Answer:
[tex]\displaystyle{52\sqrt{\dfrac{39}{\pi}} \ \: \text{cm}^3}[/tex]
Step-by-step explanation:
The surface area of the sphere has formula of [tex]\displaystyle{4\pi r^2}[/tex] where r is radius. Therefore, set the equation:
[tex]\displaystyle{4\pi r^2=156}[/tex]
Divide both sides by 156:
[tex]\displaystyle{\dfrac{4\pir^2}{4}=\dfrac{156}{4}}\\\\\displaystyle{\pi r^2=39}[/tex]
Then divide both sides by [tex]\displaystyle{\pi}[/tex]:
[tex]\displaystyle{\dfrac{\pi r^2}{\pi} = \dfrac{39}{\pi}}\\\\\displaystyle{r^2=\dfrac{39}{\pi}[/tex]
Square root both sides:
[tex]\displaystyle{\sqrt{r^2}=\sqrt{\dfrac{39}{\pi}}}\\\\\displaystyle{r=\pm\sqrt{\dfrac{39}{\pi}}}[/tex]
However, radius can only be positive. Therefore:
[tex]\displaystyle{r=\sqrt{\dfrac{39}{\pi}}}[/tex]
To find the volume, we have to know that the sphere's volume is:
[tex]\displaystyle{\dfrac{4}{3}\pi r^3}[/tex]
Thus, substitute the value of r in:
[tex]\displaystyle{\text{V} = \dfrac{4}{3}\pi \cdot \left(\sqrt{\dfrac{39}{\pi}}\right)^3}\\\\\displaystyle{\text{V} = \dfrac{4}{3}\pi \cdot \dfrac{39}{\pi}\sqrt{\dfrac{39}{\pi}}}\\\\\displaystyle{\text{V} = 52 \sqrt { \dfrac{39}{\pi}}}[/tex]
Therefore, the volume of sphere is:
[tex]\displaystyle{52\sqrt{\dfrac{39}{\pi}} \ \: \text{cm}^3}[/tex]
Find the distance between (1,0) and (9,15)\
The distance between the points is given by the equation D = 17 units
What is the distance between two points?Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )
The distance from A to B is the same as the distance from B to A
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
This formula is used to find the distance between any two points on a coordinate plane or x-y plane
Given data ,
Let the distance between the points be D
Now , the equation will be
Let the first point be P ( 1 , 0 )
Let the second point be Q ( 9 , 15 )
Now , Distance between two points is the length of the line segment that connects the two points in a plane.
And , D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
D = √ ( ( 9 - 1 )² + ( 15 - 0 )² )
D = √ ( 8 )² + ( 15 )²
D = √ ( 64 + 225 )
D = √289
D = 17 units
Hence , the distance is 17 units
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Find the value of the expression
7/8+x
for x =3/8
Write your answer as a fraction or as a whole or mixed number.
Answer:
The expression 7/8 + x = 3/8 for x = 3/8 can be solved as follows:
7/8 + 3/8 = 10/8
Therefore, the value of the expression 7/8 + x = 3/8 for x = 3/8 is 10/8, which is equal to 1 1/8 or 1.125 when expressed as a whole or mixed number.
Step-by-step explanation:
The expression 7/8 + x = 3/8 can be solved as follows:
7/8 + x = 3/8
Replace x with 3/8
7/8 + 3/8 = 10/8
Therefore, the value of the expression 7/8 + x = 3/8 for x = 3/8 is 10/8, which is equal to 1 1/8 or 1.125 when expressed as a whole or mixed number.
Lin is shopping for a couch with her dad and hears him ask the salesperson, "How much is your commission?" The salesperson says that her commission is 5 1/2% of the selling price. (Hint: 5 1/2% is what decimal number?)
In linear equation, the store will get $468.72 from the sale of the couch.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
a.
Commission can be referred to as the reward given by the company on goods for the employee to sell products in order to make more sales and more money.
Commission is calculated as follows:
Total commission = Total Sales * Commission Percentage
Given
Total Sales = $495
Commission Percentage = 5½%
Substitute in, the above values
Total Commission = $496 * 5½%
Total Commission = $496 * 5.5%
Total Commission = $496 * 0.055
Total Commission = $27.28
Hence, the total commission is calculated as $27.28
b. The amount remitted to the store is calculated as
Amount = Total Sales - Total Commission
Where Total Sales = $496
Total Commission = $27.28
Amount = $496 - $27.28
Amount = $468.72
Hence, the store will get $468.72 from the sale of the couch.
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The complete question is -
Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5½% of the selling price.
A.How much commission will the salesperson earn by selling a couch for $495?
B.How much money will the store get from the sale of the couch?
Answer:
a. The total commission is $27.28
b. The store will get $468.72 from the sale of the couch
please please please help
The exponent expression that is used to express 75 as sum of the powers of 8 is [tex]8^0+8^1+8^2+8^\frac{1}{3}[/tex].
What is an exponent?
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
The integer 75 is written as -
[tex]2^0+2^1+2^2+2^6[/tex]
75 is expressed as sum of the powers of 2, with whole number exponents.
To find 75 expressed as sum of the powers of 8, divide the integer by 8 -
[tex]8^0=1[/tex]
[tex]8^1=8[/tex]
[tex]8^2=64[/tex]
Only one integer 2 is left to complete the sum as 75.
To find what the power value is use the equation -
[tex]8^x=2\\x=\frac{2}{8} \\x=\frac{1}{3}[/tex]
So, the last exponent is [tex]8^{\frac{1}3} }[/tex].
So the expression is [tex]8^0+8^1+8^2+8^\frac{1}{3} =75[/tex].
Therefore, the exponent expression is [tex]8^0+8^1+8^2+8^\frac{1}{3}[/tex].
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Am I a function? Asking for a friend
Answer: No.
Step-by-step explanation:
This is not a function because it fails the vertical line test.
What is the vertical line test?
The vertical line test is a test used to check if a graph is a function. If we place a vertical line on the graph, we should be able to shift it left and right without intersecting the graph in two places at once. Since this is a circle, it fails this test and is not a function.
A company rents water tanks shaped like cylinders. Each tank has a radius of 4 feet and a height of 2 feet. The cost is 5 dollars per cubic foot. How much does it cost to rent one water tank? Use 3.14 for pi , and do not round your answer.
One water tank can be rented for 160 dollars, according to the provided statement.
What are circumference and radius?The radius of a circular is the separation between its centre and perimeter. Always, the circumference is twice the radius.
The volume of the cylinder-shaped water tank is given by the formula
V = πr²h, where
r is the radius
h is the height.
Substituting the given values, we get:
V = π(4 feet)²(2 feet) = 32π cubic feet
The cost of renting the water tank is given by the product of the volume and the cost per cubic foot:
Cost = 5 dollars/cubic foot × 32π cubic feet
Multiplying these values, we get:
Cost = 160π dollars
Therefore, it costs 160π dollars to rent one water tank.
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What is x if 4x + 8 = 100
Answer:
x = 23
Step-by-step explanation:
4x + 8 - 8 = 100 - 8
4x = 92
(4x) / 4 = 92 / 4
x = 23
Answer:
x = 23
Step-by-step explanation:
4x + 8 = 100 ( subtract 8 from both sides )
4x = 92 ( divide both sides by 4 )
x = 23
The product of two integers is 176. One number is 5 more than the other. Let the smaller integer be N. Which of the following quadratic equations does N satisfy?
The quadratic equation that is satisfied here is given as x^2 + 5x - 176 = 0
How to come up with the quadratic equationLet's call the two integers x and y, where x is the smaller integer (N). Then, we have:
xy = 176
and
y = x + 5
We can substitute the second equation into the first equation to get:
x(x + 5) = 176
Expanding the left side, we get:
x^2 + 5x - 176 = 0
This is a quadratic equation that N satisfies.
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Newport High School has student elections every year. Lately, the school has seen a 10% decrease in voting from election to election. If 341 students voted this year, how many will be expected to vote 9 years from now? If necessary, round your answer to the nearest whole number.
Answer:
121 voters.
Step-by-step explanation:
To answer this question, we need to find the expected number of students who will vote 9 years from now. To do this, we will apply the 10% decrease in voting every year.
Starting with 341 students who voted this year, we decrease the number of voters by 10% every year.
After 9 years, the number of voters would be:
341 * (1 - 0.10)^9 = 341 * 0.354813389233575594 = 121.05
So, it is expected that 121 students will vote 9 years from now. Rounding to the nearest whole number, we get 121.
Therefore, the answer is 121 students.
There are 121 voters expected to vote 9 years from now.
we need to determine the expected number of students who will vote 9 years from now. To do this, we will apply the 10% decrease in voting every year.
Starting with 341 students who voted this year, we decrease the number of voters by 10% every year.
After 9 years, the number of voters would be as;
341 x (1 - 0.10)^9
= 341 x 0.354813389233575594
= 121.05
So, it is expected that 121 students will vote 9 years from now. Rounding to the nearest whole number 121.
Therefore, the answer will be 121 students.
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Researchers want to study behaviors in lions. They
observe the social interactions of various groups of lions
living in zoos.
What are two limitations of this model?
A. Lions in a zoo are not related to lions in the wild, so they cannot
be compared.
B. The environment of the zoo may cause the lions to behave
differently than they would in a natural habitat.
C. Observing lions in a zoo would be just as dangerous to the
researchers as observing them in the wild.
D. The presence of the researchers may affect the lions' behavior.
Answer: A and D
Step-by-step explanation:
This is the REAL correct answer.
Answer: B. The environment of the zoo may cause the lions to behave
differently than they would in a natural habitat.
and
D. The presence of the researchers may affect the lions' behavior.
Step-by-step explanation: Studying lion behavior in zoos has limitations. The artificial environment of a zoo can affect how lions behave compared to their behavior in the wild. Additionally, the presence of researchers may influence the lions' behavior, making it difficult to observe and understand their natural interactions.
B. The environment of the zoo may cause the lions to behave differently than they would in a natural habitat.
In a zoo, lions are confined to a limited space and are provided with a controlled environment. This artificial setting may not accurately reflect their natural habitat and can influence their behavior. For example, the availability of food, different social dynamics, and reduced hunting opportunities in a zoo can lead to altered behaviors that may not be representative of how lions behave in the wild.
D. The presence of the researchers may affect the lions' behavior.
When researchers observe animals in a zoo, their presence can influence the behavior of the lions. The presence of unfamiliar humans can cause the animals to become more cautious, stressed, or exhibit abnormal behavior. This could potentially alter the social interactions and dynamics observed by the researchers, making it challenging to accurately understand and interpret natural lion behavior.
the probability that a woman with two children either has two girls or two boys is 0.5048. what is the probability that she has one child of each sex? (give the answer to four decimal places.)
The probability that a woman is having one child of each sex is 0.2548.
The probability of having two children of the same gender (either both girls or both boys) can be calculated by multiplying the probability of having a girl or a boy is (which is 1/2 or 0.5) by itself twice, as each child is independent of the other:
0.5 × 0.5 = 0.25 (probability of having either two girls or two boys)
Since the total probability of having two girls or two boys is 0.5048 as given in the question, the probability of having one child of each sex is: 0.5048 - 0.25 = 0.2548.
Therefore, the probability that a woman with two children has one child of each sex is 0.2548
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10!-6! with solution
The value of the given factorial expression is 10! - 6! will be 3,628,800.
What is the factorial of n?The factor of n is given as the production of the number n, (n - 1), (n - 2)... and 1. Then the factorial of n is given as
n! = n x (n - 1) x (n - 2) x ... 3 x 2 x 1
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 10! - 6!
Simplify the expression, then we have
⇒ 10! - 6!
⇒ 10 x 9 x 8 x 7 x 6! - 6!
⇒ 6! (10 x 9 x 8 x 7 - 1 )
⇒ 6 x 5 x 4 x 3 x 2 x 1 x (5040 - 1 )
⇒ 6 x 5 x 4 x 3 x 2 x 1 x 5039
⇒ 3,628,800
The value of the given factorial expression is 10! - 6! will be 3,628,800.
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Show how 15 + 5n and 5(3 + ) are equivalent
The two expressions 15 + 5n and 5(3 + n) are both equivalent to each other when factorized and expanded respectively.
How to solve an equivalent equation?Equivalent equations are equations which have the same value when being solved.
15 + 5n and 5(3 + n)
15 + 5n
factorize
= 5(3 + n)
5(3 + n)
open parenthesis
15 + 5n
Therefore, it can be concluded that 15 + 5n and 5(3 + n) are equivalent.
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\angle A∠A and \angle B∠B are vertical angles. If m\angle A=(8x-23)^{\circ}∠A=(8x−23) ∘ and m\angle B=(6x-5)^{\circ}∠B=(6x−5) ∘ , then find the measure of \angle A∠A.
Answer:
∠A = 49°
Step-by-step explanation:
Vertically opposite angles are congruent.
∠A = ∠B
8x - 23 = 6x - 5
Add 23 to both sides,
8x = 6x - 5 + 23
8x = 6x + 18
Subtract 6x from both sides,
8x - 6x = 18
2x = 18
Divide both sides by 2,
x = 18 ÷ 2
x = 9
∠A = 8x - 23
= 8*9 - 23
= 72 - 23
= 49°
julie is digging a square area in her backyard for a vegetable garden. if the area is 52 square feet, what is the approximate length of one side of her garden? a. 6 feet b. 7 feet c. 8 feet d. 9 feet
Step 1: Calculate the area of a square.
The area of a square is the square of one of its sides.
Therefore, the area of the square is A = s^2, where s is the length of one side.
Step 2: Find the length of one side of the garden.
The given area is A = 52 square feet.
Substituting this value into the equation for the area of a square, we get 52 = s^2.
Step 3: Solve for s.
To solve for s, we can take the square root of both sides of the equation.
This gives us s = √52 ≈ 7.21 feet.
Therefore, the approximate length of one side of Julie's garden is 7 feet.
The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. Square units are used in the measuring.
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Graph Linear equations Complete these ordered pairs for the equation: y = 3x - 6 (0,__), (__,0), (1,__)
Answer:
(0,-6), (2,0), and (1,-3)
Step-by-step explanation:
We are given the equation of the line, and are then asked to find points on that line that correspond to values of x and y (x,y). We can either graph the line and look for the points, or we can solve the equation using the given value of x or y, to find the other value of y or x. Let's do both.
Graph
See the attached graph. The line is drawn and then the three points are located using the provided value of x or y.
We find:
(0,-6)
(2,0), and
(1,-3)
Solve
Fun, but we could also put the one given value in the equation and then solve for the other:
y = 3x - 6
----------
1. (0,__)
y = 3x - 6
y = 3*(0) - 6
y = -6
The point is (0,-6)
2. (__,0)
y = 3x - 6
0 = 3x - 6
-3x = -5
x = 2
The point is (2,0).
3. (1,__)
y = 3x - 6
y=3*(1)-6
y= -3
The point is (1,-3)
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Set up as a system of equations,
Let x represent the number of 4 credit courses and y represent the 3 credit courses.
The total number of courses the student took was 15. So we can say[tex]x+y=15[/tex]
The total credits earned was 54. So we can say, [tex]4x+3y=54[/tex]
Now we have the following system of equations, solve for the value of x.
[tex]\left \{ {{x+y=15} \atop {4x+3y=54}} \right.[/tex]
Take the top equation and solving for y. We get,
=> [tex]x+y=15[/tex]
=>[tex]y=15-x[/tex]
Take the value of y above and plug it into the second equation.
=> [tex]4x+3y=54[/tex]
=> [tex]4x+3(15-x)=54[/tex]
=> [tex]4x+45-3x=54[/tex]
=> [tex]x+45=54[/tex]
=> [tex]x=54-45[/tex]
=> [tex]x=9[/tex]
Thus, the student took 9, 4 credit classes.
g(x)=|-3x+16| if g(x)=17, find x
Answer: im not sure how but i hope you can get ut
Step-by-step explanation:
Graph XY with endpoints X(-3, 1) and Y(4,-5) and its image after the composition.
Rotation: 180° about the origin
Translation: (x,y)⇒(x − 1, y + 1)
A graph of XY with endpoints X(-3, 1) and Y(4,-5) and its image after the set of transformations (compositions) is shown in the image attached below.
What is a rotation?In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
By applying a rotation of 180° to the ordered pairs of points X and Y, the coordinates of its image (X′Y′) can be calculated as follows:
(x, y) → (-x, -y)
Ordered pair X = (-3, 1) → Ordered pair X' = (-(-3), -(1)) = (3, -1).
Ordered pair Y = (4, -5) → Ordered pair Y' = (-(4), -(-5)) = (-4, 5).
Next, we would apply a translation based on this transformation rule:
(x, y) → (x − 1, y + 1)
Ordered pair X' (3, -1) → (3 − 1, -1 + 1) = X" (2, 0).
Ordered pair Y' (-4, 5) → (-4 − 1, 5 + 1) = Y" (-5, 6).
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Use substitution to solve the system of equations. How many solutions are there?
1/2x-1/3y=5
x=2/3y+10
A.
There are no solutions.
B.
There is one solution.
C.
There are infinitely many solutions.
D.
It is not possible to determine the number of solutions.
The correct statement regarding the solution to the system of equations is given as follows:
A. There are no solutions.
How to solve the system of equations?The system of equations for this problem is defined as follows:
x/2 - y/3 = 5.x = 2y/3 + 10.Multiplying the first equation by 3, we have that:
1.5x - y = 5.
Substituting the second equation into the first, the solution for y is obtained as follows:
3/2(2y/3 + 10) - y = 5.
y + 15 - y = 5
0y = -10
y = -10/0.
Division by zero is not possible, hence the system of equations has zero solutions.
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What is the answer to this I need an answer please asap! 3x − 4/5= −1/2?
Answer:
x = 1/10
Step-by-step explanation:
3x - 4/5 = -1/2
-1/2 + 4/5 =
-5/10 + 8/10 =
3/10
3x = 3/10
x = 1/10
What is 4^2 and ( 4 / 5 ) ^3 in standard form
Help w. math homework please!
Answer: 1: -8x+6
Step-by-step explanation:
About 35% of the plants in a greenhouse are tomatoes. About 20% of the tomato plants are grape tomatoes. What percent of all the plants are grape tomato plants?
Answer:
7%
Step-by-step explanation:
To find the percentage of grape tomatoes among all plants, we can multiply the percentage of tomato plants by the percentage of grape tomatoes among tomato plants:
(35%) * (20%) = 7%
So, 7% of the plants in the greenhouse are grape tomato plants.
Solve please! Steps if possible, it's pathagoream theorum
Answer:
[tex]2\sqrt{14}[/tex]
D.
Step-by-step explanation:
10 in half is 5
[tex]b = \sqrt{c^{2} - a^{2} }[/tex]
b = [tex]\sqrt{81 - 25}[/tex] = [tex]\sqrt{56}[/tex] = [tex]2\sqrt{14}[/tex]
i want to know how many web-enabled devices students have with them. i sampled 5 students. here is their data: number of devices 4 3 5 5 2 what is the for this data?
The mean number of web-enabled devices for the 5 students is 3.8.
Before, solving this question the
Define of Mean:-The mean, or average, of the data is the sum of all the values divided by the number of values.
In this case, the mean for the data can be calculated as the sum of the number of devices for all 5 students divided by the number of students.
The calculation is as:
mean = (4 + 3 + 5 + 5 + 2) / 5
= 19 / 5
= 3.8
So, the mean number of web-enabled devices for the 5 students is 3.8. This gives an estimate of the average number of devices that students have.
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In a shipping carton of juice there are 8 boxes. In each box there are 8 containers. In each container there are 8 ounces of juice. How many ounces of juice are in 8 shipping cartons of juice?
Answer:512
Step-by-step explanation:
8^3
A caterer charges $110 to cater a party for 10 people and $220 for 20 people. Assume the cost, y, is a linear function of the number of x people. Write an equation in slope-intercept form for this function. What does the slope represent? How much would a party for 60 people cost?
Answer:
a) y = 11x
b) y = $660
Step-by-step explanation:
a) For 10 people is $110, so simply divide.
110/10 = $11 per person.
y = 11x
b) So using that, substitute 60 for x.
y = 11(60)
y = $660
An objective function and a system of linear inequalities representing constraints are given. Complete parts (a) through (c).
Objective Function z=7x+13y
constraints
{x+y<=11
{x+2y<=12
Graph the system of inequalities representing the constraints on the given graph of the first Quadrant.
The graph of the system of inequalities representing the constraints on the given graph of the first Quadrant is given below.
Red region is x + y ≤ 11
Blue region is x + 2y ≤ 12
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Two systems of linear inequalities are:
x + y ≤ 11
x + 2y ≤ 12
The graph of the system of inequalities representing the constraints on the given graph of the first Quadrant is given below.
Thus,
The graph of the system of inequalities is given below.
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A pet store has both dogs and cats. The sum of the numbers of dogs and cats is 42. The difference of the numbers of dogs and cats is 18. There are me dogs than cats. How many dogs and how many cats are in the pet store?
There are 30 dogs in the store, and 12 cats.
How to determine the number of cats and dogsLet's call the number of dogs in the store "x".
Since the sum of the number of dogs and cats is 42, we know that:
x + (x - 18) = 42
Expanding and solving for x:
2x - 18 = 42
2x = 60
x = 30
So there are 30 dogs in the store, and (30 - 18) = 12 cats.
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