[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=2,143.57 \end{cases}\implies 2143.57=\cfrac{4\pi r^3}{3}\implies 6430.71=4\pi r^3 \\\\\\ \cfrac{6430.71}{4\pi }=r^3\implies \sqrt[3]{\cfrac{6430.71}{4\pi }}=r\implies \stackrel{\pi =3.14}{7.9999956 \approx r}\implies \stackrel{\textit{rounded up}}{8=r}[/tex]
How do I solve -6 1/3 + 5 5/6
Answer:
13/6
Step-by-step explanation:
-6 1/3 + 5 5/6
1. You can reduce the first equation to 2
-6 1/3, becomes -2 x 1/1. This is because 3 goes into itself 1 time, and it goes into 6, -2 times. Your new equation: -2 + 5 5/6
2. Multiply the 5's in 5 5/6 by each other to get...
25/6
Your new equation: -2 + 25/6
3. Multiply 6 by -2 to get -12
4. Now add the numerators(remember -12 is basically, -12/1) together to get your answers
-12 + 25/6 = 13/6
Hello There!
If we add -6 1/3 and 5 5/6 together, we will get a sum of -1/2
STEP 1 First, I like to convert mixed numbers into improper fractions because they are easier to work with. So, I would change -6 1/3 to -19/3. Then, I would change 5 and 5/6 to 35/6.
STEP 2 Applying the fraction formula for addition. (-19x6) + (35x3) and then i would put this over 6x3
STEP 3 -114+105
18
STEP 4
-9/18 = -1/2
which of the following is the conjugate of a complex number with 2 as the real part and -8i as the imaginary part
The conjugate of the complex number 2 - 8i is 2 + 8i, found by changing the sign of the imaginary part from negative to positive.
The conjugate of a complex number is found by changing the sign of the imaginary part.
For a complex number with a real part of 2 and an imaginary part of -8i, the complex number is represented as 2 - 8i. To find its conjugate, we change the sign of the imaginary part, resulting in 2 + 8i.
The general form of a complex number is a + bi, where a is the real part and bi is the imaginary part.
The conjugate is then written as a - bi. Therefore, if we have the complex number z = 2 - 8i, the conjugate, denoted as [tex]\( \overline{z} \)[/tex], is 2 + 8i.
I need help please??!!!):
Answer:
-13 < 16
Step-by-step explanation:
(4 is x, -5 is y)
-5 - 8 < 4(4)
-13 < 16
It is true and is a solution
Answer:
The ordered pair is not a solution to the inequality because -13 < -16 is false.
Step-by-step explanation:
Step 1: Plug x and y into the inequality
-5 - 8 < -4(4)
Step 2: Simplify the inequality
-13 < -16
Step 3: Interpret and conclude
The ordered pair is not a solution to the inequality because -13 < -16 is false.
Helppppp meehhehhhhhhhh
ANSWER
B. 10
EXPLANATION
We need to find the value of x first.
It was given that the perimeter of triangle XYZ is 24.
This means that:
XY+YZ+XZ=24
we substitute the expression in terms of x to get;
[tex](5x - 1) + (13 - x) = 24[/tex]
This implies that
[tex]5x - x = 24 - 13 + 1[/tex]
[tex]4x = 12[/tex]
Divide both sides by 4 to get;
[tex]x = 3[/tex]
|WY|=|ZX|=13-3=10
Answer:
WY = 10 units
Step-by-step explanation:
From the figure we can see a rectangle WXYZ.
Diagonals of rectangle are equal.
It is given that, Perimeter of triangle XYZ = 24
XY + YZ = 5x - 1 and XZ = 13 - x
To find the value of x
Perimeter of ΔXYZ = XY + YZ + XZ
24 = 5x - 1 + 13 - x
4x + 12 = 24
4x = 12
x = 12/4 = 3
x = 3
To find the value of WY
We have WY = XZ
XZ = 13 - x
= 13 - 3 = 10
Therefore WY = XZ = 10 units
Answer the photo question
Answer: x÷(2÷5y)
Step-by-step explanation: this is because you have to first do the quotient of 2 and try then the answer will be divided by 5
Answer:
The quotient of x and the quotient of 2 and 5y.
Expression:
x/(2/5y)
Explanation:
The quotient means to divide the numbers. The “and” after quotient is what the number is dividing with. So, x us dividing with the division of 2 and 5y.
James invests $20,000 in an account that offers a compound interest rate of
8.3% per year. Which of the following is the correct equation for how much
James will have after 6 years?
James will have $32,270.13 after 6 years
Answer:
[tex]y=20000(1.083)^6[/tex]
Step-by-step explanation:
Let y represents the amount James have after 6 years,
Given,
Principal amount, P = $ 20,000,
Compound rate of interest per year, r = 8.3 %,
Thus, the amount after x years would be,
[tex]A=P(1+\frac{r}{100})^x[/tex]
[tex]=20,000(1+\frac{8.3}{100})^x[/tex]
[tex]=20000(1.083)^x[/tex]
Therefore, the amount after 6 years would be,
[tex]y=20000(1.083)^6[/tex]
Which is the correct equation that represents the amount, James will have after 6 years.
Identify the domain for the function!!! 10 points. Help needed
Answer:
You had it correctly chosen, (9, infinity)
Step-by-step explanation:
Good job =)
ANSWER
[9,∞)
EXPLANATION
The given radical function is ;
[tex]f(x) = \sqrt{x - 9} [/tex]
This function is defined if and only if the expression under the radical sign is greater than or equal to zero.
[tex]x - 9 \geqslant 0[/tex]
[tex]x \geqslant 9[/tex]
Or
In interval notation, we have
[9,∞)
In a restaurant a diner orders an entree with vegetables foe 10.50, dessert foe 1.50, and coffee for 0.50. If the tax on the meals is 6%, what tax should be added to his check?
Answer:
$0.75 tax
Step-by-step explanation:
1. Find total cost of meal: $10.50 + $1.50 + $0.50 = $12.50
2. Find tax of meal: $12.50 * 6% = 12.5 * 0.06 = $0.75
Find the equation of the circle with center at (3, -2) and radius of 3.
Answer:
[tex](x-3)^{2} +(y+2)^{2}=9[/tex]
Step-by-step explanation:
we know that
the equation of a circle into center radius form is equal to
[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]
In this problem we have
center ( 3,-2)
radius r=3 units
substitute
[tex](x-3)^{2} +(y+2)^{2}=3^{2}[/tex]
[tex](x-3)^{2} +(y+2)^{2}=9[/tex]
Answer: A on edg
Step-by-step explanation:
Darren filled boxes with tins of orange juice and numbered the boxes in the order in which they were filled. He packed the 496th tin box 21 and then stopped for lunch. Box 21 was never completely filled. How many tins were in box 21?
udryjsexjyejyedido7r4ukdjyeilcfrkuxhrkdksirxkuwxnhrhtilctukrxkhxrkyrxrHAiltfthseukcthjxdnh fjudcjxyjxdnhcryjxryjxryjdebyxdjudrjyxd
what's -1 and 3/5 divided by -2/3
Answer:
2 2/5
Step-by-step explanation:
-1 3/5 ÷ -2/3
Change the mixed number to an improper fraction
-1 3/5 = - (5*1 +3)/5 = -8/5
-8/5÷-2/3
Copy dot flip
-8/5 * -3/2
24/10
Divide top and bottom by 2
12/5
Change to a mixed number
12/5 = 2 2/5
The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132 units. Lara wrote the following step to find the length of the unknown leg: Length of the unknown leg = 1572 − 1322 = 24,649 − 17,424 = 7,225 units Which statement best explains whether Lara's step is correct or incorrect?
Answer:
24649-17424=7225 UNITS
Step-by-step explanation:
This step implies that Lara was using the Pythagoras theorem to find the missing length of the right triangle.
a²+b²=c², taking a and b to be the two lengths adjoined by the right angle and c the hypotenuse.
Laura's step represents the step above.
157²=24649
132²=17424
157²-132²=c²
24649-17424=7225
the sum of the ages of Nicole and Kristen and 32 in two years Nicole would be three times as old as Kristen how old are they now
Answer:
Kristen would be 7.5 yo and Nicole would be 24.5 years old
Step-by-step explanation:
let x= kristen's age
3x+2= nicole's age
(3x+2)+x=32
4x+2=32
4x=30
x=7.5
3(7.5)+2= 24.5
What is the solution of the inequality?
2 x less or equal than 3 left parenthesis x minus 0.6 right parenthesis
a. x less or equal than 1.8
b. x greater or equal than 1.8
c. x less or equal than negative 1.8
d. x greater or equal than negative 1.8
Answer: Option b
b. x greater or equal than 1.8
Step-by-step explanation:
In this problem we have the following inequality:
[tex]2x\leq 3(x-0.6)[/tex]
To solve it we must group the x on one side and the constants on the other side
[tex]2x\leq 3(x-0.6)[/tex]
Apply distributive property on the right side of the inequality
[tex]2x\leq 3x-3*0.6[/tex]
[tex]2x\leq 3x-1.8[/tex]
Subtract 3x on both sides of the inequality
[tex]2x-3x\leq 3x-3x-1.8[/tex]
[tex]-x\leq-1.8[/tex]
Multiply by -1 both sides of the inequality
[tex]x\geq 1.8[/tex]
The answer is the option b
Answer:
the answer is option B
Step-by-step explanation:
PLS HELP 20 POINTS
A) How long does it take for it to rotate 225 degrees?
B) How long does it take to rotate 9π radians?
C) The diameter of the Earth is approximately 7920 miles. How far will a point on the equator rotate in 2 hours?
Answer:
A)
15 hours
B)
108 hours
C)
2074.29 miles
Step-by-step explanation:
Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.
A)
In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;
(24/360) = (x/225)
solving for x;
x = (24/360) * 225 = 15 hours
B)
In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;
(24/2π radians) = (x/9π radians)
Solving for x;
x = (24/2π radians)*9π radians = 108 hours
C)
If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;
circumference = 2*π*R = π*D
= 7920*3.142
= 24891.43 miles
Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;
(24891.43miles)/(24 hours) = 1037.14 miles/hr
The distance covered by the point in 2 hours will thus be;
1037.14 * 2 = 2074.29 miles
Identify each expression and value that represents the area under the curve y=x^2+4 on the interval [-3,2]
This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.
The area under the curve y = x^2 + 4 on the interval [-3,2] can be found using definite integration. The definite integral of a function gives us the net area between the function and the x-axis across the specified interval. To compute the area, we set up the integral from -3 to 2 of the function x^2 + 4.
To solve this, we integrate the function with respect to x:
Integrate the function x^2 to get (1/3)x^3.Integrate the constant 4 to get 4x.Combine the results to form the antiderivative, which is (1/3)x^3 + 4x.Evaluate the antiderivative from -3 to 2. This gives us:[(1/3)(2)^3 + 4(2)] - [(1/3)(-3)^3 + 4(-3)]Calculate each part to obtain:[(1/3)(8) + 8] - [-(1/3)(27) - 12]Simplify to find: (8/3 + 8) - (-9 - 12)Add up to get the total area: (8/3 + 8 + 9 + 12)Which simplifies to: (8/3 + 29)Final result: 35/3 or 11.67 square unitsThis result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.
What are the zeros of this function?
Answer:
Step-by-step explanation:
the zeroes of a function basically mean when y = 0, so basically the x-intercept(s)
in this case, the zeroes are 3 and 6
Answer:
A. x = 3 and x = 6
Step-by-step explanation:
Zeros occur when the function crosses the x - axis. In this case, the quadratic function crosses the function when x = 3 and x = 6.
graph and shade the following inequality -5x+2y<-10
Answer: The graph is attached.
Step-by-step explanation:
The equation of the line in Slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
You can solve for "y":
[tex]2y<5x-10\\\\y<\frac{5}{2}x-\frac{10}{2}\\\\y<\frac{5}{2}x-5[/tex]
You need to rewrite the expression:
[tex]y=\frac{5}{2}x-5[/tex]
You can identify that the slope of this line is:
[tex]m=\frac{5}{2}[/tex]
And the y-intercept is:
[tex]b=-5[/tex]
Substitute [tex]y=0[/tex] and solve for "x" to know the x-intercept:
[tex]0=\frac{5}{2}x-5\\\\5*2=5x\\\\x=2[/tex]
Now you know that the line passes through the points (0,-5) and (2,0).
Since the inequality is "<", you know that the line must be dashed and the shaded region must be below the line [tex]y=\frac{5}{2}x-5[/tex].
Knowing this, you can graph it (Observe the graph attached)
Why is Li incorrect in saying that the graph shows a direct variation
Answer:
The answer B
Step-by-step explanation:
Write the equation of the line that passes through the point (6, -2) and is perpendicular to the line
y = 1/3x+8.
Answer:
y = - 3x + 16
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{3}[/tex] x + 8 ← is in slope- intercept form
with slope m = [tex]\frac{1}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3, so
y = - 3x + c ← is the partial equation of the perpendicular line
To find c substitute (6, - 2) into the partial equation
- 2 = - 18 + c ⇒ c = - 2 + 18 = 16
y = - 3x + 16 ← equation of perpendicular line
Shravan is ten years older than Gaurav’s age. Five years ago, one –seventh of shravan’s age was equal to one- fifth of Gaurav’s age. Find their present ages.
Answer:
Shravan's age is 40 years old
Gaurav’s age is 30 years old
Step-by-step explanation:
Let
x-----> Shravan's age
y-----> Gaurav’s age
we know that
x=y+10 -----> equation A
(1/7)(x-5)=(1/5)(y-5) ----> equation B
substitute equation A in equation B and solve for y
(1/7)(y+10-5)=(1/5)(y-5)
(1/7)(y+5)=(1/5)(y-5)
5(y+5)=7(y-5)
5y+25=7y-35
7y-5y=25+35
2y=60
y=30 years
Find the value of x
x=y+10 ----> x=30+10=40 years
therefore
Shravan's age is 40 years old
Gaurav’s age is 30 years old
What is the area of the figure below?
A. 22 cm2
B. 24 cm2
C. 48.5 cm2
D. 56 cm2
Answer:
C. 48,5 cm²
Step-by-step explanation:
The area is 8×4 + 3×3 + 5×3/2 = 32+9+15/2 = 41+7,5 = 48,5 cm²
-27/50 write the fraction as a mixed number
Answer: It can not be a mixed number because if you divide -27 by 50 you get -0.54, so then if you turn -0.54 in fraction form it would be -27/50, so the fraction would stay the way it is. -27/50 is not an improper fraction. To be improper, the numerator must be greater than the denominator!
* Hopefully this helps:) Mark me the brainliest:)!!!
what is the value of the 5 in 15,406
Hello There!
The value of the number "5" in the number 15,406 would be the value of 5,000
40 POINTS
Simplifying exponents and rules of exponents simplify the expressions below:
2 4 3 0 4 6 4 -3 2 3 2
ANSWER
a. 16
b. 1
c. 64
d. 64
EXPLANATION
We want to simplify the following exponential expressions
a.
[tex] {2}^{4} [/tex]
This implies that
[tex] {2}^{4} = 2 \times 2 \times 2 \times 2[/tex]
[tex] {2}^{4} = 16[/tex]
b. Any non-zero number exponent zero is 1.
This implies that,
[tex] {3}^{0} = 1[/tex]
c. The given exponentiial expression is,
[tex] {4}^{6} \times {4}^{ - 3} [/tex]
The bases are the same so we add the exponents.
[tex] {4}^{6} \times {4}^{ - 3} = {4}^{6 + - 3} [/tex]
This simplifies to,
[tex]{4}^{6} \times {4}^{ - 3} = {4}^{3} [/tex]
[tex]{4}^{6} \times {4}^{ - 3} = 4 \times 4 \times 4 = 64[/tex]
d. We want to simplify:
[tex] { ({2}^{3}) }^{2} [/tex]
This is the same as
[tex]{ ({2}^{3}) }{ ({2}^{3}) }[/tex]
We add the exponents now to get:
[tex]{2}^{3 + 3} = {2}^{6} = 64[/tex]
hey can i get some help from you guys?
For this case we must find an expression equivalent to:
[tex](x ^ {\frac{1}{4}} * y ^ {16}) ^ {\frac {1} {2}}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Then, rewriting the expression:
[tex](x ^ {\frac {1 * 1} {4 * 2}} * y ^ {\frac {16 * 1} {2}}) =\\x ^ {\frac {1} {8}} * y ^ {\frac {16} {2}}) =\\x ^ {\frac {1} {8}} * y ^ {8}[/tex]
Answer:
Option B
One of these students is randomly selected what is p(a/b)?
Answer: 3/5=0.60
Step-by-step explanation:
The p(a/b) is 3/5 = 0.6
What is Bayes Theorem?The Bayes theorem predicts the likelihood that an event connected to any condition would occur. Use the concept of the conditional probability formula, P(Ei|A)=P(Ei∩A)P(A), to demonstrate the Bayes theorem (A). The Bayes' Theorem describes the likelihood that an event connected to any condition would occur.
Given
P(a) = P(student in karate ) = 3
P(b) =P(student in chess) = 5
P(a|b) = 3/5 = 0.60
To know more about Bayes theorem refer to :
https://brainly.com/question/14989160
#SPJ2
The exact value of cos5pi/12 is:
Step 1: Convert [tex]\frac{5\pi }{12}[/tex], which is in radians into degrees. To convert it multiply by [tex]\frac{180}{\pi }[/tex]
[tex]\frac{5\pi }{12} =\frac{180}{\pi }[/tex]
900/12
75
Step 2: 75 degrees isn't on the unit circle but 45 degrees and 30 degrees is. Since 45 + 30 = 75 you can use the cosine of 45 and 30 to find the exact value
cos45 = [tex]\frac{\sqrt{2} }{2}[/tex]
cos30 =[tex]\frac{\sqrt{3} }{2}[/tex]
Step 3: Add the cos45 and cos30 to get cos5pi/12
[tex]\frac{\sqrt{2} }{2} +\frac{\sqrt{3} }{2} = \frac{\sqrt{2}+\sqrt{3}}{2}[/tex]
Hope this helped!
lots of points and pretty easy!!!!
The complement of A would be the elements in U that are not in A.
A is 2, 4, 6, 8
Remove those numbers from U for the complement.
The complement would be {1, 3, 5, 7, 9, 10}
Answer: The complement is 1, 3, 5, 7, 9, 10
I hope that this helps! :3
You estimate that there are 59 marbles in a jar. The actual amount is 47 marbles. Find the percent error. Round to the nearest tenth of a percent if necessary.
Answer:
25.5%
Step-by-step explanation:
% error = | estimate - actual | / actual × 100%
% error = | 59 - 47 | / 47 × 100%
% error ≈ 25.5%
Answer:
20.3%
Step-by-step explanation:
The formula for percent error is the experimental value minus the theoretical value divided by the theoretical value all times 100.
Experimental - Theoretical
------------------------------------------ x 100
Theoretical
−12
------- ×100
59
=−0.20339×100
=−20.339
=20.339%
=20.3% error