30 on renting the meeting room.What are the possible amounts of time for which they could rent the meeting room?Use t for the number of hours the meeting room is rented, and solve your inequality for t.
As given by the question
There are given that the college charges a reservation fee of $46.
Now,
According to the question, the inequality is:
[tex]46+6.70t<106.30[/tex]Then,
To solve the above inequality, collect the constant terms on the right side
So,
[tex]\begin{gathered} 46+6.70t<106.30 \\ 6.70t<106.30-46 \\ 6.70t<60.3 \\ t<\frac{60.3}{6.70} \\ t<9 \end{gathered}[/tex]Hence, the room could be rented for up to 9 hours less than the stated amount.
I need questions 10 , 13 , 15 , and 16 solved with steps and graph
10. |x - 4| - 4 = 1/2x
⇒ Multiplying by 2,
2 |x - 4| - 8 = x
So, x - 4 = (x + 8)/2
= -(x + 8)/2
When,
x - 4 = (x + 8)/2
2x - 8 = x + 8 (Multiplying by 2)
2x - x = 8 + 8 (Adding 8 and subtracting x to both sides)
x = 16
When,
x - 4 = - (x + 8)/2
2x - 8 = -x - 8 (Multiplying by 2)
2x + x = -8 + 8 (Adding 8 and x to both sides)
3x = 0
x = 0
Hence, the solution is x = 16 and x = 0.
13. (3/4)x = 2x - 10
⇒ Subtract 2x from both sides.
-5x/4 = -10
Multiply both sides by 4/(-5).
(-5x/4)×4/(-5) = -10 × 4/(-5).
x = 8 is the solution of the equation.
15. x² - 7x - 8 > 0
⇒ Solve the quadratic equation by splitting the middle term,
x² - 8x + x - 8 > 0
x(x - 8) + 1(x -8) > 0
(x + 1)(x- 8) > 0
-1 and 8 are the critical points of the inequality.
x < -1 and x > 8 are the solutions of the inequality which are represented by the shaded red region in the graph.
16. x - 5 > - 2x + 4
⇒ Adding 2x to both sides.
3x - 5 > 4
Adding 5 to both sides.
3x > 9
Divide both sides by 3.
x > 3 is the required solution represented by blue shade region in the graph.
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Four of the twelve members of the panel were late for
the meeting. What fraction of the members were on
time?
Answer:
2/3
Step-by-step explanation:
If 4 were late, then 8 were on time.
8/12 Divide the top and bottom by 4
2/3
Can you please help me solve this questions. I want a clear explanation thank you.
Given:
[tex]\begin{gathered} \text{Mean}=\mu=21.4 \\ \text{Standard deviation=}\sigma=5.0 \\ \text{Smple size=n=66} \end{gathered}[/tex]The z-score for 90 percent is 1.64.
To find the 90 percent confidence interval,
[tex]\begin{gathered} \mu+(\frac{\sigma}{\sqrt[]{n}}\times1.64)=21.4+(\frac{5}{\sqrt[]{66}}\times1.64) \\ =21.4+1.0094 \\ =22.4094\ldots\ldots(\text{ upper limit)} \\ \text{And} \\ \mu-(\frac{\sigma}{\sqrt[]{n}}\times1.64)=21.4-(\frac{5}{\sqrt[]{66}}\times1.64) \\ =21.4-1.0094 \\ =20.3906\ldots\ldots\ldots(\text{lower limit)} \end{gathered}[/tex]Answer: The 90 % confidence interval is ( 20.3906 , 22.4094 )
Rajan climbed to a height of 15 ft from the bottom of a climbing wall. He then climbed up an additional 10 ft.
What must he do to return to the bottom of the climbing wall?
In the first blank, say whether Rajan must climb up or down. In the second blank, state the number of feet Rajan must travel up or down.
Rajan must climb_____ft to return to the bottom of the climbing wall.
Rajan must climb down 25 ft to return to the bottom of the climbing wall
Height climbed from the bottom of the wall = 15ft
Height: The measurement of an object's height from the base to the top is known as height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.
Additional height climbed = 10ft
Total height climbed = 25ft
He should climb down the distance, as climbing up will further move him away from the bottom of the wall
Distance to climb down to the bottom of the wall = 25ft
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If you spend 1 hours a week studying for English and 3.5 hours studying for math what is the ratio of time spent studying in math to studying for English?
The ratio of time spent studying math to studying English is 7:2.
According to the question,
We have the following information:
One spends 1 hour a week to study English and 3.5 hours to study math.
Now, we know that the ratio can be simply understood as the division.
So, we will divide the number of hours devoted to math by the number of hours devoted to English.
Ratio of time spent studying math to studying English = 3.5/1
Ratio of time spent studying math to studying English = 35/10
(Now, we will convert this fraction into the simplest form by dividing both the numerator and denominator of the fraction by 5.)
Ratio of time spent studying math to studying English = 7/2
Ratio of time spent studying math to studying English = 7:2
Hence, the ratio of time spent studying math to studying English is 7:2.
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How many times larger is 8.1 than 2.7
can you help me factor the expression x^2+4x-21
To factor this expression we need to find two numbers which sum is 4 and the product is -21.
Now, 21 has only 2 factors (besides 1 and 21), 7 and 3, se we need to write them in a way such that they sum 4, so
[tex]x^2+4x-21=(x+7)(x-3)[/tex]we see that 7-3=4 and 7(-3)=-21, so the factorization is correct.
Solve for x
12x-6 need answer please
Answer:
-72
Step-by-step explanation:
Answer:
Step-by-step explanation:
12x-6 = 90 because opposite angles are equal if intercepted in parallel lines
12x=96
x= 8
What is the exact decimal equivalent of 7/12
Answer:
0.58333333333
A person tosses a coin 14 times. In how many ways can he get 10 heads?
If f (x) = x
2 − 2 x , g (x) = x − 2
1) prove that : f(2) = g(2)
2) If g (K) = 7 , find : the value of k
1. The value of f(2) = 0 and g(2) = 0
2. The value of k is 9
What is a function?A function can simply be described as a law, rule, theorem or expression that explains the relationship between two terms.
These terms are known as;
The dependent variableThe independent variableGiven the functions;
f(x) = x^2 - 2xg(x) = x - 21To prove that f(2) = g(2)
Substitute the value of x as 2 in the functions, we have;
f(2) = 2^2 - 2(2)
expand the bracket
f(2) = 4 - 4
f(2) = 0
Then for g(2), we have;
g(2) = 2 - 2
g(2) = 0
Then, f(2) = g(2) = 0
If g(k) = 7
Then, we have;
k - 2 = 7
collect like terms to determine the value of k
k = 7 + 2
k = 9
Hence, the value is 9
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Find sinθ, tanθ, and secθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.sinθ=tanθ=secθ=
1) We have here a right triangle, so we can use the Pythagorean Theorem to find the adjacent leg. Note that the hypotenuse is leg opposite to the right angle. In this case, a=4.
a²=b²+c²
4²=b²+3²
16=b²+9
16-9=b²
b=√7
2) Let's find the trigonometric functions. The first one is the sine (θ), which relates the opposite side and the hypotenuse:
[tex]\sin (\theta)\text{ =}\frac{3}{4}[/tex]2.2)Moving on, we can deal with the tangent of theta, relating the opposite side over the adjacent, for this one we have to rationalize it:
[tex]\begin{gathered} \tan (\theta)\text{ =}\frac{3}{\sqrt[]{7}} \\ \tan (\theta)=\frac{3\sqrt[]{7}}{7} \end{gathered}[/tex]Finally, let's find the reciprocal function of the cosine function by setting this as the reciprocal of the cosine, and then calculating it:
[tex]\begin{gathered} \sec \text{ (}\theta)=\frac{1}{\cos(\theta)}\Rightarrow\sec (\theta)=\frac{1}{\frac{\sqrt[]{7}}{4}}\Rightarrow\sec (\theta)\text{ =}\frac{4}{\sqrt[]{7}} \\ \sec (\theta)\text{ =}\frac{4\sqrt[]{7}}{7} \end{gathered}[/tex]Find X.
Cirucumscribed angles
Answer:
x = 64
Step-by-step explanation:
to find x add make an equation to solve for x. the equation is 90+90+44+2x+8=360. after solving for x, x will equal 64.
Question 10The table below shows the amount of water that is in a bathtub that is being filled.Minutes1234Gallons ofWater12172227Which of the following functions could model the amount of gallons of water, f(x), that the bathtub will contain after x minutes of being filled?Аf(x) = 5x + 7Bf(x) = 5x + 12сf(x) = 7x + 5Df%) = 12x + 5No
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the difference. Write your answer in simplest form.
The mixed fraction 11 [tex]\frac{7}{16}[/tex] - 4[tex]\frac{7}{12}[/tex] is equivalent to the fraction to 6 41/48
How to solve an equation?An equation shows the relationship between two or more numbers and variables.The mixed fraction 11 7/16 is equivalent to the fraction (11 * 16 + 7)/16 = 183/16
The mixed fraction 4 7/12 is equivalent to the fraction (4 * 12 + 7)/12 = 55/12
Substituting:= 18 [tex]\frac{3}{16}[/tex] - 5 [tex]\frac{5}{12}[/tex]
Simplifying:= 329/48
= 6 41/48
11 [tex]\frac{7}{16}[/tex] - 4 [tex]\frac{7}{12}[/tex] is equal to 6 [tex]\frac{41}{48}[/tex]
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Graph the following inequalities.4x + y ≥ 0I need TWO COORDINATES
We need to graph the following inequality:
[tex]4x+y\ge0[/tex]First, let's apply the same operations on both sides of the inequality to isolate the variable y on the left side of the inequality. We obtain:
[tex]\begin{gathered} 4x+y-4x\ge0-4x \\ \\ y\ge-4x \end{gathered}[/tex]Now, notice that:
[tex]y=-4x[/tex]represents a line containing all points with coordinates (x,y) such that y=-4x.
The solution to the inequality includes those points, and also the points for which y is greater than -4x.
Thus, the solution to this inequality consists of all the points on that line (solid line) and the whole region above that line:
Notice that, to graph the solid line, we can choose two points on the line, and then join them. We can use the points:
[tex]\begin{gathered} x=0\Rightarrow y=0\text{ point }(0,0) \\ \\ x=1\Rightarrow y=-4\text{ point }(1,-4) \end{gathered}[/tex]Helping my son with homework.. I have no clue what this is
Answer:
45 times
Step-by-step explanation:
it is 45 times because it can land on blue or green 5 out of 8 times so u do 72 divided by 8 and u get 9 so I do 9 times 5 and u get 45
Premises:
If you have a cat, then it will chase mice.
You have a cat.
Conclusion:
Your cat will chase mice.
The Law of _____ makes this
argument true.
A premise or premiss is a true or false statement that helps form the body of an argument, By law of syllogism the statement is true. Your cat will chase mice.
What are premises?A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion.
If the following two statements are true: (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .
If you have a cat, then it will chase mice.
is the given statement.
Let p is you have a cat
q is chase mice.
r is cat will chase mice.
iby the law of syllogism Your cat will chase mice. because (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .
Hence by law of syllogism the statement "if you have a cat, then it will chase mice" is true.
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which number is the closest approximation to the value of 3/94?
Answer:
[tex] \frac{1}{3} [/tex]
Step-by-step explanation:
[tex] \frac{3}{94} = 0.31 \\ \\ \frac{1}{3} = 0.33[/tex]
(3ax - n) ÷ 5
Solve for X.
Answer:
x = 10/a; restrictions a ± 0
Answer:
[tex]x = \cfrac{n+5}{3a}[/tex]=============================
Given expression
[tex](3ax - n) : 5 = 1[/tex]Solve it for x in steps below:
[tex]3ax - n = 5[/tex][tex]3ax = n + 5[/tex][tex]x = \cfrac{n+5}{3a}[/tex]HELP ASAP HELP ASAP PLEASEEEEE
The distance between the parallel lines measured in the y direction is 3 units.
How to find the distance between the two given linesgiven data
y = - 3x + 4
y = - 3x + 1
let line 1 be y = - 3x + 4 and line two be y = -3x + 1
Analyzing the two lines show that the slope is equal hence parallel
slope = -3
The y intercept of the line or just the intercept is what varied
line 1 = 4line 2 = 1The difference between these two pints represents the distance between them measured in the y direction.
The difference is solved as
4 - 1 = 3 units
The distance is 3 units
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Help my hw is due by 12:00 am for final grade!!
Length has 5 cubes
width has 3 cubes
height has 7 cubes
Volume = length x width x height
5/2 * 3/2 * 7/2 = 105/8 = 13.125 ft^2
what is 84i?I'm learning about imaginary numbers but I need extra help
The imaginary number 'i" can be written in another form below:
[tex]i=\sqrt[]{-1}[/tex]Whenever we have the root of a negative number, we use the imaginary number 'i' to write it in an easier form.
For example:
[tex]\begin{gathered} \sqrt[]{-4}=\sqrt[]{-1\times4} \\ =\sqrt[]{-1}\times\sqrt[]{4} \\ =2\times\sqrt[]{-1} \\ =2\times i \\ =2i \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 84i=84\sqrt[]{-1} \\ =\sqrt[]{84^2\times-1} \\ =\sqrt[]{-7056} \end{gathered}[/tex]5 tons of rocks cost $7,000.00. What is the price per pound ??
Answer: Per rock or pound?
IXL Transversals of parallel lines: prove angle relationships 6QF for geometry, please help
4) [tex]m\angle XWY=m\angle HGY[/tex] (definition of congruent angles)
5) [tex]\angle HGY \cong \angle GTU[/tex] (corresponding angles theorem)
6) [tex]m\angle HGY=m\angle GTU[/tex] (definition of congruent angles)
7) [tex]\angle GTU[/tex] and [tex]\angle UTR[/tex] are supplementary (linear pair)
8) [tex]m\angle GTU+m\angle UTR=180^{\circ}[/tex] (definition of supplementary angles)
9) [tex]m\angle HGY+m\angle UTR=180^{\circ}[/tex] (substitution)
10) [tex]m\angle RTU+m\angle XWY=180^{\circ}[/tex] (substitution)
it says on top that the image is not drawn to scale.
D; Both statements are correct
Here, we want to check the correct statement
Basically from the diagram, it is confirmed that what we have is a 30-60-90 triangle
Now, for a 30-60-90 degrees triangle, the side lengths are in a particular ratio
From the diagram, MO faces the right angle and thus, it is the longest side and the hypotenuse
Now, let us take a look at the ratio of the sides in both submissions
For a 30-60-90 degrees triangle, the ratio of the sides is;
[tex]1\colon\sqrt[]{3}\text{ :2}[/tex]Hence, one side must be twice the length of the other
From Kellie's statement we can see MO is twice NO
From Eddie's statement, we can also see that MO is twice NO
Lastly, we can also see in both that dividing MN by NO yields the root of 3 in both statemets which confirms the existence of the theoretical ratio
So the conclusion here is that;
Both students are correct
I just need to know how to work it out for future problems. (Business Calc)
Find the price elasticity of the demand function as a function of p.
1. q=D(p)=600-3p
A)E(p)= p/p-200
B)E(p)= p/600-3p
C)E(p)= p/200-p
D)E(p)= p(200-p)
The price elasticity of the demand function as a function of p is C. E(p)= p/200-p
How to illustrate the information?It should be noted that the price elasticity of demand simply means the ratio of the percentage change in quantity demanded to the percentage change in price.
In this case, the function is given as:
q = D(p) = 600-3p
Differentiate with respect to p
D'(p) = 3
The elasticity of demand will be:
= (P / 600 - 3p) × (-3)
= P / (200 - P)
In conclusion, the correct option is C.
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