The diameter of the sphere tank is 27.2 ft.
Volume of a sphere:Every point on the surface of the sphere is equally spaced from its center, making it a three-dimensional round solid object.
The capacity of a sphere is defined as its volume or the area that the sphere occupies. Cubic units are used to measure a sphere's volume.
The formula for the Volume of a sphere is given by
Volume of a sphere = 4/3 πr³
Here we have
A spherical water tank holds 10,500 ft³ of water.
Here capacity of the sphere = Volume of the sphere
As we know the volume of the sphere = 4/3 πr³
=> 4/3 πr³ = 10500
=> πr³ = 10500(3/4)
=> (22/7)r³ = 7875
=> 22r³ = 7875(7)
=> r³ = 55125/22
=> r³ = 2505
=> r = 13.6 (Approx)
As we know diameter = 2 × Radius
=> Diameter of sphere = 2(13.6) = 27.2 ft
Therefore,
The diameter of the sphere tank is 27.2 ft.
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a large pipe and a small pipe are both being used to fill a swimming pool. if the large one can fill it in 6 hours and the small one can do it in 10 hours, how long does it take if they are both working together?
The combined rate of the two pipes is 8/30 of the pool per hour.
To find the time it takes for both pipes to fill the pool together, we can use the formula for finding the combined rate of two processes.
Let's call the rate of the large pipe L and the rate of the small pipe S. We know that L can fill the pool in 6 hours and S can fill the pool in 10 hours, so we can set up the following equations:
L = 1/6
S = 1/10
The combined rate of the two pipes is simply the sum of the individual rates:
L + S = 1/6 + 1/10
We can simplify this expression by finding a common denominator:
L + S = (5/30) + (3/30) = 8/30
So, the combined rate of the two pipes is 8/30 of the pool per hour. To find the time it takes for both pipes to fill the pool together, we can use the formula:
Time = Pool size / Combined rate
Since we do not have the pool size, we cannot determine the exact time it takes. However, we can see that the combined rate is greater than either of the individual rates, so it would take less time for both pipes to fill the pool together than for either one alone.
Therefore, The combined rate of the two pipes is 8/30 of the pool per hour.
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The combined rate of the two pipes is 8/30 of the pool per hour.
To find the time it takes for both pipes to fill the pool together, we can use the formula for finding the combined rate of the two processes.
Let's call the rate of the large pipe L and the rate of the small pipe S. We know that L can fill the pool in 6 hours and S can fill the pool in 10 hours, so we can set up the following equations:
L = 1/6
S = 1/10
The combined rate of the two pipes is simply the sum of the individual rates:
L + S = 1/6 + 1/10
We can simplify this expression by finding a common denominator:
L + S = (5/30) + (3/30) = 8/30
So, the combined rate of the two pipes is 8/30 of the pool per hour. To find the time it takes for both pipes to fill the pool together, we can use the formula:
Time = Pool size / Combined rate
Since we do not have the pool size, we cannot determine the exact time it takes. However, we can see that the combined rate is greater than either of the individual rates, so it would take less time for both pipes to fill the pool together than for either one alone.
Therefore, The combined rate of the two pipes is 8/30 of the pool per hour.
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At the store, 60 Brand A diapers costs $24. 94, while 100 diapers of Brand B costs $39. 99. Which is the better buy,
Brand A or Brand B diapers? Round your answer to the nearest cent if necessary.
The diapers of brand B that cost $39.99 for 100 diapers is a better buy that the diapers of brand A that cost $24.94 for 60 diapers.
We must utilize the unitary method in this elementary algebra issue, which is nothing more than figuring out the price per diaper in both of the cases. The cost per diaper from Brand A which has 60 diapers worth $24.94 is to be determined. As a result, since 60 diapers cost $24.94, 1 diaper must cost $24.94/60, or around 42 cents per diaper. When we repeat the job for the Brand B, we see that 100 diapers cost $39.99, making 1 diaper cost $39.99/100, or 40 cents per diaper. Now that each diaper costs less when bought from Brand B, it turns out to be a superior purchase.
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The barber cuts 61 haircuts in 4 days. Determine the rate for a ratio of the two different quantities.
The rate of the number of haircuts to the number of days as -
{r} = 15.25.
What are ratios?In mathematics, a ratio shows how many times one number contains another.In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the barber cuts 61 haircuts in 4 days.
We can write the rate for the ratio of the number of haircuts to the number of days as mentioned below -
{r} = 61/4
{r} = 15.25
Therefore, the rate of the number of haircuts to the number of days as -
{r} = 15.25.
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Air pressure may be represented as a function of height above the surface of the Earth as shown below. P(h)=Poe^(-0.0012h) In this function, P0 is air pressure at the surface of the earth, and h is the height above the surface of the earth, measured in meters. at what height will the air pressure equal 65% of the air pressure at the surface of the earth
The height at which the air pressure equals 65% of the air pressure at the surface of the earth is -ln(0.65P0)/0.0012 meters.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It can be written in a variety of forms, including an equation with an equals sign, an inequality with a greater than or less than sign, or a system of equations with multiple variables. Equations can be used to solve problems, model real-world scenarios, and explore relationships between different quantities.
To solve this problem, we can rearrange the equation to find the height h, given the pressure P. The rearranged equation is h=-ln(P/P0)/0.0012. Substituting 65% of the surface pressure for P, we get h=-ln(0.65P0)/0.0012. Therefore, the height at which the air pressure equals 65% of the air pressure at the surface of the earth is -ln(0.65P0)/0.0012 meters.
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Can someone help me pls
4x+y<2
y>-2
As given 4x+y<2 but y>-2, so the only linear inequality are 4x+(-1)<2, 4x+(0)<2 and 4x+(1)<2, graph these three and we have it.
What is linear inequality?Linear functions are used in mathematical linear inequalities. Because both sides in these functions are not equal, an equal sign cannot be used to denote them. In general, an inequality can be both an algebraic inequality and a generic inequality.
The definition of a linear inequality includes expressions with unequal sides. In this case, the equal sign is replaced by the symbols greater than, less than, greater than or equal to, and less than or equal to. Inequality can take many different forms. These three types of inequality are rational, absolute value, and polynomial.
The graph for the given linear inequality is given below↓↓↓
Every point in the dark purple zone represents
4x + y < 2
y > -2
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The diagram shows the graph of y=f(x) and the tangent drawn to the graph at x=3. Use the tangent to work out an estimate for the gradient of the curve at x=3
The estimated gradient of the curve at x=3 is given by the value of m.
What is tangent?Tangent is a line or surface that touches a curve or curved surface at one point and is perpendicular to the curve or surface at that point. It is a fundamental concept in geometry and calculus and can be used to calculate the slope of a curve at any given point. It also has many applications in engineering, physics, and other fields.
The gradient of the curve at x=3 can be estimated by the tangent drawn on the graph. In the diagram, the gradient of the tangent is given by the slope of the line, m. This can be determined using the formula, m= $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
Plugging in the coordinates of the point of tangency on the graph and the coordinates of a point on the tangent, we get:
m= $\frac{f(3)-f(4)}{4-3}$
Therefore, the estimated gradient of the curve at x=3 is given by the value of m.
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6. 0.3k - 4m
k = 20 and m = -2
Please help me and show the work please giving 20 points need in 20mins
The value of the expression 0.3k - 4m is 14. 14 is a constant term.
What is an expression?
There are numerous branches of mathematics. Arithmetic is the branch of mathematics that deals with numbers and their operations. Arithmetic taught us how to add, subtract, multiply, and divide two or more numbers.
An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4a - 5 is an expression in which the terms 4m and 5 are separated by the arithmetic sign - and a is the variable of the given expression.
Given expression is 0.3k - 4m.
To find the value of 0.3k - 4m, when k =20 and m =-2 put the values in the given expression.
Putting k =20 and m =-2 in 0.3k - 4m
0.3k - 4m
= 0.3 × 20 - 4 × (-2)
=6.0 + 8
= 14
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Enrique is recording the number of hamburgers and
hot dogs that he eats each week. The table shows
the nutritional information for hot dogs and hamburgers that he found on the Internet.
From the hamburgers and hot dogs Enrique eats each week, he decides to have around 1,200 total calories and 60 total grams of fat.
Part A: 2 points
Write two equations to represent the number of hot dogs and hamburgers he will need to eat to meet the total calories and grams of fat.
Part B: 2 points
On the coordinate plane on the left, graph the two lines that represent the maximum number of hot dogs and hamburgers Enrique can eat in one week, and identify the solution as a coordinate.
Part C: 1 point
Interpret the solution of the system of equations in the context of the situation being modeled.
Explain your answer.
Answer:
write a letter to your friends in another school and direct him or her to visit your school
please help me answer the question belowww
Answer:
m<1=41°
Step-by-step explanation:
m<1 and m<4 are vertically opposite angles, making them equal. We know m<4=41°, so we can say m<1=41° too.
Grandpa has a bag of coins. The bag contains 5 silver dollars,6quarters,2dimes and 2 nickels.He is going to let his graduator randomly select and keep 2 coins from the bag one at a time without replacement. What. Is the probability that she will select a silver filler both times.
The Thompson family wants to plant grass, build a circular pool, and install a concrete walkway to the pool in their back yard.
How many square feet of grass will their backyard have once everything is installed?
The exact amount of grass will depend on the size of the backyard, how large the pool and walkway will be, and any other features that will need to be included.
The amount of grass the Thompson family will need to plant in their backyard will depend on the size of their backyard, as well as the size of the pool and walkway they plan to install. The larger the backyard, the more grass they will need. The size of the pool and walkway will also factor into the equation, as these will take up space in the backyard and reduce the amount of grass that can be planted. Additionally, any other features, such as a patio or deck, will also need to be taken into account, as these will also reduce the amount of grass that can be planted. Ultimately, the exact size of the grass area in their backyard will depend on all of these factors and can only be determined once these details are known.
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Use the binomial formula to find the coefficient of the t^17q^2 term in the expansion of (t+2g) ¹⁹
The binomial formula to find the coefficient of the t^17q^2 term in the expansion of (t+2g) ¹⁹ is 32.06.
What is the purpose of the binomial coefficient formula?The binomial coefficient in combinatorics is used to represent the variety of ways that a given subset of objects of a specific numerosity can be selected from a bigger collection. It may be used to express the coefficients of the expansion of a power of a binomial, which is how it got its name.If your x term is being multiplied by a number, you must divide both sides of your equation by that number in order to solve a binomial issue. You multiply both sides of your equation by the number that your x term is being divided by.To learn more about binomial refer to:
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The hypotenuse of a right triangle is equal to 4 times the shorter leg. The longer leg is [tex]\sqrt[4]{15}[/tex] cm. Find the length of the shorter leg of the triangle.
Answer:
Shorter leg of triangle: 4cm
Step-by-step explanation:
So, we are told is the longer leg, let's say this is a. [tex]4\sqrt{15} = \sqrt{240}[/tex], the Pythagorean theorem is [tex]a^2+b^2=c^2[/tex] , we'll say b = shortest leg, which is what we're solving for.
Since the hypotenuse (c), is 4 times b I changed it to 4b in my equation. [tex]\sqrt{240} + b =4b[/tex], square this to get [tex]240 + b^2 = 16b^2[/tex], -b^2 on both sides, [tex]240 = 15b^2[/tex] then divide by 15. [tex]16=b^2[/tex] , use square root and you get 4 = b. To find hypotenuse, which isn't needed for your answer multiply by 4.
Hypotenuse: 16 cm
Shorter leg: 4 cm
What are the solutions of the equation x4 5x2 36 0 use factoring to solve?
The factor of the given expression [tex]x^4-5x^2-36=0[/tex] is -2i, 2i, -9 and 9.
In the given question, we have to find the solutions of the equation [tex]x^4-5x^2-36=0[/tex] using factoring to solve.
The given polynomial is [tex]x^4-5x^2-36=0[/tex].
We can write this expression as
[tex](x^2)^2-5x^2-36=0[/tex]
The multiplication of first and third term is 36 and the middle term is 5. So the possible factors are 4 and 9.
So the factor of the given expression is
[tex](x^2)^2-(9-4)x^2-36=0[/tex]
[tex](x^2)^2-9x^2+4x^2-36=0[/tex]
Now taking the common
[tex]x^2(x^2-9)+4(x^2-9)=0[/tex]
[tex](x^2+4)(x^2-9)=0[/tex]
Now taking the factor equal to zero.
[tex]x^2+4=0[/tex]
Subtract 4 on both side, we get
[tex]x^2 = -4[/tex]
Now taking the square root on both side, we get
[tex]x = -2i,+2i[/tex]
The second factor is
[tex]x^2-9=0[/tex]
Add 9 on both side, we get
[tex]x^2=9[/tex]
Taking square root on both side, we get
[tex]x = 9,-9[/tex]
Now the factor of the given expression [tex]x^4-5x^2-36=0[/tex] is -2i, 2i, -9 and 9.
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There are 60 people in a club. Half of the people in the club are women. The number of women in the club is three times the rest of men in the club. The rest of the people are children. The ratio of the number of children in the club to the number of men in club is n:1. Work out the value of n.
Answer:
Step-by-step explanation:
Let's call the number of women in the club "W", the number of men in the club "M", and the number of children in the club "C".
We may deduce from the facts provided that:
The club has a membership of 60 people.
Because women make up half of the club's membership, W = 60 / 2 = 30.
Because there are three times as many women as males in the club, W = 3M.
The remaining members of the club are youngsters, therefore C = 60 - W - M
The male-to-child ratio is n:1.
We know that W=30 from the first equation.
We may use the second equation to replace in the value of W to get 3M = 30. So, M = 30/3 = 10.
We can calculate the number of children in the club by inserting the values of W and M: C = 60 - W - M = 60 - 30 - 10 = 20
Now we may calculate the child-to-male ratio: C:M = 20:10 = 2:1. As a result, the value of n is 2.
Answer:
n=2
Step-by-step explanation:
Total 60 people in the club
Half are women ==> number of women = 60/2 = 30
Rest are are men and women so rest = 30
This number is 3 times number of men
Number of men = 30/3 = 10
Number of children = 30 -10 = 20
Ratio of children to men: 20:10 or 2:1
So n= 2
1
Two lines intersect at the point (2,-5). The lines cross the y-axis at
(0, 1) and (0, -6).
a. Graph the system.
b. What are the equations of the lines?
c. Check that (2,-5) is the solution of the system of equations you
wrote in problem 2b.
a. Graph the system:
The two lines will intersect at the point (2,-5). The first line will cross the y-axis at (0, 1), and the second line will cross the y-axis at (0, -6). The lines will be in different slope-intercept form.
What exactly is a math graph?
In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).
b. What are the equations of the lines:
To find the equations of the lines, we can use the point-slope form of a line: y - y1 = m(x - x1)
Given the point (0,1) on the first line, the slope of the first line is m = (y2 - y1) / (x2 - x1) = (-5 - 1) / (2 - 0) = -3
so the equation of the first line is y = -3x + 1
Given the point (0,-6) on the second line, the slope of the second line is m = (y2 - y1) / (x2 - x1) = (-5 - (-6)) / (2 - 0) = 1/2
so the equation of the second line is y = 1/2x - 6
c. Check that (2,-5) is the solution of the system of equations you wrote in problem 2b.
To check that (2,-5) is the solution of the system of equations we need to substitute x=2 and y=-5 in both equations
for the first equation:
-5 = -3*2 + 1 = -6 + 1 = -5
for the second equation
-5 = 1/2*2 - 6 = 1 - 6 = -5
as we can see that both equation are true for x=2 and y=-5 so the point (2,-5) is the solution of the system of equations.
The graph will be two lines crossing each other at point (2,-5) and both lines crossing the y-axis at different points (0,1) and (0,-6) respectively.
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For what value of k will the system of linear equations have infinite number of solutions KX 4y k − 4 16x Ky K?
The required value of k will the system of linear equations has infinite number of solutions is 8.
What is Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
According to question:Given set of equations is
kx + 4y = k - 4 ...(i)
16x + ky = k ...(ii)
We apply Cramer's rule to find the value of k.
Here,
D = k² - (16 × 4)
= k² - 64
= (k + 8) (k - 8)
D1 = k (k - 4) - 4k
= k² - 4k - 4k
= k² - 8k
= k (k - 8)
D2 = k² - 16 (k - 4)
= k² - 16k + 64
= (k - 8)²
= (k - 8) (k - 8)
For infinite number of solutions, we must have
D = 0 = D1 = D2
⇒ k = 8,
since (k - 8) is the common factor in D, D1 and D2.
∴ the required value of k is 8.
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If QS represents the angle bisector solve for x
Numbers are 31.2,26,5
The value of x for the triangle is 11 units.
What is an angle bisector?In geometry, the ray, line, or segment that divides a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. It splits one angle into two smaller congruent angles, to put it another way.
Given a Triangle PQR,
QS is the angle bisector
and measure of sides as given in the figure,
QP = 31.2, QR 26, and SR = 5,
let the measure of PS be a
and x = PS + SR
according to angle bisector property,
A triangle's opposite side is split into two segments by an angle bisector that is proportional to the triangle's other two sides.
so QP/PS = QR/SR
31.2/a = 26/5
a = 31.2*5/26
a = 6
x = PS + SR
x = 6 + 5 = 11
Therefore, a measure of x is 11 units.
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The complete question is in the image,
Is negative 1 a real number?
Determine the exact surface area of the cylinder in terms of π.
cylinder with radius labeled 1 and one fourth centimeters and a height labeled 2 and three fourths centimeters
6 and 9 over 16 times pi square centimeters
10 times pi square centimeters
15 and 15 over 16 times pi square centimeters
19 and three eighths times pi square centimeters
Answer:
Surface area = 31.42
Step-by-step explanation:
A=2πrh+2πr²=2·π·1.25·2.75+2·π·1.25²≈31.41593
The two prism below are similar. What is the value of x?
Answer:
[tex]x = 4[/tex]
Step-by-step explanation:
Since the two prisms are similar, the ratios of each of the sides of the larger prism to the corresponding sides of the smaller prism must be the same
[tex]\dfrac{16}{4} = \dfrac{24}{6} = \dfrac{x}{1} = 4[/tex]
So each side of the larger prism is 4 times the corresponding side of the smaller prism
[tex]\dfrac{x}{1} = 4\\\\x = 4[/tex]
What is the product of X A and X+ b?
when two values are multiplied together, the result will be a new value that is the sum of the two original values multiplied by each other. Therefore, the product of XA and X+b is X2 + Xb.
The product of XA and X+b is XA(X+b).
XA(X+b) = X(A)(X+b) = X2 + Xb
The product of XA and X+b can be expressed as XA(X+b). This is the same as X(A)(X+b), which can be further expanded to X2 + Xb. This means that when two values, XA and X+b, are multiplied together, the result is a new value that is the sum of X2 and Xb. In other words, the product of XA and X+b is the sum of X multiplied by itself and X multiplied by b. This means that when two values are multiplied together, the result will be a new value that is the sum of the two original values multiplied by each other. Therefore, the product of XA and X+b is X2 + Xb.
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Binita is going to buy 450 envelopes.
Here is some information about the cost of envelopes in two shops.
Value World
Letters2go
Pack of 25 envelopes for £3. 29
Pack of 10 envelopes for £1. 95
Buy 2 packs get 1 pack free
How much less, in pounds (£), will it cost Binita to buy
the envelopes from Value World?
Answer please!
450 envelopes if Binita decides to purchase them. Binita will have to pay 0.72 pounds (£) in order to purchase the envelopes from Value World.
Calculating the cost of value in the world is the second step.
Cost = 450 / 25 × 3.29
Cost = 59.22
The second step is to calculate the cost of value world
Cost = 450 /30 × (1.95 ×2)
Cost = 58.50
Let's now determine how much it would cost to purchase envelopes from Value World.
Cost = 59.22 - 58.50
Cost = 0.72 pounds
As a result, the price is 0.72 pounds.
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For a set population, does a parameter ever change? sometimes always unknown never if there are three different samples of the same size from a set population, is it possible to get three different values for the same statistic?
For a set population, a parameter does not change. A parameter is a numerical value that describes some aspect of a population, such as the mean, median, or standard deviation.
It is a fixed value that represents the entire population and does not change as new data is collected.
If there are three different samples of the same size from a set population, it is possible to get three different values for the same statistic.
Because a sample is a subset of a population, the values of statistics calculated from samples will vary depending on the specific individuals or observations that are included in the sample. Even if the samples are of the same size, they will likely have different values for the statistics because of the randomness of sampling.
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32% of the field is red. If the field is 600 square feet, how many square feet of the field is red?
18 3/4 because 600/32
twenty percent of the shoes in a factory are black. one shoe is chosen and replaced. a second shoe is chosen and replaced. and then a third shoe is chosen. what is the probability that none of the shoes are black?
helppp
The probability that none of the shoes are black is 51.2%.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.
Given twenty percent of the shoes in a factory are black,
probability of black shoes = 0.2
probability of not getting a black shoe = 1 - 0.2
probability of not getting a black shoe = 0.8
shoes selected three times and each time the shoe is replaced,
probability for each time is 0.8
for three times = 0.8 x 0.8 x 0.8
total probability = 0.512
probability in percent = 0.512 x 100 = 51.2%
Hence the probability is 51.2%
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Try this one → Trent is observing the growth of an insect population. He started with 125 insects and the
population doubles every month. Use x to represent the numbers of months and y to represent the insect
population. Create an equation to represent this scenario.
What is the difference between orowth & deroy functione
Answer:
Step-by-step explanation:
x represents the numbers of months and y represents the insect
population.
We are told that:
1) we start with 125 insects, and
2) the rascals double each month
Lets use m for months they double from the start of 125 insects.).
We can form an equation that will predict the insect population as a function of the numbers of months, m, from the start (125 insects).
Month 0 is 125
Month 1 would be 125*(1+1) or 125*2
We can rewrite this as 125*2^1
Month 2 125*2^2 [It dounbes again]
Month 3 125^3 [It dounbes yet again]
Month 4 125^4 [And again]
Month 5 125^5 [And so on to Infinity and Beyond]
The pattern is 125*(2)^m. where m is months since the starting month of 0.
Insect Population(m) = 125*(2)^m
See the attached graph.
I just need the answer
x + y = 1
2x - y = 4
The answer is: (5/3; -2/3)
Which segment is not a radius of Circle P?
Segment QS is not a radius of Circle P because it is diameter.
Why do we study distance formula?
To determine the separation between two points in a coordinate plane, we analyze the distance formula. We can use this to study the connections between points and resolve mathematical issues.
A mathematical method called the distance formula is used to determine how far apart two points in a coordinate plane are from one another. The Pythagorean Theorem, which states that the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, is the source of the formula. We must first ascertain the coordinates of each point in order to compute the distance between them. The first point's coordinates are (x1, y1), and the second point's coordinates are (x2, y2). then, the separation between The formula d = (((x2-x1)2 + (y2-y1)2) can be used to identify the two points. This formula can be applied to several mathematical issues, including the analysis of point relationships.
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