Answer:
7/12
Step-by-step explanation:
If the probability of winning a race is 5/12, the odds in favor of winning the race is 7/12.
Probability of winning a race: 5/12 or a 5 out of 12 chance.
12 - 5 = 7
Numerator = 7
The denominator would stay 12.
Denominator = 12
Therefore, the odds of winning the race is 7/12.
The two spheres above have the same center. One has a radius of 4 cm, and the other has a radius of 5 cm
Answer:
Step-by-step explanation:
Lets assume that a sphere with greater radius = R = 5cm
And a sphere with smaller radius = r = 4cm
Volume of a sphere = 4/3 π * r³
To find the volume of a sphere with radius 5.
Put the value in the formula.
=4/3π * r³
=4/3π *(5)³
5³ = 5*5*5=125
=4/3π * 125
=4/3 *3.14 *125
=1570/3
=523.3 cm³
Now find the volume of sphere with radius= 4
4/3π*r³
=4/3π * 4³
4³= 4*4*4=64
=4/3*3.14*64
=803.84/3
=267.9cm³
Now to find the space between the spheres subtract the volume of smaller sphere from the volume of larger sphere.
We can write it as:
Space between the spheres = Volume of larger sphere - Volume of smaller sphere
= 523.3 cm³ - 267.9cm³
= 255.4cm³ ....
URGENTTTTTTT!!!!!!!!!!
Prove that circle A with center (–1, 1) and radius 1 is similar to circle B with center (–3, 2) and radius 2.
Answer:
Circle A and circle B are similar
Step-by-step explanation:
* Lets explain similarity of circles
- Figures can be proven similar if one, or more, similarity transformations
reflections, translations, rotations, dilations can be found that map one
figure onto another
- To prove all circles are similar, a translation and a scale factor from a
dilation will be found to map one circle onto another
* Lets solve the problem
∵ Circle A has center (-1 , 1) and radius 1
∵ The standard form of the equation of the circle is:
(x - h)² + (y - k)² = r² , where (h , k) are the coordinates the center
and r is the radius
∴ Equation circle A is (x - -1)² + (y - 1)² = (1)²
∴ Equation circle A is (x + 1)² + (y - 1)² = 1
∵ Circle B has center (-3 , 2) and radius 2
∴ Equation circle B is (x - -3)² + (y - 2)² = (2)²
∴ Equation circle B is (x + 3)² + (y - 2)² = 4
- By comparing between the equations of circle A and circle B
# Remember:
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
∵ -3 - -1 = -2 and 2 - 1 = 1
∴ The center of circle A moves 2 units to the left and 1 unit up to
have the same center of circle B
∴ Circle A translate 2 units to the left and 1 unit up
∵ The radius of circle A = 1 and the radius of circle B = 2
∴ Circle A dilated by scale factor 2/1 to be circle B
∴ Circle B is the image of circle A after translation 2 units to the left
and 1 unit up followed by dilation with scale factor 2
- By using the 2nd fact above
∴ Circle A and circle B are similar
If x= yand y = Z, which statement must be true?
Answer:
The answer is
B. x =>z
They all equal the same.
Which of the following expressions are equivalent? Justify your reasoning.
4√x3
1
x−1
10√x5•x4•x2
x
1
3
•x
1
3
•x
1
3
Answer:
b and d
Step-by-step explanation:
b. 1/x^-1
=(1/x)^-1
=x
d. x^1/3 * x^1/3 * x^1/3
=x^1/3+1/3+1/3
=x^3/3
=x^1
=x....
The length of a rectangle exceeds its width by 3
inches, and the area is 54 square inches. What
are the length and width of the rectangle?
Answer:
The length is 9 and the width is 6.
Step-by-step explanation:
6*9 = 54 and 9 is 3 greater than 6.
This circle is centered at the point (3, 2), and the length of its radius is 5. What
is the equation of the circle?
Answer:
(x-3)² + (y-2)² = 25
Step-by-step explanation:
A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².
So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.
What is the slope of a line that includes the points (-5, 1) and (-2, 3).
Select one:A.2/3 b.-2/7 c.-2/3 d.3/2
Answer:
A
Step-by-step explanation:
Work with the two points
Formula
m = (y2 - y1)/(x2 - x1)
Givens
y2 = 3
y1 = 1
x2 = - 2
x1 = - 5
Solution
m = (3 - 1) / (-2 - - 5)
m = 2 / (-2 + 5)
m = 2 / 3
Answer: A
Answer:
[tex]\large\boxed{\text{A.}\,2/3}[/tex]
Step-by-step explanation:
In this question ,we're trying to find the slope with the given points.
We would use the slope-formula to find the slope.
Slope-formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
We would plug in the numbers to their right spots in the formula. The second y-coordinate going to y2, the second x coordinate going to x2, and etc.
Your equation should look like this:
[tex]m=\frac{3-1}{-2-(-5)}[/tex]
Now we solve:
[tex]m=\frac{3-1}{-2-(-5)} \\\\m=\frac{2}{-2-(-5)}\\\\\text{Carry the negative over to the 5, turning it to a positive 5}\\\\m=\frac{2}{-2+5}\\\\\text{Add the denominators}\\\\m=\frac{2}{3}[/tex]
When you're done solving, you should get 2/3
This means that the slope is 2/3
I hope this helped you out.Good luck on your academics.Have a fantastic day!(04.05 MC)
Which of the following is a solution to this inequality?
[tex]y < \frac{2}{3} x + 2[/tex]
A.(0,3)
B.(-3,1)
C.(3, 5)
D.(1,2)
Answer:
D
Step-by-step explanation:
Plug in and see.
Check A: Lets plug in (0,3) into y<2/3 x+2.
3<2/3 (0)+2
3<2 is not true so not A
Check C: Lets plug in (3,5) into y<2/3 x+2.
5<2/3 (3)+2
5<2+2
5<4 is not true so not C
Check B: Lets plug in (-3,1) into y<2/3 x+2.
1<2/3 (-3)+2
1<0 is not true so not B
Check D: Lets plug in (1,2) into y<2/3 x+2.
2<2/3 (1)+2
2<2/3+2 is true so D
when you use ____ you form general ideas and rules based on your experiences and observations
a. symmetry
b. logic
c. deduction
d. induction
Induction is the correct answer; when you use induction form general ideas and rules based on your experiences and observations. I hope this will help you! Have a wonderful day!
Answer:
d. induction
Step-by-step explanation:
When you use induction you form general ideas and rules based on your experiences and observations.
Determine algebraically whether f(x) = x^2(x^2 + 9)(x^3 + 2x) is even or odd.
[tex]f(x) = x^2(x^2 + 9)(x^3 + 2x)\\\\f(-x) = (-x)^2((-x)^2 + 9)((-x)^3 + 2\cdot(-x))\\f(-x)=x^2(x^2+9)(-x^3-2x)\\f(-x)=-x^2(x^2+9)(x^3+2x)\\\Large f(-x)\not =f(x)\implies\text{not even}\\\\-f(x)=-x^2(x^2+9)(x^3+2x)\\ -f(x)=f(-x)\implies \text{odd}[/tex]
Three times a number increases by 4 is the same as four
times that number decreased by 11. Find the number.
Answer:
15 is your answer.
Step-by-step explanation:
Let "a number" = x
"Three times a number increase(d) by 4" = 3x + 4
"...is the same as" = "="
"four times that number decreased by 11" = 4x - 11
Set the equation:
3x + 4 = 4x - 11
Isolate the variable, x. Subtract 4x and 4 from both sides:
3x (-4x) + 4 (-4) = 4x (-4x) - 11 (-4)
3x - 4x = -11 - 4
Simplify. Combine like terms:
-x = -15
Isolate the variable, x. Divide -1 from both sides:
(-x)/-1 = (-15)/-1
x = (-15)/(-1)
x = 15
15 is your answer.
~
What are the new vertices of triangle FGH if the triangle is translated three units to the right?
A. F′ = (–2,–3), G′ = (0,4), H′ = (4,–6) B. F′ = (–2,–2), G′ = (0,5), H′ = (4,–5) C. F′ = (–5,–5), G′ = (–3,3), H′ = (1,–8) D. F′ = (–1,–2), G′ = (1,5), H′ = (5,–5)
Answer:
G'(0,5)
H'(4,-5)
F'(-2,-2)
Step-by-step explanation:
We need to identify the three vertices from the figure on the graph:
G(-3,5)
H(1,-5)
F(-5,-2).
If we translate these points 3 units to right, then that effects the x-coordinates.
So 3 more than -3, is 0.
3 more than 1 is 4.
3 more than -5 is -2.
So the new points are:
G'(0,5)
H'(4,-5)
F'(-2,-2).
what is the median of the following distribution?
Answer:
37
Step-by-step explanation:
So this is probably not the correct mathematical way to do it, but it is really easy so you'll probably understand quicker. So a median is the middle number, so how do you find it. First, I counted how many numbers there were (17). Then I subtracted by one to get an even number (if you already have an even number skip this step, and just divide by 2). So now we have 16, so I divided it by 2 to get 8 and just added that 1 that we took out and got 9. So i counted from 24 and the 9th number was 37. To double check I did the same from 56 and got 37.
find the area of a sector with a central angle of 170° with the radius of 17 mm. Round to the nearest 10th.
For f(x)=3x+1 and g(x)=x•x-6,find (f - g)(x)
Answer:
[tex]\large\boxed{(f-g)(x)=-x^2+3x+7}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=3x+1,\ g(x)=x^2-6\\\\(f-g)(x)=(3x+1)-(x^2-6)=3x+1-x^2+6=-x^2+3x+7[/tex]
Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t^2, where t is time in seconds. The height of a certain tower is 944 feet. How long would it take an object to fall on the ground from the top of the building?
In the physics context of free fall, it would take an object approximately 7.67 seconds to fall from a 944-foot tower, neglecting air resistance. This is calculated using the formula for distance of a freely falling object s(t)=16t^2.
Explanation:The question deals with the physics concept of free fall, specifically directed to the time it would take an object to fall from a certain height. Given that the distance s(t) of a freely falling object is given by the equation s(t)=16t^2, we can find the time t for an object to fall from a height of 944 feet, which is the height of the specific tower.
Setting s(t) equal to the height of the tower, we get: 944=16t^2. Solving this equation for t, we'll get the square root of 944/16 which is approximately 7.67 seconds. Therefore, it would take an object about 7.67 seconds to fall to the ground from the top of the 944-foot tower, neglecting air resistance.
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To determine how long it takes for an object to fall from a 944-foot tower, we use the formula s(t) = 16t^2. Solving for t, we find that it takes approximately 7.68 seconds. Thus, the object hits the ground after 7.68 seconds.
Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t^2, where t is time in seconds. The height of a certain tower is 944 feet. How long would it take an object to fall on the ground from the top of the building?
To solve this problem, we need to determine the time t it takes for the object to hit the ground. Given the height h = 944 feet, we'll use the formula for the distance fallen:
s(t) = 16t^2
We set s(t) equal to the height of the tower:
944 = 16t^2
Next, solve for t:
Divide both sides by 16:
944 / 16 = t^2
t^2 = 59
Take the square root of both sides:
t = √59
t ≈ 7.68 seconds
Therefore, it would take approximately 7.68 seconds for an object to fall to the ground from the top of the building.
Write a function rule for the table
For this case we must construct a function of the form [tex]y = f (x)[/tex] taking as reference the values of the table.
It is observed that if we evaluate the following function we have:
[tex]f (x) = x + 4[/tex]
Different signs are subtracted and the sign of the major is placed.
[tex]f (-3) = - 3 + 4 = 1\\f (-2) = - 2 + 4 = 2\\f (-1) = - 1 + 4 = 3\\f (0) = 0 + 4 = 4[/tex]
So, the function is:[tex]f (x) = x + 4[/tex]
Answer:
[tex]f (x) = x + 4[/tex]
A single die is rolled twice. Find the probability of rolling a 2 the first time and a 5 the second time.
Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
All die rolls have a 1 in 6 chance of landing on any specific number (because they have 6 equal sides). In probability, two independent events with probabilities a and b will occur concurrently [tex]a*b[/tex] of the time. In this case, [tex]a=b=\frac{1}{6} \to p=a*b=\frac{1}{6}*\frac{1}{6}=\frac{1}{36}[/tex]
Answer:
Required probability = 1/36
Step-by-step explanation:
It is given that,single die is rolled twice
The outcomes of rolling a die are
1, 2, 3, 4, 5, and 6
Total = 6
To find the probability
Probability of getting 2 = 1/6
Probability of getting 5 = 1/6
Therefore probability of rolling a 2 the first time and a 5 the second time. = 1/6 * 1/6 = 1/36
A pathway divides a rectangular garden into two parts as shown. Find the measure of angle A
Answer:
m < A = 101 degrees.
Step-by-step explanation:
The transverse line crosses 2 parallel lines (opposite angles of a rectangle are parallel) , so the same side angles add up to 180 degrees.
m < A + 79 = 180
m < A = 101 degrees.
Answer:
A=101°
Step-by-step explanation:
The two lengths of the rectangle are parallel and therefore the sides of the path form two parallel transversals.
The angle marked 79° and the angle marked A are supplementary ( they add up to 180°)
A+79=180°
A=180-79
=101°
Solve 3x − 2 = 37. please help me
To solve the equation 3x - 2 = 37, you add 2 to both sides to get 3x = 39. Then, you divide by 3 to solve for x, obtaining x = 13.
Explanation:To solve the equation
3x − 2 = 37
for x, you start by moving the -2 to the other side of the equation by adding 2 to both sides. This gives you
3x = 39
. Then, you isolate x by dividing every term by 3. After dividing, you find that
x = 13
. So the solution to the equation 3x - 2 = 37 is x = 13.
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To solve the equation, add 2 to both sides and then divide by 3 to isolate the variable x. The solution is x = 13.
Explanation:To solve the equation 3x - 2 = 37, we need to isolate the variable x. Here are the steps:
Add 2 to both sides of the equation to get rid of the constant term. This gives us 3x = 39.Divide both sides of the equation by 3 to solve for x. This gives us x = 13.Therefore, the solution to the equation is x = 13.
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After eating lunch together, Jay and Paul start walking in opposite directions. Jay walks 0.75 miles every 15 minutes and Paul power walks 2.5 miles every 30 minutes. In miles, how far apart are they after 1.5 hours?
Answer:
12 miles
Step-by-step explanation:
Jay walks 0.75 miles in 15 minutes, or 1/4 hour, so his speed is:
0.75 mi / 0.25 hr = 3 mi/hr
Paul walks 2.5 miles in 30 minutes, or 1/2 hour, so his speed is:
2.5 mi / 0.50 hr = 5 mi/hr
After 1.5 hours, Jay has walked a distance of:
3 mi/hr × 1.5 hr = 4.5 mi
And Paul has walked a distance of:
5 mi/hr × 1.5 hr = 7.5 mi
So the total distance between them is:
4.5 mi + 7.5 mi = 12 mi
WILL GIVE BRAINLEIST DUE AT 9:45 P.M. PLS HURRY SUPER EASY. Bella rollerblades 8 miles in one hour. The function rule that represents this situatrion is 8x, where x is the numger of hours. Make a table to find how many hours she had skated when she traveled 16,24, and 32 miles. Then graph the function. After refer to the exercise. How many miles would Bella travel if she skated for 7 hours?
Hours ] 8x ] Miles
? ] ? ] ]
? ] ? ] ]
? ] ? ] ]
Answer:
I hope this helps! <3
Step-by-step explanation:
(4^((-11/3))/(4^((-2)/3))
simplify the following expression
Answer:
[tex]\large\boxed{\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}=\dfrac{1}{64}}[/tex]
Step-by-step explanation:
[tex]\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=4^{-\frac{11}{3}-\left(-\frac{2}{3}\right)}=4^{-\frac{11}{3}+\frac{2}{3}}=4^{-\frac{9}{3}}=4^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{4^3}=\dfrac{1}{64}[/tex]
The simplification of the expression is [tex]\dfrac{1}{64}[/tex].
What are some basic properties of exponentiation?Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\[/tex]
Given ;
[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})}[/tex]
We know that
[tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex]
[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})} = 4^({-11/3 + 2/3})\\\\\\= 4 ^{-9/3}\\\\= 4^{-3}\\\\[/tex]
Hence, [tex]\dfrac{1}{4^3} = \dfrac{1}{64}[/tex]
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Kiemanh is solving the equation 15r- 6r=36. What is the value of r?
Answer:
r equals 4- this is the value of r
hope this helps
Step-by-step explanation:
Answer:
[tex]\large\boxed{r=4}[/tex]
Step-by-step explanation:
In this question, we're going to need to solve the equation for r.
This means that we need to get the r by itself to see what it equals to.
Lets solve:
[tex]15r- 6r=36\\\\\text{Subtract 15r and -6r}\\\\9r=36\\\\\text{Now you will divide}\\\\r=4[/tex]
When you're done solving, you should get r = 4
This means that the value of r is 4 (or r = 4)
I hope this helped you out.Good luck on your academics.Have a fantastic day!
1. The table below shows the cost of some apples. Which function C(a) is represented in the table?
Apples
Cost
3
$1.95
6
$3.90
9
$5.85
A. C(a) = 0.65a
B. C(a) = 1.95a
C. C(a) = 3a
D. C(a) = 0.85a
2. Which function below translates the parent function f(x) = x4 five units to the right and seven units downward?
A. g(x) = (x – 7)4 – 5
B. g(x) = (x – 5)4 + 7
C. g(x) = (x – 5)4 – 7
D. g(x) = (x + 5)4 – 7
3. Use the mapping shown to show the value of the function f(x) at each point.
A. f(5) = –1, f(3) = 0, f(5) = 1, f(11) = 2, f(21) = 3
B. f(1) = 5, f(0) = 3, f(1) = 5, f(2) = 11, f(3) = 21
C. f(–1) = 5, f(0) = 3, f(1) = 5, f(2) = 21, f(3) = 11
D. f(–1) = 5, f(0) = 3, f(1) = 5, f(2) = 11, f(3) = 21
Detailed solution to math problems involving functions and mappings.
1. The function represented by the table:
Identify the pattern in the table to determine the function.
The cost increases by $1.95 for every 3 apples, so the function is C(a) = 0.65a (A).
2. Translating a function:
To shift f(x) = x^4 five units right and seven units down, the correct function is g(x) = (x+5)^4 - 7 (D).
3. Mapping the function:
Using the mapping provided, the correct values are: f(5) = 1, f(3) = 0, f(11) = 2, f(21) = 3 (A).
Translate the following into algebraic expressions:
Divide the product of a and b by the quotient of c and d.
I Need Help Plz I’m Failingggg!!
Answer:
I believe it would be B
Step-by-step explanation:
take x and y values and figure it out what it is by itself
Jennifer stores her fishing pole in a cylindrical case. The cylinder has a diameter of 5 inches and a height of 50 inches.Which is closest to the volume, in cubic inches, of the cylinder?
Answer:
Volume of Cylinder = 981.75 cubic inches
Step-by-step explanation:
There is no answer choice shown, but i will answer this using formula for volume of cylinder and round the answer to 2 decimal places.
You match it with the choices that u have.
The volume of a cylinder is given by the formula [tex]V=\pi r^2 h[/tex]
Where
V is the volume
r is the radius (half of diameter)
h is the height
We know diameter is 5, so radius is 2.5
also, the height is 50
We simply plug it in the formula and solve:
[tex]V=\pi r^2 h\\V=\pi (2.5)^2 (50)\\V=981.75[/tex]
PLEASE HURRY 10 POINTS What is the solution to the equation 3(2x+5)=3x+4x
A x=0
B x=4
C x=5
D x=15
Answer:
D x=15
Step-by-step explanation:
3(2x+5)=3x+4x
Distribute the 3
6x +15 = 3x+4x
Combine like terms
6x+15 = 7x
Subtract 6x from each side
6x+15 -6x = 7x-6x
15 =x
The product of a rational and irrational number is rational
Answer:
False
Step-by-step explanation:
I think this is a true or false question.
The statement is false.
Here is an example of it being false:
Choose the irrational number to be [tex]\sqrt{2}[/tex] and the rational to be 1.
The product of these numbers is [tex]\sqrt{2}[/tex] which is irrational, not rational.
Answer:
False
Step-by-step explanation:
Ight so any irrational number times a rational number is irrational. But keep in mind that If its 0 times an irrational number, its going to be 0, which is a rational number. So irrational x rational = irrational. Irrational x 0=rational 0.
Hope this helped