Answer:
The surface area of a sphere is given by the formula:
surface area = 4 * pi * r^2
Where r is the radius of the sphere.
Using this formula, the surface area of an orange with a radius of 3.5 cm is:
surface area = 4 * pi * (3.5 cm)^2
= 4 * pi * 12.25 cm^2
= 49.0307 cm^2
The volume of a sphere is given by the formula:
volume = (4/3) * pi * r^3
Where r is the radius of the sphere.
Using this formula, the volume of an orange with a radius of 3.5 cm is:
volume = (4/3) * pi * (3.5 cm)^3
= (4/3) * pi * 42.875 cm^3
= 113.097 cm^3
Step-by-step explanation:
Given ,
Radius of a spherical orange is 3.5 cmTo Find : The Surface Area and the volume of a spherical orange
In order to find the surface area of a spherical orange we use the formula,
[tex]SA = 4\pi r^{2}[/tex]
[tex]SA = 4X\frac{22}{7} X 3.5X3.5[/tex]
[tex]SA =[/tex] [tex]154cm^{2}[/tex]
And now to find the volume of a sphere
[tex]V = \frac{4}{3} \pi r^{3}[/tex]
[tex]V = \frac{4}{3} X \frac{22}{7} X (3.5)^{2}[/tex]
[tex]V[/tex] [tex]= 179.59cm^{2}[/tex]
Hence, the surface area is 154[tex]cm^{2}[/tex]and the volume of a sphere is [tex]179.59cm^{2}[/tex]
A piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels. Which expression correctly shows the amount remaining in the piggy bank?
The expression that correctly shows the amount remaining in the piggy bank will be; 22d + 7n + 15q - (8d + 3n) = $4.85
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels.
LEt consider
→ dimes = d
→ nickels = n
→ quarters = q
Now the expression will be;
22 dimes + 7 nickels + 15 quarters - 8 dimes - 3 nickels
22d + 7n + 15q - 8d - 3n = $4.85
22d + 7n + 15q - (8d + 3n) = $4.85
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A store creates a mixture using only peanuts and almonds.
There are 20 pounds of the mixture.
Peanuts cost $2. 95 per pound.
Almonds cost $5. 95 per pound.
The mixture costs $4. 00 per pound.
How many pounds of peanuts are in the mixture?
There are 13 pounds of peanuts present in the mixture.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.
Let's consider Almonds be a and Peanuts be p.
from given conditions,
a + p = 20
and 5.95 a + 2.95 p = 4(20)
5.95 a + 2.95 p = 80
take, a = 20 - p
5.95 (20 - p) + 2.95 p = 80
119 - 5.95 p + 2.95 p =80
119 - 3 p = 80
3p = 39
p = 39/3
p = 13
Therefore, there are 13 pounds of peanuts present in the mixture.
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A new social media site is increasing its user base by approximately 5% per month. If the site currently has 27,870 users, what will be the approximate user base be 6 months from now?
Answer:
37,349
Step-by-step explanation:
month 1
27870 x .05 = 1394
27870 + 1394 = 29264
month 2
29264 x .05 = 1463
29264 + 1463 = 30727
month 3
30727 × .05 = 1536
30727 + 1536 = 32263
month 4
32263 x .05 = 1613
32263 + 1613 = 33876
month 5
33876 x .05 = 1694
33876 + 1694 = 35570
month 6
35570 x .05 = 1779
35570 + 1779 = 37349
Answer:
35,570
Step-by-step explanation:
solution 1 - Multiply by 5%, 6 times. Easter to calculate without a calculator, long process.
1. 27870*1.05= 29,263.5
2. 29263.5*1.05=30726.675
3.repeat
4.repeat
5.repeat
6.repeat
if it's hard for you to multiply by 1.05, you can always divide by 20 or divide by 10 then by 2 (like the below)
1. 27870÷10= 2,787
2. 2787÷2= 1393.5
3. 27870+1393.5 = 29263.5
solution 2 -Fast but probably needs a calculator
1. 27870*1.05^(5)= 35570
1.05 = monthly increase
power of 5 = ^(5) = 6 months - 1 = 5
Why is it called revolution?
The term "revolution" is often used to refer to a dramatic and sudden change in a situation, especially number of a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another.
Revolution is a term used to refer to a dramatic and sudden change in a situation, especially a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another, thus making it a revolution.
The term "revolution" is often used to refer to a dramatic and sudden change in a situation, especially number of a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another.
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You lose 0.3 point for stepping out of bounds during a gymnastics floor routine. Your final score is 9.124. Write and solve an equation to find your score $x$ without the penalty.
Your score without the penalty is 9.424.
To find your score without the penalty, we need to add 0.3 points back to your final score of 9.124. We can use the linear equation:
x = 9.124 + 0.3
This equation represents the original score, represented by x, plus the penalty of 0.3. To solve for x, we need to add 0.3 to 9.124:
x = 9.124 + 0.3
x = 9.424
So your score without the penalty is 9.424.
In this equation, x is being used to represent the original score, before the 0.3-point penalty was applied. The equation x = 9.124 + 0.3 represents that the original score was 9.124 and 0.3 points were taken off due to stepping out of bounds. By solving the equation, we are able to find the original score without the penalty which is 9.424
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6. Shenandoah's test scores were 70, 80, 80, and 90. What was his weighted average if the
tests were weighted 1, 3, 5, and 4, in that order?
The weighted average of Shenandoah's test scores is 82.3.
What is the weighted average?
To find a weighted average, multiply each number by its weight, then add the results. If the weights don't add up to one, find the sum of all the variables multiplied by their weight, then divide by the sum of the weights.
To calculate a weighted average, we need to multiply each score by its corresponding weight, and then add those products up and divide by the sum of all the weights.
To calculate a non-weighted average such as a mean average, all we need to do is, sum up, the scores and divide this sum by the number of scores. For a weighted average, each score must have a frequency attached to it. This frequency is called specific weight.
So in this case,
Weighted average = (701 + 803 + 805 + 904) / (1+3+5+4) = (70 + 240 + 400 + 360) / 13 = 1070/13 = 82.3
Hence, The weighted average of Shenandoah's test scores is 82.3
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What is the solution of the system of equations y =- 2x 8 y x 4?
The solution of the system of equations y =0 x=4
To solve the system of equations, we must set the two equations equal to each other and solve for x.
y = -2x + 8
y = x - 4
We start by subtracting the second equation from the first equation.
-2x + 8 = (x - 4)
We then add 4 to both sides of the equation.
-2x + 12 = x
We then subtract 12 from both sides of the equation.
-3x = -12
Finally, we divide both sides of the equation by -3.
x = 4
Now that we have solved for x, we can substitute 6 for x in either equation and solve for y.
y = -2(4) + 8
y = -8 + 8
y = 0
Therefore, the solution of the system of equations is (4, 0).
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The complete question:What is the solution of the system of equations y= -2x + 8 and y = x - 4?
What is the simplest form of 2√3 / √6
√2
√√3
3√2
2√3
O
The simplest form [tex]\frac{2\sqrt{3} }{\sqrt{6} }[/tex] is [tex]\sqrt{2}[/tex]
Step-by-step solution:
[tex]=\frac{2\sqrt{3} }{\sqrt{6} }[/tex]
[tex]=\frac{2\sqrt{3} }{\sqrt{2*3} }[/tex] (write factors of [tex]\sqrt{6}[/tex] i.e. [tex]\sqrt{2*3}[/tex])
[tex]=\frac{2\sqrt{3} }{\sqrt{2}\sqrt{3} }[/tex]
[tex]=\frac{2\ }{\sqrt{2}\ }[/tex]
[tex]=\frac{2\ }{\sqrt{2}\ } * \frac{\sqrt{2} }{\sqrt{2} }[/tex] (Rationalize it by [tex]\sqrt{2}[/tex])
[tex]=\frac{2\sqrt{2} }{2}[/tex]
[tex]=\sqrt{2}[/tex]
Therefore, the correct solution to this question is [tex]\sqrt{2}[/tex]
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Please answer the question below
How do you find the sides of a triangle with only the angles?
The Sides of triangle when only the angles of triangles are given can be found by using the Law Of Sines .
What is Law Of Sines ?
The Law Of Sines states that the ratio of sides of a triangle and their respective Sine angles are equivalent to each other. The other names by which the law of sines is known are Sine Law, Sine Rule and Sine Formula.
The Sine Law is used to find unknown side of an oblique triangle. The oblique triangle is defined as a triangle that is not a right triangle.
Let a , b and c be the sides of a triangle ABC , and A , B and C be the angles .
So , by Sine Law : [tex]\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}[/tex] ;
Therefore , The Law Of Sines help in finding the sides of triangle that has only angles .
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A calculator cost 32.00 if the sales tax is 6% what is the price ?
Answer:
Step-by-step explanation:
Here is how to solve the given problem above.
Given that the calculator costs $32 and has a tax of 6%, what we are going to do is to find how much is 6% of 32. So 32 times 0.06 is 1.92. So, we add this amount to 32 dollars, and the total price would be 33.92 dollars. Hope this answer helps.
Answer:
33.92
Step-by-step explanation:
32 times 6 divided by 100 gives you 1.92, the sales tax,
add it to 32 and then you get 33.92
What type of triangle do the points 3 2 (- 2 3 and 2/3 form a right triangle B equilateral triangle C isosceles triangle d none of these?
Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).
Let the given points be,
A = (3, 2), B = (-2, -3) and C = (2, 3)
The formula for the distance between two points:
The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].
Therefore,
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)
[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex] units
B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex] units
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex] units
By using the Pythagorean theorem:
According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.
Now, we can see that,
[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]
[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]
Therefore, the given triangle is a right angled triangle.
Therefore, option(A) s correct.
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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.
A. right triangle
B. equilateral triangle
C. isosceles triangle
D. none of these
The drama club put on the play, “The wizard of Oz.” There were student tickets and adult tickets. There were 150 tickets sold to the play. Student tickets cost $3 per ticket, and adult tickets cost $5 per ticket. If the total sales were $580, how many student tickets and how many adult tickets were sold to the play? Use system of equations to solve.
On solving the provided question, we can say that - by the help of the unitary method 150* 3 = $450
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
so, we have
There were = 150 tickets sold to the play
Student tickets cost $3 per ticket
so, total will be = 150* 3 = $450
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What is parallel lines Class 7?
Parallel lines are those lines that lie in the same plane and never intersect each other. They are equidistant from each other at every point and have the same slope.
Two lines are stated to be parallel when they do not meet at any point in a plane. This means that lines which do not have a common intersection point and never cross paths with each other are parallel to each other. The symbol used for representing parallel lines is ‘||’.
Two parallel lines are represented as:
AB║CD
That is line AB is parallel to CD.
The perpendicular length between the two parallel lines is always constant.
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To find the distance from the edge of a lake to the tree on the island in the lake, Lisa sets up a
triangular configuration as show in the diagram. The distance from Location A to Location B is 97
meters. The measures of the angles at A and B are 46 and 103 °. What is the distance from the
edge of the lake at B to the tree on the island at C? Round the distance to the nearest tenth of a
meter.
A
B
C
Therefore ,the result is. It means that there exist 17 units between the two points supplied as the answer to the given distance problem.
Specify the distance.An object's travels are quantified by distance. Simply explained, distance, or t, is the amount of space an object covers within a specific period of time. Displacement is still the quickest route a moving object can travel. We frequently take into account the concepts of range and displacement.
Here,
6 and -3 are given (2, -2)
Points (a, b) and (c, d) are now separated by
d= √(c-a)² + ( d- b) ²
d= √(-3+2)² + (2-6)² as a result.
=>d = √ 1 + 16 = √17
The distance between the two places is therefore 17 units.
the result is. It follows there are 17 units between the two points supplied as the answer to the given distance problem.
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Can you let me know the answer please
Answer:
The answer is A
Step-by-step explanation:
When looking at this image, look at A, notice how it says y and the equal to symbol is facing it? then notice at the end of answer a is -4, look at the graph and the line intercepts -4, remeber, the end number, whether positive or negative will always be the on the y axis
A regular pentagon is a pentagon with five sides of the same length. If the length of one side of the pentagon is represented by 2X -1, what expression would represent the perimeter of this pentagon
Step-by-step explanation:
one side : 2x - 1
so, 5 sides (the perimeter is the sum of all sides) :
5 × (2x - 1) = 10x - 5
how do i answer this q
Answer: -1/4
Step-by-step explanation:
Rate of change is just another term for slope. To calculate slope, we just need any 2 points on the graph and apply the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]m=\frac{1-2}{4-0} =\frac{-1}{4} =-\frac{1}{4}[/tex]
This means -1/4 is the rate of change.
Melissa tutors math. For each hour that she tutors, she earns dollars. Let be her earnings (in dollars) after tutoring for hours. Write an equation relating to . Then use this equation to find Melissa's earnings after tutoring for hours.
After H hours of coaching, let E indicate her profits (in dollars). She receives $20 for every hour she tutors. This indicates that her total earnings in H hours would be E = 20H.
What is meant by equation?Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7. An equation is a mathematical expression with two equal sides and an equal sign in between. An equation is something like 4 + 6 = 10. Your example is by definition an equation as an equation is any expression that contains the equals sign. Since mathematicians adore equal signs, equations frequently appear in mathematical texts. A formula is a list of steps to follow in order to produce the intended outcome.After H hours of coaching, let E indicate her profits (in dollars). She receives $20 for every hour she tutors. This indicates that her total earnings in H hours would be
E = 20H.
We would enter H = 17
into the formula to get Mai's pay after 17 hours of tutoring.
E = 20 × 17 E = $340 is the result.
The complete question is:
Mai tutors history. For each hour that she tutors, she earns 20 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H . Then use this equation to find Mai's earnings after tutoring for 17 hours.
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2789\36 help me psss i have to take this test lie be so fl i like right nowww pls haelp me
Answer:
77.472222 etc
Step-by-step explanation:
If an investment company pays 6% compounded continuesly, how much should you deposit now to have $10,000 5 years from now?
The amount of money should you deposit now to have $10,000 5 years from now is $7407.
What is compound interest?Theoretically, continuously compounded interest means that interest is continuously earned on an account balance as well as reinvested into the balance to increase future interest earnings.
Given that If an investment company pays 6% compounded continuously and $10,000 for 5 years.
The amount of money invested will be calculated by the formula below,
[tex]P = P_o(e)^{rt}\\10000 = P_o ( e)^{0.06\times5}\\[/tex]
P₀ = 10000 / 1.35
P₀ = 7407
The amount of money invested would be 7407.
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How do you find the longest angle?
The longest angle is the straight line, or 180 degrees. To find it, draw two lines so that they form a straight line. Then measure the angle between the two lines using a protractor.
What is angle?Angle is a figure formed by two lines or rays intersecting each other. It is measured in degrees, and is generally represented by the symbol ∠. The lines or rays that form the angle can be extended indefinitely, and the angle can be either acute, obtuse, right, reflex, or full. An acute angle is one that is less than 90°, an obtuse angle is one that is greater than 90°, a right angle is one that is exactly 90°, a reflex angle is one that is greater than 180°, and a full angle is one that is 360°.
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Can u please help...................
Answer:
(-2, 2)
Step-by-step explanation:
You want the circumcenter of the triangle with vertices A(2, -3), B(2, 7), and C(-6, -3).
CircumcenterThe circumcenter is the center of the circle that circumscribes the triangle. Here, the triangle is a right triangle, so the circumcenter is the midpoint of the hypotenuse.
MidpointThe midpoint of segment BC is the average of the coordinates of B and C:
X = (B +C)/2 = ((2, 7) +(-6, -3))/2 = (2 -6, 7 -3)/2 = (-4, 4)/2
X = (-2, 2)
The circumcenter is (-2, 2).
__
Additional comment
The right angle subtends an arc of twice its measure, 180°, so the circumscribed triangle occupies a semicircle, and the hypotenuse is a diameter. That puts the center of the circle at the midpoint of the hypotenuse.
please give a step by step explanation for this question
Answer:
[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]
Step-by-step explanation:
The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].
[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]
We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].
Now add these equations together to get our equation.
[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]
Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].
=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]
d. -(y² - 2) = y²-5-2y², solve for y
Answer:
No solution
Step-by-step explanation:
-(y² - 2) = y²-5-2y²
= y^2 - 5 - 2y^2 = - (y^2 - 2)
= -y^2 - 5 = - (y^2 - 2)
= −(y^2 − 2)
= -y^2 - 5 = -y^2 + 2
-5 = 2
We know that -5 is not equal to 2
So, there is no solution
Answer:
2
Step-by-step explanation:
At a benefit concert, fifteen bands have volunteered to perform but there is only enough time for eight of the bands to play. How many lineups are possible?
On solving the provided question, we can say that - he need 56 answers he need to get correct if he want a grade of 80 percent on a test with 70 questions
what is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.
Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56 Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.
So, the maximum number of questions you may omit is 14. As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.
20% of 70
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can someone please help ( check link for question )
Hence, The equation of the line is y=5x/3-3
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The line 3x+5y=15 , Rearranging in the slope intercept form we get y=-3x/5+3 and thus slope of the line that is perpendicular to this line must be equal to 5/3 and it passes through (3,2) then we get the equation of the line as y=5x/3+c and putting (3,2) in the equation we get the value of c as c=-3
∴ The equation of the line is y=5x/3-3
Hence, The equation of the line is y=5x/3-3
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maddox has $12.25 to spend on sports drinks. Each drink costs $1.75. Use the guess, check, and revise strategy to solve the equation 1.75d=12.25 to find d, the number of drinks Maddox can buy.
Determine and state an equation of the line perpendicular to the line 5x-4y=10 and passing through the point (5,12)
The equation of the line perpendicular to the line 5x-4y=10 and passing through the point (5,12) is y = 4x/5 + 8.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given:
The line 5x-4y=10.
Simplifying,
y = (-5/4)x + 5/2
Comparing with the slope-intercept form,
y = mx + b,
where m is the slope and b is y-intercept.
The slope is = -5/4
The slope of the perpendicular line,
= negative reciprocal of the slope of the line where the line is perpendicular.
= 4/5
So, the line:
If a line passes through one point (x₁ ,y₁) and have slope m,
then the equation of line is
y - y₁ = m (x - x₁)
y - 12 = (4/5)(x-5)
y = 4x/5 + 8
Therefore, the equation of the line is y = 4x/5 + 8
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Dalis' employer pays $2,150 in health insurance and $86
in life insurance per year. She also gets $3,520 in paid time
off per year. Her monthly gross pay is $4,370. What are
Dalis' total job benefits?
Answer: chiki
Step-by-step explanation: