To find the area of the base of the column, we need to find the expression for the radius of the column, r, in terms of x.
The volume of a column can be calculated as V = πr²h, where r is the radius, h is the height, and π is pi.
Using the given expression for the volume of the column, we can write:
πr²h = x³ + 37x² - 110x + 400
Since h = x + 40, we can substitute to get:
πr²(x + 40) = x³ + 37x² - 110x + 400
Dividing both sides by π(x + 40) gives us:
r² = (x³ + 37x² - 110x + 400) / (π(x + 40))
Finally, taking the square root of both sides gives us the expression for the radius in terms of x:
r = √((x³ + 37x² - 110x + 400) / (π(x + 40)))
So, the expression that approximates the area of the base of the column in terms of x and π is:
A = πr² = π √((x³ + 37x² - 110x + 400) / (π(x + 40)))²
Find the geometric number between 4 and 5.
The geometric mean of x and y is [tex]\sqrt{xy}[/tex]
So the geometric mean of 4 and 5 is [tex]\sqrt{4*5} = \sqrt{20} \approx 4.472[/tex]
Answer:
[tex]2\sqrt{5}[/tex]
-------------------
Geometric mean of two numbers is the square root of their product.
The number we are looking for is:
[tex]\sqrt{4*5}=2\sqrt{5}[/tex]Divide a restaurant bill of $204 evenly among six people
Answer: $34
Step-by-step explanation:
204 divided by 6 = 34
Which of the following will form the composite functions G(F(x)) shown below
The answer is Option B (F(x) = x + 1 and G(x) = √3x).
Which of the following will form the composite functions G(F(x)) ?The composite function G(F(x)) means we first apply the function F(x) to x and then apply the function G(x) to the result. So, we need to find F(x) and G(x) such that:We can use substitution method to verify that F(x) = x + 1 and G(x) = √3x forms the composite function G(F(x)) = √3(x + 1).Let's start by applying F(x) to x:F(x) = x + 1Next, we apply G(x) to the result of F(x):G(F(x)) = G(x + 1) = √3(x + 1)Since the above result matches with the given composite function G(F(x)) = √3(x + 1), we can conclude that F(x) = x + 1 and G(x) = √3x forms the composite function G(F(x)) = √3(x + 1).G(F(x)) = G(x + 1) = √3(x + 1)So, F(x) = x + 1 and G(x) = √3x.To learn more about composite function refer:
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The drama club has 72 members. 1/4 of the drama club members are in 5th grade and the rest of the members are in 6th grade. How many drama club members are in 6th grade?
answer choices
72
54
18
3
Answer:
54
Step-by-step explanation:
1/4 of 72 is 18. 72-18=54.
Please explain with steps
Write as a single power using the rule
A and B part question You Try
Answer:
Check below
Step-by-step explanation:
Laws of indices applied in this worksheet:
[tex]a^{n} . a^{m} = a^{n + m[/tex]
[tex]a^{n} .b^{n} = (ab)^{n}[/tex]
Example 1:
a) [tex]x^{2} . x^{3} . x[/tex]
= [tex]x^{2 + 3 + 1}[/tex]
= [tex]x^{6}[/tex]
b) [tex](-3.1)^{3}[/tex]×[tex](-3.1)^{4}[/tex]
= [tex](-3.1)^{3 + 4}[/tex]
= [tex](-3.1)^{7}[/tex]
You Try:
a) [tex]a^{5} . a^{2} . a^{2}[/tex]
= [tex]a^{5 + 2 + 2}[/tex]
= [tex]a^{9}[/tex]
b) [tex](-1)^{100} . (-1)^{37}[/tex]
= [tex](-1)^{100 + 37}[/tex]
= [tex](-1)^{137}[/tex]
A and B are two similar 2D shapes. The area of shape A is 200cm^2. Calculate the area of shape B.
The area of shape B which is of 15 cm, is 312.5 cm²
Let us assume that the area of the shape B is x square units.
The dimensions of shape A is 12 cm
The area of the shape A is 200 cm²
The dimensions of shape B is 15 cm
The area of the shape B is x cm²
Since A and B are two similar 2D shapes their dimensions must be in proportion.
So, we get an equation,
A² / B² = 200 / x
12² / 15² = 200 / x
144 / 225 = 200 / x
x = 312.5 cm²
Therefore, the area of shape B is 312.5 cm²
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The complete question is:
A and B are two similar 2D shapes. The area of shape A which is 12cm is 200cm squared. Calculate the area of shape B which is 15cm.
De las 2000 vacunas que llegaron a bolivia para el covid-19 la mitad se usará en vacunar a médicos, la tercera parte se la usará en pacientes con patología de base y la sexta parte lo guardad en refrigeración, ¿cómo representarías eso en forma algebraica? representaremos por x el valor que no conocemos
ayuda
Answer:
pues quien sabe
Step-by-step explanation:
Kristi has a circular pool her house. The radius of the swimming pool is 22.5 Find the area and circumference of the pool.
Answer:
circumference: 141.4
Step-by-step explanation:
formula for circumference: 2πr
2 x π x 22.5
= 141.37
The area and circumference of the pool is 1590.43 square units and 141.37 units.
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
We are given that;
Radius= 22.5
Now,
we can plug it into the formulas and get:
A=π(22.5)2
≈1590.43
C=2π(22.5)
≈141.37
Therefore, by circumference the answer will be 1590.43 square units and 141.37 units.
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Do any whole numbers have a cube root between 0 and 1? Explain your reasoning
No, there are no whole numbers with a cube root between 0 and 1. A cube root of a number is a value that, when multiplied by itself three times, gives the original number.
The cube root of a number is a value that, when multiplied by itself three times, gives the original number. The cube root of a positive number is always positive. If a positive number is between 0 and 1, then its cube will be even smaller.
For example, the cube root of 8 is 2, and the cube root of 27 is 3. If we take the cube root of a number less than 1, such as 0.5, the result is less than 1. However, since we are talking about whole numbers, 0.5 is not a whole number and therefore not in the scope of the question.
Therefore, it can be concluded that there are no whole numbers with a cube root between 0 and 1 because any positive whole number raised to the power of 1/3 will result in a value greater than 1.
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can you Identify the initial amount a and the growth factor b in the exponential function g(x) = 14 × 2x ?
The initial amount, a, in the exponential function g(x) = 14 × 2x is 14, and the growth factor, b, is 2.
This can be determined by looking at the equation and noting that the coefficient of x is 2, which indicates that the base of the exponential is 2. We can also calculate the initial amount and growth factor mathematically.
To calculate the initial amount, a, we can take the equation g(x) = 14 × 2x and set x = 0, yielding g(0) = 14 × 20, which simplifies to 14. To calculate the growth factor, b, we can take the natural log of both sides of the equation to yield ln(g(x)) = ln(14 × 2x).
Simplifying this gives
ln(g(x)) = ln(14) + ln(2x).
We can then divide both sides by x to yield
ln(g(x))/x = ln(14) + ln(2)/x.
We can then take the limit as x approaches 0, which yields
ln(g(0))/0 = ln(14) + ln(2)/0.
This simplifies to
ln(g(0)) = ln(14) + ln(2), which can be rearranged to
ln(2) = ln(g(0)) - ln(14).
Taking the exponential of both sides gives us
2 = e^(ln(g(0)) - ln(14)), which simplifies to
2 = g(0)/14, or b = g(0)/14 = 2.
This shows that the initial amount, a, is 14, and the growth factor, b, is 2.
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12sec²x-16=0
Solve for the following equation by the quadratic formula or factoring
Answer:
Step-by-step explanation:
The equation 12sec²x - 16 = 0 is not a polynomial equation and cannot be factored into the product of two or more polynomials.
To solve for x, we need to isolate sec²x by adding 16 to both sides and then dividing by 12:
12sec²x - 16 + 16 = 0 + 16
12sec²x = 16
sec²x = 16 / 12
sec²x = 4/3
Now that we have isolated sec²x, we can find x by finding the inverse secant of 4/3.
Note that the inverse secant is a multi-valued function, so there may be multiple solutions for x, which can be obtained using a calculator or tables of trigonometric functions.
The length of a rectangular poster is 4 more inches than three times its width. The
area of the poster is 340 square inches. Solve for the dimensions (length and width)
of the poster.
The dimensions are Width = 10 inches and Length = 13 inches
Draw a rectangle. If the length is 4 inches longer than three times its width, we can write the width as "w" and the length as the 3*width + 4
Area is (width)(Length) = (width)(3*width+4)
W
----------
| |
| |
| | L = 3w+4
| |
| |
-----------
A = (3w+4)(w)
A = 3w² + 4w = 340.
(Problem states that area is 340 sq in)
Need to solve this quadratic equation
3y² + 4y - 340 = 0
Factor:
(w - 10) (w + 13) = 0
So
w - 10 = 0. or. w + 13 = 0
Solve these and get
w = 10. or. w = -13
Only one that makes sense in real life is the positive one.
So the dimensions are
Width = 10 inches
Length = 13 inches
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if deja is to perform an appropriate t-test to determine if there is a mean difference between the number of abrasions per leaf produced by the two strains, how many degrees of freedom should she use?
The number of degrees of freedom in a t-test is calculated as the sample size -2.
In this case, if Deja is performing a t-test to determine if there is a mean difference between the number of abrasions per leaf produced by the two strains, she needs to have the sample size of both strains.
Assuming she has n1 and n2 samples for each of the two strains, the degrees of freedom can be calculated as:
df = n1 + n2 - 2
The degrees of freedom represent the number of independent pieces of information in the sample data that are used to estimate the population parameters. The t-test statistic is then compared to a t-distribution with the calculated degrees of freedom to determine the significance of the results.
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Suppose that f(x)= x^2 and g(x)= 4/5x^2.Which statement best compares the graph of g(x) with the graph of f(x).
The graph of G(x) is the graph of F(x) compressed vertically.
Why is the expression?The equation of the graph of F(x) is given by x^2 and that of G(x) is given by 4/5 x^2.
The coefficient of x^2 in the equation of G(x) is 4/5, which is smaller than the coefficient of x^2 in the equation of F(x), which is 1.
This means that for a given value of x, the value of G(x) will always be less than the value of F(x). In other words, the graph of G(x) will be closer to the x-axis compared to the graph of F(x), which is equivalent to compressing the graph of F(x) vertically.
Therefore, the statement that best compares the graph of G(x) with the graph of F(x) is "The graph of G(x) is the graph of F(x) compressed vertically".
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Suppose that F(x) = x^2 and G(x) =4/5x^2 Which statement best compares the graph of G(x) with the graph of F(x)? The graph of G(x) is the graph of F(x) compressed vertically and flipped over the x-axis. The graph of G(x) is the graph of F(x) stretched vertically. The graph of G(x) is the graph of F(x) stretched vertically and flipped over the x-axis. The graph of G(x) is the graph of F(x) compressed vertically.
40 points!!!!! PLease HELP!!!!!!
Joshua walked on a treadmill for 1/3 of an hour. How many seconds is this?
Answer:
20
Step-by-step explanation:
1 hour is 60 minutes 1/3x60=20
Answer:
1200 seconds
Step-by-step explanation:
1/3 of an hour is 20 minutes. There are 60 seconds in a minute. 60 times 20 = 1200.
If f(x)=5x+12, what is f(2)
Answer:
To find f(2), we simply substitute 2 for x in the function f(x)=5x+12 and simplify:
f(2) = 5(2) + 12
= 10 + 12
= 22
Therefore, f(2) = 22.
Step-by-step explanation:
How to solve
2x*2 +5x+3/X*2+x-2
On solving the provided question, we can say that the question we have here is [tex]2x\times2 +5x+\frac{3}{X}\times 2-2[/tex], by bodmas [tex]\frac{9x^{3} + 6 - 2x}{x}[/tex]
Describe bodmas.The acronym BODMAS helps children remember the order of mathematical operations (the correct order for solving math problems). The words B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction make up the acronym BODMAS.
In some places, BODMAS is also referred to as PEDMAS.
Exponents, division, multiplication, addition, and subtraction are represented by this. It serves as a parentheses as well. Parentheses must be handled first, then powers or roots (i.e., of), divisions, multiplications, additions, and finally subtractions, according to the BODMAS rule.
In India and the UK, he is referred to as BODMAS, but in the US, he is more commonly called PEMDAS. They are, nonetheless, exact replicas of one another.
the question we have here is
[tex]2x\times2 +5x+\frac{3}{X}\times 2-2[/tex]
by BODMAS
Firstly, division them multiplication,
⇒ [tex]4x + 5x + \frac{6}{x} - 2[/tex]
Now we will add the addends,
⇒ [tex]9x^{2} + \frac{6}{x} - 2[/tex]
⇒ [tex]\frac{9x^{3} + 6 - 2x}{x}[/tex]
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6x-3 + 2x-1 = 10x -18
find X and AC
Answer:
#7: x = 7
#8: AC = 52
Step-by-step explanation:
We know that part + part = whole.
Thus, AB + BC = AC
Using this fact, we can solve for x:
[tex]6x-3+2x-1=10x-18\\8x-4=10x-18\\8x=10x-14\\-2x=-14\\x=7[/tex]
We can simply plug in x in 10x-18 to find the length of AC:
[tex]10(7)-18=AC\\70-18=AC\\52=AC[/tex]
You can also check that AB + BC = AC by plugging in x for 6x -3 and 2x -1 and finding the sum of the two parts of the line:
[tex]6(7)-3+2(7)-1=52\\42-3+14-1=52\\39+13=52\\52=52[/tex]
Caroline's gross earnings are $1, 126 for the current pay period. Find the state disability insurance (SDI) amount deducted from
her paycheck based on a rate of 1%of her gross earnings. Caroline has not earned $31, 800 this year.
$11.26
$13.98
$10.59
$12.52
Answer:
A) 11.26
Step-by-step explanation:
To find the state disability insurance (SDI) amount deducted from Caroline's paycheck, we need to calculate 1% of her gross earnings.
1% of $1,126 is (1/100) x $1,126 = $11.26
So, the SDI amount deducted from Caroline's paycheck would be $11.26.
Please solve for a and b:
Answer:
42=7
15=0.6
Step-by-step explanation:
1 3/8 divided by 1 4/9
Answer:
99/104
Step-by-step explanation:
1 3/8 divided by 1 4/9
1 3/8 = 11/8
1 4/9 = 13/9
11/8 divided by 13/9
= 11/8 times 9/13
= 99/104
Carnival ride tickets cost $5 each. Let C(n) = 5n be the amount of money you spend on n tickets. What is the domain of this function?
The domain of the function is composed by all the integer numbers that are greater than or equal to zero.
What is the domain of the function?The domain of a function is the set containing all the possible input values that the function can accept.
For this problem, the input is the number of tickets purchased, which must be a countable amount (you cannot purchase a negative number of tickets nor a decimal number of tickets), hence the domain of the function is composed by all the integer numbers that are greater than or equal to zero.
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A theater owner is looking to maximize his profits and needs to increase his ticket
prices. The function P(t) = -50t2 + 100t + 14,400 represents his total profit, P, based on
the amount, in dollars, he raises the ticket price, t.
The ticket price that would maximize the profit is $1 and the maximum profit would be $14,450.
How did we get the values?To maximize the profit, we need to find the maximum value of the function P(t) = -50t^2 + 100t + 14,400.
The maximum value can be found by finding the vertex of the parabolic equation. The vertex can be found using the formula:
t = -b / 2a
where a, b, and c are the coefficients of the equation in the form of y = ax^2 + bx + c. In this case, a = -50, b = 100, and c = 14,400.
Substituting the values into the formula, we get:
t = -b / 2a = 100 / (-2 * -50) = 100 / 100 = 1
So, the ticket price that would maximize the profit is $1. To find the maximum profit, we can plug in t = 1 into the function:
P(1) = -50 * 1^2 + 100 * 1 + 14,400 = -50 + 100 + 14,400 = 14,450
So the maximum profit would be $14,450.
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What is 1.047x 5-0.88
last week we calculated the standard deviation by hand, and then used that to find the standard error. can we find the standard error now?
Yes, you can find the standard error now by taking the standard deviation divided by the square root of the sample size.
The standard deviation in a data set is the mean deviation of the data from their mean.
For sample size n for a data set with data points X1, X2, X3……..Xn for exact standard deviation:
1. Calculates the arithmetic mean M of the set data by adding them all and dividing by n.
M = ( X1+X2+ X3+…..+Xn) / n
2. Calculate the deviation (D) for each data point from the mean M
D = (Xi-M) for all
3. Squaring and sum of all deviations, sum of squares (SS)
4. Divide SS by n.This quantity is the sample variance V
5. Take the square root of V.
6. This quantity is the sample standard deviation, SD.
There are some specific terms and issues to consider. If you are estimating the standard deviation of a population from a sample and the population mean $ is not known, M serves as an unbiased estimate of $. Again, SS is divided by (n-1), not n.
The resulting standard deviation is an unbiased estimate of the population standard deviation based on the sample size, n. If the population mean is known, use that mean instead of the sample mean. , and the SD of the sample is only calculated for n through SS dives.
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the minimum of two independent exponential random variables is also exponential. true or false? why?
False. The minimum of two independent exponential random variables is not necessarily exponential.
For two independent exponential random variables X and Y, with rate parameters λ1 and λ2 respectively, the minimum of X and Y is a random variable Z with the cumulative distribution function (CDF) given by
[tex]F_Z(z) = 1 - e^(-(λ1+λ2)z)[/tex].
The survival function of Z is given by
[tex]S_Z(z) = e^(-(λ1+λ2)z)[/tex].
Therefore, the probability density function of Z is
[tex]f_Z(z) = (λ1 + λ2)e^(-(λ1+λ2)z)[/tex].
This is not an exponential distribution because the form of the probability density function is not of the form [tex]f(z) = λe^(-λz)[/tex].
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what is the minimal number such that any 3-by-3 matrix with of its entries equal to zero is non-invertible
Any 3 of those entries are equal to 0, the determinant will be 0, meaning the matrix is non-invertible.
The minimal number such that any 3-by-3 matrix with of its entries equal to zero is non-invertible is 3. This can be calculated by finding the determinant of the matrix. The determinant is the sum of the products of the entries in the matrix, each multiplied by its corresponding minor. If a 3-by-3 matrix has 3 of its entries equal to zero, the determinant will be equal to 0, which means the matrix is non-invertible. To calculate the determinant of a 3-by-3 matrix, use the formula.
Where a, b, c, d, e, f, g, h, i are the entries of the matrix. If any 3 of those entries are equal to 0, the any 3 of those entries are equal to 0, the determinant will be 0, meaning the matrix is non-invertible determinate will be 0, meaning the matrix is non-invertible.
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Wildlife conservationists want to estimate the deer population in a region. They place an identifying tag on 220 deer. Several months later, researchers investigate 8 samples of 50 deer and record how many have a tag. Based on these results, how many deer should they estimate live in the region?
The number of deer that should be estimated live in the region is:
50.
To estimate the deer population, the method of capture-recapture is commonly used.
This method involves counting the number of tagged animals (in this case 220) and then counting the number of tagged animals in a subsequent sample (in this case 8 samples of 50 deer each).
By comparing the number of tagged deer in the sample to the total number of tagged deer, we can estimate the total population.
Let N be the total population of deer. The estimated population size can be calculated using the formula:
N = (220 * 50) / (the number of tagged deer in the sample)In this case, the number of tagged deer in the sample is 220. So, the estimated population size is:
N = (220 * 50) / 220 = 50Therefore, it is estimated that there are 50 deer living in the region.
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una caja de refrescos cuesta 104.40 y esta contiene 24 refrescos ¿m cual es el costo de cada refresco?
El precio de cada refresco es de 4.35$
⭐Explicación paso a paso:
En este caso lo que hay que hacer es el precio unitario de cada refresco.
El precio unitario se obtiene al dividir el total de dinero entre la cantidad de refrescos que trae cada caja:
Precio de cada refresco = Precio total/Cantidad de refrescos
Precio de cada refresco = 104.40$/24
Precio de cada refresco = 4.35$ Por lo tanto, el precio de cada refresco es de 4.35$