Volume of a sphere:
(4/3)(pi)r^3
.
radius (r) is half the diameter or 8 inches.
(4/3)(3.14)8^3
2144 cubic inches
The volume of the sphere would be 2144 cubic inches
What is the Volume of a sphere?A sphere is a three-dimensional shape analouge of a circle.
The Volume of a sphere = 4/3πr^3
We are given that the diameter of the sphere as 16 cm.
Since radius (r) is half the diameter or 8 inches.
Volume of a sphere:
= 4/3πr^3
= (4/3)(3.14)8^3
2144 cubic inches
Learn more about sphere;
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YO PLS HALP MEH I'LL GIVE BRAINLIEST
GIVE EXPLANATION AS WELL PLS
The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas. Write the ratios as fractions in simplest form.
Ratio (red to blue) of the perimeters:
Ratio (red to blue) of the areas:
Answer:
it is 11/6 and the second one I have no idea. sorry
Step-by-step explanation:
Answer:
The ratio of the perimeters is 11/6
The ratio of the areas is 121/36
Step-by-step explanation:
For the area, you need to do 11/6 squared which means 11 * 11 / 6 * 6 which = 121/36
And for the perimeter it's 11/6 = 11/6 because you cannot really do anything with that so it stays the same
if you are wondering why it is 11/6 is because the red = original and blue = image so since red is the original it goes on top.
I hope this helped
Jethro walked at an average speed of 3 miles per hour for 2 hours. Randy walked at an average of 4 miles per hour for 3 hours.
Which explanation correctly tells how to calculate the total number of miles the two boys walked?
A.Step 1: Multiply 3 × 2.
Step 2: Multiply 4 × 3.
Step 3: Add the two products.
B.Step 1: Divide 3 ÷ 2.
Step 2: Divide 4 ÷ 3.
Step 3: Add the two quotients.
C.Step 1: Divide 3 ÷ 2.
Step 2: Divide 4 ÷ 3.
Step 3: Subtract the two quotients.
D.Step 1: Multiply 3 × 2.
Step 2: Multiply 4 × 3.
Step 3: Subtract the two products.
the answer is A multiply 3x2 and multiply 4x3 then add hope that helps
Answer:
A
Step-by-step explanation:
It is asking for the total amount of miles the boys walked therefore addition for step 3.
Need help ASAP what’s the answer for This question
Quick answer, it's B.
For this case we must rationalize the following expression:
[tex]\frac {2 \sqrt {5}} {- 3 \sqrt {50}}[/tex]
Multiply the numerator [tex]\sqrt {50}:[/tex]
[tex]\frac {2 \sqrt {5} * \sqrt {50}} {- 3 \sqrt {50} * \sqrt {50}} =\\\frac {2 \sqrt {5 * 50}} {- 3 (\sqrt {50}) ^ 2} =\\\frac {2 \sqrt {250}} {- 3 * 50} =\\\frac {2 \sqrt {250}} {- 150}[/tex]
Answer:
Option B
At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 32 years old, with a standard deviation of 10 years. Find the percent of new employees that are at least 25 years old. Round to the nearest percent.
Answer:
P = 76%
Step-by-step explanation:
We look for the percentage of employees who are at least 25 years old.
We know that:
μ = 32 years
[tex]\sigma = 10[/tex] years
And we want to find
[tex]P(X\geq25) [/tex]
Then we find the z-score
[tex]Z =\frac{X - \mu}{\sigma}[/tex]
So
[tex]Z = -0.7[/tex]
Then
[tex]P (X\geq25) = P(\frac{X- \mu}{\sigma}\geq\frac{25-32}{10})\\\\\P (X\geq25) = P (Z\geq -0.7)[/tex]
By symmetry of the distribution
[tex]P(Z\geq -0.7)= 1-P(Z<-0.7)[/tex]
[tex]P(Z\geq -0.7)= 1-0.242[/tex]
Looking in the normal standard tables
[tex]P(Z\geq -0.7)= 0.758[/tex]
Finally P = 76%
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Simplifying Exponential Expressions
Warm-Up
Match the expression to its simplified form.
1/16
125
24
125
Answer: 1/16=1/4*1/4
125=5*5*5
24= (2*6)*2
125= 5*5*5
Step-by-step explanation:
Over the last month, a florist used 736 flowers to make 46 different arrangements. If each of the arrangements used the same number of flowers, how many flowers were in an arrangement? PLzz help its fro math homework
16 flowers per arrangement
What is the volume of a rectangular pyramid with a 10" base and an 8" base and a 12" height?
Answer:
320in^3
Step-by-step explanation:
V=lwh/3
V=(10)(8)(12)/3
V=960/3
V=320
For this case we have by definition, that the volume of a rectangular pyramid is given by:
[tex]V = \frac {a * b * h} {3}[/tex]
Where:
a, b: Are the sides of the rectangular base
h: It's the height of the pyramid
Substituting the values:
[tex]V = \frac {10 * 8 * 12} {3}\\V = \frac {960} {3}\\V = 320[/tex]
Thus, the volume of the pyramid is 320 cubic inches
Answer:
[tex]320 \ in ^ 3[/tex]
Evaluate C= 2 A r, for r= 8.
C=10,
C = 16
C= 28.7
C= 16
Answer: Second Option
[tex]C = 16\pi[/tex]
Step-by-step explanation:
We are evaluating aarco lengths
The formula for the arc length is:
[tex]C = 2\pi r[/tex]
We want to know what is the arc length for a radius of r = 8
Then we substitute r = 8 in the equation and solve
[tex]C = 2 \pi * 8[/tex]
[tex]C = 16\pi[/tex]
The correct answer is the second option
Answer:
Correct choice is [tex]C=16 \pi [/tex].
Step-by-step explanation:
Given equation is [tex]C=2 \pi r[/tex].
Now we need to find the value of C using given equation [tex]C=2 \pi r[/tex] and [tex]r=8[/tex].
To find that, we just need to plug [tex]r=8[/tex] into [tex]C=2 \pi r[/tex] and simplify.
[tex]C=2 \pi r[/tex]
[tex]C=2 \pi \times 8[/tex]
[tex]C=16 \pi [/tex]
Hence correct choice is [tex]C=16 \pi [/tex].
I don’t understand” please help!!
It’s due tomorrow
Answer: The answer to the first question is C(20%)
Step-by-step explanation: 1. you need to find the absolute decrease which is subtracting 350-280= 70.
2. now you need to find the percent decrease which is dividing the absolute decrease by the whole price.. so.. 70/350= .20
3. now just multiply .20 *100 = 20%
Since we're trying to find out how much the price was reduced by, first you will do this
[tex]350 - 280 = 70[/tex]
The price was dropped by $70.
Then we find out how much $70 is of the original price which is 350
[tex]70 \div 350 = 0.2[/tex]
Then you convert 0.2 into a percentage which is 20%.
The price of the digital camera was reduced by 20%.
Find the equation of the directrix of the parabola x2=+/- 12y and y2=+/- 12x
Answer:
x^2 = 12 y equation of the directrix y=-3x^2 = -12 y equation of directrix y= 3y^2 = 12 x equation of directrix x=-3y^2 = -12 x equation of directrix x= 3Step-by-step explanation:
To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.
We have 4 parts in this question i.e.
x^2 = 12 yx^2 = -12 yy^2 = 12 xy^2 = -12 xFor each part the value of directrix will be different.
For x² = 12 y
The above equation involves x² , the axis will be y-axis
The formula used to find directrix will be: y = -a
So, we need to find the value of a.
The general form of equation for y-axis parabola having positive co-efficient is:
x² = 4ay eq(i)
and our equation in question is: x² = 12y eq(ii)
By putting value of x² of eq(i) into eq(ii) and solving:
4ay = 12y
a= 12y/4y
a= 3
Putting value of a in equation of directrix: y = -a => y= -3
The equation of the directrix of the parabola x²= 12y is y = -3
For x² = -12 y
The above equation involves x² , the axis will be y-axis
The formula used to find directrix will be: y = a
So, we need to find the value of a.
The general form of equation for y-axis parabola having negative co-efficient is:
x² = -4ay eq(i)
and our equation in question is: x² = -12y eq(ii)
By putting value of x² of eq(i) into eq(ii) and solving:
-4ay = -12y
a= -12y/-4y
a= 3
Putting value of a in equation of directrix: y = a => y= 3
The equation of the directrix of the parabola x²= -12y is y = 3
For y² = 12 x
The above equation involves y² , the axis will be x-axis
The formula used to find directrix will be: x = -a
So, we need to find the value of a.
The general form of equation for x-axis parabola having positive co-efficient is:
y² = 4ax eq(i)
and our equation in question is: y² = 12x eq(ii)
By putting value of y² of eq(i) into eq(ii) and solving:
4ax = 12x
a= 12x/4x
a= 3
Putting value of a in equation of directrix: x = -a => x= -3
The equation of the directrix of the parabola y²= 12x is x = -3
For y² = -12 x
The above equation involves y² , the axis will be x-axis
The formula used to find directrix will be: x = a
So, we need to find the value of a.
The general form of equation for x-axis parabola having negative co-efficient is:
y² = -4ax eq(i)
and our equation in question is: y² = -12x eq(ii)
By putting value of y² of eq(i) into eq(ii) and solving:
-4ax = -12x
a= -12x/-4x
a= 3
Putting value of a in equation of directrix: x = a => x= 3
The equation of the directrix of the parabola y²= -12x is x = 3
Factor the following quadratic equation;
[tex]12 {x}^{2} + 22x - 14[/tex]
Answer:
2(3x + 7)(2x - 1)
Step-by-step explanation:
You can see it a little easier if you take out a common factor of 2
2(6x^2 + 11x - 7)
The 6 leaves you with a lot of factors, the 7 does not. It only has 2 factors.
Let 6 factor into 2 and 3 and the 7 into 7 and 1
2(3x - 1 )(2x + 7)
Now remove the brackets.
2(6x^2 + 21x - 2x - 7) This obviously does not work but we'll combine like terms anyway.
2(6x^2 + 19x - 7)
So we'll try it again
2(3x + 7)(2x - 1)
2(6x^2 + 14x - 3x - 7) Looks like we have it.
2(6x^2 + 11x - 7)
So the right factors are
2(3x + 7)(2x - 1)
Please Help! 35 points! Brainliest awarded!
What value of x would make the expression below equal to 8?
Answer:
x = 5/3
Step-by-step explanation:
We have the fifth root of 8^3 and we want it equal to 8
(8^3) ^ (1/5) ^x = 8
We know that a^b^c = a^ (b*c)
8 ^ (3*1/5x) = 8
8 ^ (3/5x) = 8
We can rewrite 8 as 8^1
8 ^ (3/5x) = 8^1
The exponents must be the same
3/5 x = 1
Multiply each side by 5/3 to isolate x
5/3 * 3/5x = 1 * 5/3
x = 5/3
What percent is the shaded portion of the entire diagram?
9%
40%
45%
90%
45% :) Step-by-step explanation:
In this diagram, there are a total of 20 squares, and 9 of them are shaded. This means that 9/20 of them are shaded, and to find what percent this is, divide 9 by 20 and multiply what you get by 100.
9 divided by 20 =0.45
0.45 x 100 = 45%.
45% is your final answer!
I hope this helps and have a great rest of your day!
What two numbers can you multiply and add to get 4 and 7
Answer:
2x2,2+2=4
Step-by-step explanation:
2*2=4
2+2=4
a circular platform has a circumference of 308 feet , determine the area of the platform
Answer:
A = 7552.866242 ft^2
Step-by-step explanation:
Circumference = 2 * pi *r
308 = 2 * pi *r
Divide each side by 2
154 = pi *r
Divide each side by pi
154/pi = pi *r/ pi
154/pi = r
The area of a circle is given by
A = pi r^2
A = pi * (154/pi)^2
A = pi * 154/pi * 154/pi
A = 154*154 /pi
A =23716/pi
Let pi be approximated by 3.14
A = 23716/3.14
A = 7552.866242 ft^2
Answer:
Area of circular platform is 7549.25 feet ².
Step-by-step explanation:
in the given question we have to find the area of Circle, where circumference of circle is given.
Area of Circle A = πr²
and Circumference of circle C = 2πr => r = C/2π
Putting value of r in area of circle:
A = π (c/2π)²
A = C²/4π
Putting value of C = 308 feet and π = 3.1415
A = (308)² / 4*3.1415
A = 7549.25 feet ²
So, Area of circular platform is 7549.25 feet ².
Dernea Gardening sells wheelbarrows. A wheelbarrow costs $6.94 to produce and it sells for $42.50. The company employs two salespeople, each of whom earns a different commission per wheelbarrow sold, as shown in the table below.
Answer:
The answer is C! I just took the quiz and got 100% shout out to all the cheaters out there, let's get this E2020 bread!
The percentage profit on a wheelbarrow is 512%
What is percentage profit?The percentage profit of an item is the amount of profit when the item is sold, expressed in terms of percentage
The selling price is given as:
SP = $42.50
The cost price is given as:
CP = $6.94
The percentage profit is then calculated as:
[tex]Profit = \frac{SP - CP}{CP} * 100\%[/tex]
This gives
P = (42.50 - 6.94)/6.94 * 100%
Evaluate the difference
P = 35.56/6.94 * 100%
Evaluate the quotient
P = 5.12 * 100%
Evaluate the product
P = 512%
Hence, the percentage profit on a wheelbarrow is 512%
Read more about percentage profit at:
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Can y’all help me plz
Answer:
trey
Step-by-step explanation:
he reads one page per every 2.5 minutes
Answer:
Roderick
Step-by-step explanation:
Just divide the number of pares by the time it too then to read them.
Which inequality describes the graph?
Answer:
y ≥ 3x +4
Step-by-step explanation:
The line is solid, so the inequality will include the "or equal to" case. The shading is above the line, so values of y greater than or equal to those on the line are in the solution set. The only choice with the correct (≥) inequality symbol is ...
y ≥ 3x +4
Question 2(Multiple Choice Worth 4 points)
(08.06)A student wants to report on the number of movies her friends watch each week. The collected data are below:
2
14
1
2
0
1
0
2
Which measure of center is most appropriate for this situation and what is its value?
Median, 1.5
Median; 3
Mean, 1.5
Mean; 3
Answer:
In this case, the median would be the best measure since there is the outlier of 14 in the data. This set of data will have the median of 1.5.
Step-by-step explanation:
The median would be 1.5
Evaluate -a+(-b) where a= 6.05 and b= 3.611
Answer:
-6.05-3.611=-9.661
Step-by-step explanation:
Answer: -9.661
i used khan academy and make sure to add the - sign otherwise it will be wrong
Solve for x: 15x – 30 = 45
Answer:
x = 5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
15x-30=45
+30 +30
15x=75
15/15=1
75/15=5
x=5
Which inequality represent all values of x for which the quotient below is defined??
Answer:
D. [tex]x>0[/tex]
Step-by-step explanation:
We have been given a quotient [tex]\sqrt{6x^2}\div\sqrt{4x}[/tex]. We are asked to find an inequality that represents all values of x for which the quotient below is defined.
We can rewrite our given expression as:
[tex]\sqrt{6x^2}\div\sqrt{4x}[/tex]
We know that a square root expression is defined for all values of x greater than or equal to 0. We also know that a fraction is defined when its denominator is greater than 0.
So our fraction will be defined for all values of x greater than 0.
[tex]4x>0[/tex]
Upon dividing both sides of our inequality by 4, we will get:
[tex]\frac{4x}{4}>\frac{0}{4}[/tex]
[tex]x>0[/tex]
Therefore, the inequality [tex]x>0[/tex] represents all values of x for which the given quotient is defined and option D is the correct choice.
what are two ways to describe a transformation shown on the grid?
They can be described as a horizontal movement, a vertical movement, or a combination of the two (horizontal and vertical.)
8x-4[2x-5(3x+1)]-2[x-(x-1)] I hate math
Answer:
60x + 18
Step-by-step explanation:
8x - 4 [2x - 5 ( 3x + 1 )] - 2 [x - (x - 1)]
distribute
8x - 4 [2x - 15x - 5] - 2 [x - x + 1]
combine like-terms
8x - 4 [- 13x - 5] - 2 [1]
distribute again
8x + 52x + 20 - 2
combine like-terms again
60x +18
Solve for t
3t-15 < -3 and -4t < 12
solution
-4t < 12 3t-15<-3
-4 -4 3t<-3+15
t>-3 3t<12
3 3
t<4
therefore the numbers that makes both equations right is -3<t<4
Answer:
t<4
dont worry its right
plz answer this asap first answer gets brainliest
determine which function has the larger maximum value
Answer:
g(x) has the greater max: 11 versus 6
Step-by-step explanation:
One can readily discern the max value of the graph; it is 6 and occurs at x =1.
Regarding the function g(x) = (-1/2)x^2 + 4x + 3: Find the vertex, which also represents the max value:
Here the coefficients are a = -1/2, b = 4 and c = 3, so that the axis of symmetry is:
x = -b/(2a), which here is x = -4 / ( 2·[-1/2] ) = -4 / (-1) = 4
At x = 4, the function (y) value is
g(4) = (-1/2)(4)² + 4(4) + 3, or
g(4) = -8 + 16 + 3, or 11
This is greater than the max value of the graphed function.
To assess which function has a larger maximum value, analyze their critical points or endpoints, using the derivative and evaluating the function's values at those points, which reveal the function with the higher maximal value.
Explanation:To determine which function has the larger maximum value, we must analyze the behavior of the functions and examine their critical points, endpoints, or any given constraints. For polynomial functions, the extreme value theorem ensures the existence of a maximum, provided the function is continuous over a closed interval. In many cases, finding where the derivative equals zero can indicate the location of a maximum. However, if the derivative does not equal zero at any real number, it suggests that the maximum may occur at the endpoints of the given interval.
When calculating the maximum, it's crucial to evaluate the function at the endpoints, which often reveal the highest value, especially when the turning points are not located within the interval of interest. This approach is validated through both algebraic manipulation, such as the application of the quadratic formula, and graphical analysis of the function.
In comparing two functions for their maximum values, we analyze each function similarly, derive their respective derivatives, solve for critical points, and evaluate the endpoints. Deductions are then made based on the calculated values to determine which function has the greater maximum value.
State the center and radius of x^2+y^2=2
Answer:
Center: (0, 0), Radius: √2Step-by-step explanation:
The equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex]x^2+y^2=2[/tex]
Convert to the standard form:
[tex](x-0)^2+(y-0)^2=(\sqrt2)^2[/tex]
State the center and radius of x^2+y^2=2
Simplify (4x^– 4)^– 3
Answer:
1/64x^12
Step-by-step explanation:
Answer: x^12/64
Step-by-step explanation:
Apply exponent rule: a^-b = 1/a^b
(4x^-4)^-3 = 1/(4x^-4)^3 : 64/x^12
= 1/64/x^12
Apply the fraction rule: 1/b/c = c/b
=x^12/64
Find the fifth roots of 32(cos 280° + i sin 280°)
ANSWER
[tex]2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]
EXPLANATION
The complex number given to us is in the polar form,
32(cos 280° + i sin 280°)
The fifth root is
[tex] {32}^{ \frac{1}{5} } ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]
This is equal to:
[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]
According to the DeMoivre's Theorem,
[tex]( { \cos \theta \: \degree + i \sin\theta \degree) }^{ \frac{p}{q} } = ( { \cos \frac{p}{q} \theta \degree + i \sin \frac{p}{q} \theta \degree) }[/tex]
We now use the DeMoivre's Theorem to obtain:
[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: \frac{1}{5} \times 280 \degree + i \sin \:\frac{1}{5} \times 280 \degree) }[/tex]
[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]
which arc is a minor arc?
Answer:
The arc PS would be a minor arc
Step-by-step explanation:
As a minor arc is one that is less that 180 degrees, it would be the only viable solution.
Line SO is not an arc, so it cannot be chosen
the measures of arcs SQ and PSR are each 180 degress, so they would not be minor.
The arc which is a minor arc is:
Arc PS.
Step-by-step explanation:Minor arc--
A minor arc is a arc which subtend an angle of measure less than 180 degree in the center.
i.e. such a arc should be smaller than a semicircle.
1)
Arc SQ
This arc subtend an angle of 180 degree in the center,
This means it is a semicircle and not a minor arc.
2)
arc PSR
This is again a semicircle and not a minor arc.
Since PR is the diameter of the circle and hence the arc so formed will be a semicircle.
3)
arc PS
The angle subtended at the center of the circle by this arc is less than 180 degree and hence it is a minor arc.
4)
Line SO
O is the center of the circle and S is a point on the circumference of the circle and hence it denotes the radius of the circle.