Area of circle = [tex]\pi[/tex][tex]r^{2}[/tex]
First, we can put in our values. For now, we can leave [tex]\pi[/tex] alone.
Our radius is 5.5 so we have to square it which gives us a product of 30.25
then, we can multiply our radius squared by [tex]\pi[/tex] and we get
Area, A = 95.033177771091 [tex]in^{2}[/tex]
Two seniors, one from each government class are randomly selected to travel to Washington, D.C. Wes is in a class of 18 students and Maureen is in a class of 20 students. Find the probability that both Wes and Maureen will be selected.
Answer: 1 out of 19
Step-by-step explanation:
add up all of the students, wes and maureen are two people, so it's two out of thrity eight, then just simplify it and you're done <3
The probability that both Wes and Maureen will be selected is 1/360.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, Wes is in a class of 18 students and Maureen is in a class of 20 students.
Now, this is an independent event, therefore, the probability that both Wes and Maureen will be selected will be,
= (1/18)×(1/20).
= 1/360.
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Please help
No idea how to do
Answer:
see explanation
Step-by-step explanation:
He cycles [tex]\frac{3}{4}[/tex] Km and jogs [tex]\frac{3}{4}[/tex] - [tex]\frac{1}{6}[/tex]
Adding the 2 together gives the total he cycled/ jogged
[tex]\frac{3}{4}[/tex] + [tex]\frac{3}{4}[/tex] - [tex]\frac{1}{6}[/tex]
We require the denominators to be common before adding/ subtracting
The lowest common denominator of 4 and 6 is 12, hence
= [tex]\frac{9}{12}[/tex] + [tex]\frac{9}{12}[/tex] - [tex]\frac{2}{12}[/tex]
= [tex]\frac{9+9-2}{12}[/tex]
= [tex]\frac{16}{12}[/tex] = [tex]\frac{4}{3}[/tex] = 1 [tex]\frac{1}{3}[/tex] Km
Do 3/4 x 3 = 9/12
Do 1/6 x 2 = 2/12
Then do 9/12 - 2/12 = 7/12
Next you do 7/12 + 9/12 = 16/12
Then simplify. 1 4/12
Simplify again. 1 1/3
535 invenstment compounded continuosly for 10 years at 6 percent
Answer:
[tex]\$974.83[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=10\ years\\ P=\$535\\ r=0.06[/tex]
substitute in the formula above
[tex]A=\$535(e)^{0.06*10}=\$974.83[/tex]
Subtract 6 ounces from 3 pounds.
5 lb., 7 oz.
6 lb., 3 oz.
2 lb., 10 oz.
2 lb., 13 oz.
Answer:
the answer is c
Step-by-step explanation:
Final answer:
To subtract 6 ounces from 3 pounds, convert 3 pounds to ounces (3 x 16 = 48 ounces), subtract 6 ounces (48 - 6 = 42 ounces), then convert back to pounds and ounces (42 ounces = 2 pounds and 10 ounces). The answer is 2 pounds, 10 ounces.
Explanation:
Subtracting Ounces from Pounds
The question asks to subtract 6 ounces from 3 pounds. In order to compare or subtract different units of weight, it is essential to convert them to the same unit. Firstly, we must remember the unit equivalence where 1 pound = 16 ounces. Now, to start the conversion, we multiply the number of pounds by 16 to get the total number of ounces, which is a step in solving these types of conversion problems.
Therefore, for 3 pounds:
3 pounds × 16 ounces/pound = 48 ounces.
Now subtract the given ounces: 48 ounces - 6 ounces = 42 ounces.
Since we know there are 16 ounces in a pound, we divide the total ounces by 16 to convert back to pounds and ounces.
42 ounces ÷ 16 ounces/pound = 2 pounds with a remainder of 10 ounces.
Hence, subtracting 6 ounces from 3 pounds gives us 2 pounds, 10 ounces.
Hey can someone answer this ASAP
Answer:
csc θ = [tex]\sqrt{85}[/tex]/6
sec θ = [tex]\sqrt{85}[/tex]/7
tan θ = 6/7
Step-by-step explanation:
The first thing to do will be to compute the length of the hypotenuse using the Pythagoras theorem;
6^2 +7^2 = hypotenuse^2
hypotenuse = [tex]\sqrt{85}[/tex]
csc θ = 1/sinθ
sinθ = opposite side/hypotenuse
= 6/[tex]\sqrt{85}[/tex]
csc θ = [tex]\sqrt{85}[/tex]/6
sec θ = 1/cosθ
cosθ = adjacent side/hypotenuse
sec θ = hypotenuse/adjacent side
= [tex]\sqrt{85}[/tex]/7
tan θ = Opposite side/adjacent side
= 6/7
in the figure PQ is parallel to RS. the length of RP is 6 cm; the length of PT is 18 cm; the length of QT is 21 cm; what is the length of SQ?
Answer:
Option A. [tex]SQ=7\ cm[/tex]
Step-by-step explanation:
we know that
In the figure
The triangles PTQ and RTS are similar by AA Similarity Theorem
so
Remember that
If two figure are similar, then the ratio of its corresponding sides is equal
so
[tex]\frac{PT}{RT}=\frac{QT}{ST}[/tex]
we have
[tex]PT=18\ cm[/tex]
[tex]RT=RP+PT=6+18=24\ cm[/tex]
[tex]QT=21\ cm[/tex]
[tex]SQ=ST-21\ cm[/tex] ------> equation A
substitute the values and solve for ST
[tex]\frac{18}{24}=\frac{21}{ST}[/tex]
[tex]ST=21*24/18[/tex]
[tex]ST=28\ cm[/tex]
substitute the value of ST in the equation A to find the value of SQ
[tex]SQ=28-21=7\ cm[/tex]
Answer: 77cm
Step-by-step explanation:
Consider the table of values.
x y
-2 0
-1 2
0 6
1 12
2 20
3 30
4 42
Select the statement that is true about the table.
A.
The relationship between the variables in the table is linear because the first differences are constant.
B.
The relationship between the variables in the table is quadratic because the second differences are constant.
C.
The relationship between the variables in the table is linear because the second differences are constant.
D.
The relationship between the variables in the table is quadratic because the first differences are constant.
Answer:
B. The relationship between the variables in the table is quadratic because the second differences are constant.
Step-by-step explanation:
We have to look for the differences in the y values of the given table.
The y values are:
0, 2, 6, 12, 20, 30, 42
The differences between the consecutive values are:
2, 4, 6, 8, 10, 12
These are the first differences and are not constant. This means the relationship is not linear. Now we again find the differences between the consecutive values:
2, 2, 2, 2, 2
These are the second differences. The second differences are constant. So this means the given relationship is quadratic.
Therefore, option B gives the correct answer. The relationship between the variables in the table is quadratic because the second differences are constant.
According to the tree diagram below, what is the probability that someone buys a book that is hardcover and nonfiction
Whenever you have a decision tree like this, the probability of reaching a specific leaf is the multiplication of the probabilities of each step you have to reach the leaf.
So, in order to reach the "hardcover and nonfiction" leaf, we have to take the "buys hardcover" branch (probability 0.35), and then the "buys nonfiction" branch (probability 0.55).
Given what we said above, the probability for "hardcover and nonfiction" is
[tex]0.35\cdot 0.55=0.1925[/tex]
The probability of buying a hardcover and non-fiction book is 0.1925
How to determine the stated probabilityWe have the below parameters for our Calculation;
P(hard cover) = 0.35 P(non - fiction) = 0.55The probability that someone buys a hardcover and non- fiction book ;
P(hard cover n Non-fiction) = P(hard cover) × P(non-fiction)Now we have;
P(hard cover n Non-fiction) = 0.35 × 0.55 = 0.1925
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Which type of function is the result of adding a quadratic function and a linear function?
A. a linear function
B. a quadratic function
C. a rational function
D. a cubic function
Answer:
B
Step-by-step explanation:
D: You will not get a cubic function. Nothing adds to give a term with x^3 in it.
C: A rational function is of the form (x^2 + 3x + 2) / (x^2). In other words it has a numerator and a denominator that are polynomials. Unless one or both started out like that, the answer is not a rations function.
A: It can't be linear. The x^2 term will carry over after addition.
The answer is B. One of the polynomials started out as a quadratic. It will remain that way.
Write the equation is logicrithmic form 3^3=27
Answer:
[tex] 3^3 = 27 \Longleftrightarrow \log_3 27 = 3 [/tex]
Step-by-step explanation:
[tex] b^y = x \Longleftrightarrow \log_b x = y [/tex]
A logarithm is an exponent. The base of the logarithm is the base of the power.
[tex] 3^3 = 27 \Longleftrightarrow \log_3 27 = 3 [/tex]
Answer:
[tex] log_3 2 7 = 3 [/tex]
Step-by-step explanation:
We are given the following equation and we are to write it in logarithmic form:
[tex] 3 ^ 3 = 27 [/tex]
We know that [tex] a ^ n = b [/tex] is written as [tex] log _ a b [/tex] when expressed in logarithmic form.
So here we have [tex] 3 ^ 3 = 27 [/tex], converting it logarithmic form we get:
[tex] log_3 2 7 = 3 [/tex]
In a bag of candy there are 12 blue candies, six red candies, four yellow candies, and two purple candies. What is the ratio of red to all candies? Simplify if possible
?? hold on I'ma work the problem out
Answer:
6/22
Step-by-step explanation:
Just add wanted outcomes over all outcomes
Harry made fruit punch using 2 parts orange juice to 2 parts soda water. The amount of soda water that Harry used is directly proportional to the amount of orange juice he used. How many cups of orange juice should Harry use with 18 cups of soda water?
Final answer:
To find out how many cups of orange juice Harry should use with 18 cups of soda water, set up a proportion and solve for x.
Explanation:
In this problem, we know that Harry uses 2 parts orange juice to 2 parts soda water for his fruit punch. This means that for every 2 cups of orange juice, he uses 2 cups of soda water. Since the amount of soda water is directly proportional to the amount of orange juice, we can set up a proportion to find out how many cups of orange juice Harry should use with 18 cups of soda water.
2 cups orange juice / 2 cups soda water = x cups orange juice / 18 cups soda water
To solve the proportion, we can cross multiply:
2 cups orange juice * 18 cups soda water = x cups orange juice * 2 cups soda water
36 cups orange juice = 2x cups soda water
By dividing both sides of the equation by 2, we find that Harry should use 18 cups of orange juice with 18 cups of soda water.
I need the answer plz show me the step
Answer:
f(x)/g(x) = x+6
Step-by-step explanation:
f(x) = 3x^2 +16x -12
g(x) = 3x-2
f(x) 3x^2 +16x -12
---- = -------------------
g(x) 3x-2
Factor
f(x) (3 x - 2) (x + 6)
---- = -------------------
g(x) 3x-2
Cancel the common terms
f(x) (x + 6)
---- = -------------------
g(x) 1
Bonita said that the product of 5/6 × 1 2/3 is 7/ 3. How can you tell that her answer is wrong?
Answer:
See below
Step-by-step explanation:
Because her answer is greater than 2 (7/3 = 2 1/3)
We are multiplying a number less than 2 (1 2/3) by a number less than 1 (5/6), so we have less than one of the number 1 2/3, which has to be less than 1 2/3.
let's firstly convert the mixed fraction to improper fraction.
[tex]\bf \stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{6}\times \cfrac{5}{3}\implies \cfrac{25}{18}\implies 1\frac{7}{18}[/tex]
the point slope form of the equation of a line that passes through (8,4) and (0,2) is y-4=1/4(×-8) what is the slope intercept form of the equation for this line.
Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x+2}[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The point-slope form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the equation of a line:
[tex]y-4=\dfrac{1}{4}(x-8)\to m=\dfrac{1}{4}[/tex]
and the point (0, 2) → b = 2.
Substitute:
[tex]y=\dfrac{1}{4}x+2[/tex]
Answer:
Step-by-step explanation:
DDD
How do I find and what is the x?
Answer:
STEP ONE: 2x
STEP TWO: 5=X (should be the final answer)
Step-by-step explanation:
Hi Lasagna!
So basically, this is extremely simple. In order to "solve" that equation, the x has to be on one side. The easiest way to do this would be to take the 2x to the other side. If you want the 2x to go to the other side, you need to subtract it (since it is already positive, therefore it needs to cancel out). Once you do that, you must always do the same thing to the other side: subtract 2x from 3x. That should get you one x there, which you can just write as x if it's just one. Then you're all set! :D
Answer: step 1. 2 from both sides
Step-by-step explanation:
just take away the = number by doing the opposite action for ex. if it it 2x then divide both sides by 2.
Last option is none of the above
Answer:
A and B
Step-by-step explanation:
When rotating a point (or any shape around a certain point), none of the diameters of the shape will change. So for example, with this circle, when you rotate it around a point, the radius and circumference will not change because it has just rotated. It wont be on the x-axis though because point P is not on the x-axis an it is being rotated 180 degrees about point P. Just know that when you are rotating, nothing about the shape changes, all angles or measurements will be the same, it is just moving to a different place.
Hope this helped ^-^
Josephina is five years older than Cameron and the sum of their ages is 31. Can you write or type an equation and solve it to figure out their ages? Or, must you use the 5-D process to solve? Either way, find a way to solve it. How old are Josephina and Cameron? Show that your answer is correct.
Cameron - х years
Josephina is five years older than Cameron = х+5 years
sum of their ages is 31
х+х+5=31
2х=31-5
2х=26
х=13 Cameron
13+5=18 Josephina
The age of Josephina and Cameron is 13 and 18.
The calculation is as follows:
here Cameron be х years
And, Josephina is five years older than Cameron so х+5 years
Also,
The sum of their ages is 31
Now
х+х+5=31
2х=31-5
2х=26
х=13 Cameron
13+5=18 Josephina
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Answer:
C
Step-by-step explanation:
sqrt(200)
Find the highest square multiple.
200 = 100 * 2
sqrt(100) = 10
10 goes on the outside, and the one that is left, 2, goes on the inside.
Answer:
Your answer is C) [tex]10\sqrt{2}[/tex]
Step-by-step explanation:
This is because [tex]10\sqrt{2}[/tex] is [tex]\sqrt[4]{200}[/tex] simplified.
Confirming the answer above!
I hope this helps!~
Length of the missing leg is:
Pythagorean theorem - Integers -
Find the missing leg
PLEASE HELP
(need to show work)
Im so confused!!
The lengths of the legs of each triangle are:
1) Leg = √19
2) Leg = √105
3) Leg = √60
How to use Pythagoras Theorem?
Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
a = √(c² - b²)
1) We are given that:
Hypotenuse = 10
Opposite side = 9
Thus, using Pythagoras Theorem, we have:
Leg = √(10²- 9²)
Leg = √19
2) We are given that:
Hypotenuse = 19
Opposite side = 16
Thus, using Pythagoras Theorem, we have:
Leg = √(19²- 16²)
Leg = √105
3) We are given that:
Hypotenuse = 8
Opposite side = 2
Using Pythagoras Theorem, we have:
Leg = √(8²- 2²)
Leg = √60
Figure ABCD is a parallelogram what are the measures of angles B and D?
Answer:
B=65 degrees, c=65 degrees
Step-by-step explanation:
Opposite angle in a parallelogram are equal. 3n+20 = 6n-25. n=15. You then plug n in into the equations. B=65 and D=65
Answer:
the answer to this question is B. Trust me I'm not wrong.
The total, t, divided into 5 groups is 45
URGENT! Which of the following correctly expresses sin(2θ)−sin(6θ) as a product?
Select the correct answer below:
2sin(4θ)cos(2θ)
2sin(2θ)cos(4θ)
−2sin(2θ)cos(4θ)
−2sin(2θ)sin(4θ)
Answer:
−2sin(2θ)cos(4θ)
Step-by-step explanation:
sin(2∅)-sin(6∅)
Sum product Identity
sinα - sinβ = 2cos((α+β)/2)sin((α-β)/2)
Putting α= 2∅ and β= 6∅ in the identity we get
sin(2∅)-sin(6∅) = 2cos((2∅+6∅)/2)sin((2∅-6∅)/2)
=2cos(8∅/2)sin(-4∅/2)
=2cos(4∅)sin(-2∅)
= -2sin(2∅)cos(4∅)
explain how to convert numbers from standard form to scientific.
Answer:
Start by moving the decimal place in the number until you have a coefficient between 1 and 10. The number of places to the left that you had to move the decimal point is the exponent. so for example, 0.000345 would be 3.45(10)^4
Step-by-step explanation:
Hope that helps!
what is 15456415 times 45415
Answer: 701953087225 is the answer
X-10<6-5x , I need the inequality solved please:)
Answer:
x < [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
Given
x - 10 < 6 - 5x ( add 5x to both sides )
6x - 10 < 6 ( add 10 to both sides )
6x < 16 ( divide both sides by 6 )
x < [tex]\frac{16}{6}[/tex], that is
x < [tex]\frac{8}{3}[/tex]
Based on the records for the past several seasons a sports fan believes the probability the red team wins is 0.55. The fan also believes the probability the blue team will wins is 0.60. In a season with 180 games, how many fewer games should the fan expect the red team to win?
Answer:
The fan should expect the red team to win 9 more games than the blue team.
Step-by-step explanation:
Using proportions, it is found that over the entire season, the fan should expect the red team to win 9 less games.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, considering the proportions of the red and of the blue teams, the number of games they are expected to win is given by:
R = 0.55 x 180 = 99.B = 0.6 x 180 = 108.108 - 99 = 9, hence the fan should expect the red team to win 9 less games.
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Which function is represented by the graph
f(x)= -|x|+4
f(x)= -|x|-4
f(x)= -|x+4|
f(x)= -|x-4|
It’s the forth one
The answer is -|x-4|.
Answer:y=-|x-4|
Step-by-step explanation:
we know the graph of y=|x| touches at x=0 and opens upward towards y axis
but this graph is facing downwards therefore it should be of form
y=-|x|
but it touches the x axis at x=4
therefore the graph is represented by
y=-|x-4|
4 is added inside the mod because it intersect x axis at x=4
The graph would be y=-|x-4|+1 if it shifts 1 unit upwards.
the sum of two numbers is 21 and their difference is 5
X+Y = 21 ---> Y = 21-x
X-y = 5
x - (21-x) = 5
2x - 21 = 5
2x = 26
x = 13
13 and 8
The two numbers are 13 and 8.
13 + 8 = 21
The difference (13 - 8) is 5.
Disuss the difference between fixed expenses and variable expenses as they relate to a budget?
The difference between fixed expenses and variable expenses is that fixed expenses do not change, regardless of how many items are produced. Variable expenses change based on the number of items produced.
An example of a fixed expense is the rent. The rent is always the same amount, regardless of production.
Materials would be a variable expense. You need enough material to make each item, so the more items you produce, the more material you need.