The water level is rising at a rate of 0.1 cm/min when the water is 50 cm deep
Let's begin by finding the volume of water in the trough when the water is 50 cm deep. We know that the trough has an isosceles trapezoid cross-section, so we can find the area of the cross-section using the formula for the area of a trapezoid
A = ((b1 + b2)/2) × h
where b1 and b2 are the lengths of the parallel sides of the trapezoid, and h is the height of the trapezoid.
In this case, b1 = 20 cm, b2 = 80 cm, and h = 60 cm. So the area of the cross-section is
A = ((20 + 80)/2) × 60
A = 3000 cm^2
To find the volume of water in the trough when the water is 50 cm deep, we need to multiply the cross-sectional area by the length of the trough and the depth of the water
V = A × L × d
V = 3000 cm^2 × 10 m × 0.5 m
V = 15000 L
Now that we know the volume of water in the trough, we can find how fast the water level is rising by taking the derivative of the volume with respect to time
dV/dt = 0.3 m^3/min
We need to convert this rate to units of L/min, so we can multiply by 1000 to convert m^3 to L
dV/dt = 0.3 m^3/min × 1000 L/m^3
dV/dt = 300 L/min
Finally, we can use the formula
dV/dt = A × dh/dt
to find how fast the water level is rising when the water is 50 cm deep. We know A = 3000 cm^2, and we want to find dh/dt when d = 50 cm. We can rearrange the formula to solve for dh/dt
dh/dt = dV/dt / A
dh/dt = 300 L/min / 3000 cm^2
dh/dt = 0.1 cm/min
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The given question is incomplete, the complete question is:
A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 80 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when the water is 50 cm deep?
If p is inversely proportional to the square of q, and p is 9 when q is 5, determine p
when q is equal to 3.
Answer:
p = 125
Step-by-step explanation:
Given p is inversely proportional to q³ then the equation relating them is
p = [tex]\frac{k}{q^3}[/tex] ← k is the constant of proportion
To find k use the condition p = 9 when q is 5, then
9 = [tex]\frac{k}{5^3}[/tex] = [tex]\frac{k}{125}[/tex] ( multiply both sides by 125 )
k = 1125
p = [tex]\frac{1125}{q^3}[/tex] ← equation of proportion
When q = 3, then
p = [tex]\frac{1125}{3^3}[/tex] = [tex]\frac{1125}{9}[/tex] = 125
List all possible rational zeros for the function. (Enter your answers as a comma-separated list.)
f(x) = 2x3 + 3x2 − 10x + 7
The rational zeros for the function, f(x) = 2·x³ + 3·x² - 10·x + 7, found using the rational roots theorem are;
-7, -7/2, -1, -1/2, 1/2, 1, 7/2, 7
What is the rational roots theorem?The rational roots theorem is a theorem in algebra that can be used to find the roots of a polynomial equation. According to the theorem, the rational roots of a polynomial that has integer coefficients have the form p/q, where, p is a factor of the constant term and q is a factor of the leading coefficient.
The rational roots theorem can be used to find the possible rational zeros of a polynomial.
The rational roots theorem states that if a polynomial function has integer coefficients, then any rational zero of the function must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient
The specified function, f(x) = 2·x³ + 3·x² - 10·x + 7, the constant term is 7 and the leading coefficient is 2. Therefore, the possible rational zeros of the function are of the form p/q, where p is a factor of 7 and q is a factor of 2.
The factors of 7 are 1, and 7, and the factors of 2 are 1 and 2, Therefore, the possible rational zeros of the functions are;
±1/1, ±7/1, ±1/2, ±7/2
The possible rational zeros of the function f(x) = 2·x³ + 3·x² - 10·x + 7 are;
-7, -7/2, -1, -1/2, 1/2, 7/2, 7
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What is the measure of angle ABC?
I measured it with a protractor and it is around 135 degrees.
I honestly don't know if this is correct but I hope this helps. Feel free to remove my answer if you think this is wrong.
A pilot of an airplane flying at 12,000 feet sights a water tower. The angle of depression to the base of the tower is 25°. What is the length of the line of sight from the plane to the tower?
Answer: Let's draw a diagram to visualize the situation:
C (water tower)
/|
/ | 25°
12000 / |
/ |
/ |
/ |
/θ | B (plane)
A |
In this diagram, the pilot of the airplane is located at point B and the water tower is located at point C. The angle of depression from the airplane to the base of the tower is 25°. We are asked to find the length of the line of sight from the airplane to the tower, which is the distance AC.
We can use trigonometry to solve for AC. In particular, we can use the tangent function, which relates the opposite side to the adjacent side of a right triangle:
tan(θ) = opposite / adjacent
In this case, the opposite side is BC (the height of the water tower) and the adjacent side is AB (the distance from the airplane to the base of the tower). We can rearrange the equation to solve for AB:
AB = BC / tan(θ)
We know that BC is the height of the water tower, but we don't have that information. However, we can use the fact that the angle of depression is 25° to find BC. The angle of depression is the angle between the horizontal line (which we can assume is the same as the ground level) and the line of sight from the airplane to the base of the tower. Therefore, the angle between the line of sight and the vertical line (which is perpendicular to the ground) is 90° - 25° = 65°. This means that the triangle ABC is a right triangle, with angle θ = 65°.
Now we can use trigonometry again to find BC, using the sine function:
sin(θ) = opposite / hypotenuse
In this case, the opposite side is BC (the height of the water tower) and the hypotenuse is AC (the line of sight from the airplane to the tower). We can rearrange the equation to solve for BC:
BC = sin(θ) x AC
We know that θ = 65° and sin(θ) ≈ 0.9063 (you can use a calculator to find this value). Substituting these values into the equation gives us:
BC = 0.9063 x AC
Now we can substitute this expression for BC into the equation we derived earlier:
AB = BC / tan(θ) = (0.9063 x AC) / tan(65°)
We can simplify this expression by noting that tan(65°) ≈ 2.1445 (you can use a calculator to find this value). Substituting this value gives us:
AB = (0.9063 x AC) / 2.1445
Multiplying both sides by 2.1445 gives us:
2.1445 x AB = 0.9063 x AC
Dividing both sides by 0.9063 gives us:
AC = (2.1445 x AB) / 0.9063
We know that AB is the altitude of the airplane, which is given as 12,000 feet. Substituting this value gives us:
AC = (2.1445 x 12,000) / 0.9063 ≈ 28,406 feet
Therefore, the length of the line of sight from the airplane to the water tower is approximately 28,406 feet.
Step-by-step explanation:
at the westside zoo there are 6 gorillas and 4 orangutans. at the central zoo there are 4 gorillas and 3 orangutans. do the two zoos have the same ratio of gorillas to orangutans? explain.
2:1
Step-by-step explanation:
So first you want to lay down all the information by writing down the number of gorillas and orangutans at Westside Zoo (6,4)
Next you want to write down the number of gorillas and orangutans at Central Zoo (4,3)
Now we want to put them in a subtraction like-form of equation
6-4 4-3
Now we take the remaining values and that's our answer for the ratio to gorillas and orangutans (2:1)
-Hope this helps!
during a 5 day week, there is a 1/2 chance of rain falling on the first day, and every day thereafter there is a 2/3 chance of the same outcome as the previous day (rain or no rain) and 1/3 chance of opposite outcome. what is the probability that there are at least 3 days of rain?
Answer:
Step-by-step explanation:
Depending on the correlations between the days, the answer can be anywhere from 25% (perfect correlation) to 100% (for example, first four days mutually exclusive).
If you assume the days are independent, which may be what you intended to ask but is not actually a good assumption when it comes to the weather, then the probability is 1 - (1-0.25)^5 = 76%
The issue pertains to probability theory, and specifically the calculation of the likelihood of precipitation on a particular day. We need to find the total probability that it rains at least three out of five days, and this would require enumerating and counting all possible outcomes.
Explanation:This is a problem of probability related to weather forecasts, specifically concerned with the chance of rain. The first day has an independent probability of 1/2 (rain or no rain). Thereafter each day's weather depends on the previous day's. If it rained the day before, there's a 2/3 chance it will rain the next day, and 1/3 chance it won't. If it didn't rain, those chances are reversed.
To get the probability that it rains at least three out of five days, we will think about it in terms of the total possible outcomes and the desired outcomes. The problem can be solved by counting the number of ways that we can have 3, 4 or 5 rainy days out of 5 and then multiplying each by the probability of that particular event.
By following these steps, we will arrive at the total probability, which might require a sophisticated understanding of probability theory.
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the cost c of a bottle of ketchup was $0.22 in 1966. in 2007, the cost was $1.39. assuming the exponential growth model applies: a. find the exponential growth rate to the nearest tenth of a percent and write the equation. b. find the cost of a bottle of ketchup in 2012.
The exponential growth rate is approximately 3.1% per year, and the equation is C(t) = 0.22 * e^(0.031t). The cost of a bottle of ketchup in 2012 would be approximately $1.72.
To find the exponential growth rate, we use the formula:
r = (ln(P2/P1)) / (t2 - t1)
where P1 is the initial value, P2 is the final value, t1 is the initial time, t2 is the final time, and ln denotes the natural logarithm. Substituting the values we get:
r = (ln(1.39/0.22)) / (2007-1966) = 0.0271 or 2.7% (to the nearest tenth of a percent)
The equation for exponential growth is:
C(t) = C0 * e^(rt)
where C0 is the initial cost and C(t) is the cost at time t. Substituting the values we get:
C(t) = 0.22 * e^(0.0271t)
To find the cost of a bottle of ketchup in 2012, we substitute t = 2012 in the above equation:
C(2012) = 0.22 * e^(0.0271 * 2012) = $1.72 (rounded to the nearest cent)
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pq and qr are 2 sides of a regular 12 sided polygon pr is a diagonal of the polygon work out the size of angle prq you must show ur working
The size of the angle PRQ is 300 degrees.
What is congruent?
The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.
In a regular 12-sided polygon, each interior angle has a measure of:
(12 - 2) × 180° / 12 = 150°
Since PR is diagonal, it divides the 12-sided polygon into two congruent triangles. Therefore, the angle PQR is half of the angle PRQ.
Let x be the measure of angle PRQ. Then we have:
x + 150° + 150° = 180° (sum of angles in triangle PQR)
Simplifying the equation, we get:
x = 180° - 150° - 150° = -120°
However, since x is an angle in a triangle, it must be positive. Therefore, we take the supplement of x, which is:
180° - x = 180° - (-120°) = 300°
Hence, the size of the angle PRQ is 300 degrees.
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45. a survey conducted by the american automobile association showed that a family of four spends an average of $215.60 per day while on vacation. suppose a sample of 64 families of four vacationing at niagara falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50. develop a 95% confidence interval estimate
The required 95% confidence interval representing the true population mean falls within the given interval, based on the given sample mean is equals to (233.00, 271.90).
Use the t-distribution,
To construct a confidence interval for the population mean,
The sample size is relatively small (n = 64)
And the population standard deviation is unknown.
The formula for the confidence interval is,
[tex]\bar{x}[/tex] ± tα/2 × (s/√n)
where [tex]\bar{x}[/tex] is the sample mean,
s is the sample standard deviation,
n is the sample size,
And tα/2 is the critical value of the t-distribution with (n-1) degrees of freedom, corresponding to the desired confidence level.
For a 95% confidence interval, the critical value of the t-distribution with 63 degrees of freedom is approximately 1.998.
Plugging in the given values, we get,
252.45 ± 1.998 × 74.50/√64)
Simplifying we get,
252.45 ± 19.45
This implies,
The 95% confidence interval for the mean amount spent per day by a family of four visiting Niagara Falls is (233.00, 271.90)
Therefore, 95% confidence interval that the true population mean falls within this interval, based on the given sample is (233.00, 271.90).
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The above question is incomplete , the complete question is:
A survey conducted by the American automobile association showed that a family of four spends an average of $215.60 per day while on vacation. suppose a sample of 64 families of four vacationing at Niagara falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50.
a. Develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting Niagara Falls (to 2 decimals).
which equations would you use the subtraction property of equality to solve? check all that apply. 5 y
answer 5y - 12 = 8.
In order to use the subtraction property of equality to solve equations, the subtraction of the same quantity should be done on both sides of the equation.
Here are the equations in which you can use the subtraction property of equality to solve:7x + 2 = 25-2y = 10-4r = 28-1/3p = 15+9z = -27
The only equation from the options given in the question is 5y - 12 = 8. So, we can use the subtraction property of equality to solve this equation as follows:5y - 12 = 8Add 12 to both sides5y - 12 + 12 = 8 + 125y = 20Divide both sides by 55y/5 = 20/5y = 4 Therefore, the equation in which we can use the subtraction property of equality to solve is 5y - 12 = 8.
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168=18×x+12×2x
What is the value of x?
Answer:
X=4
Step-by-step explanation:
First you would simplify the numbers on the right which would give you 168=18x+24x. Since the two numbers have the same variable you can add them which would then give you 168=42x. Lastly you isolate the x by dividing 42 so that x=4.
Tele brushes her teeth 1/6 hour each day use properties of operations to find how many weeks della brushes her teeth One week
Answer:
6.17 hours every week
Step-by-step explanation:
Can someone help me solve this please? I’ll give brainliest!
Answer: If it is pythagorean theorem than it is 10
Step-by-step explanation:
8^2+6^2=100
Squareroot of 100 is 10
A(-6,3), B(2,5) and C(0,-5). D is the midpoint of BC. State the coordinates of D
Answer:
D(1,0)
Step-by-step explanation:
to find midpoint add x1 and x2 then divide by 2 same with y
Work out the perimeter of this quarter circle.
Take n to be 3.142 and write down all the digits given by your calculator.
Radius is 7 cm
Answer:
Step-by-step explanation:
The perimeter of a quarter circle can be calculated by adding the length of the arc and the two radii that make up the quarter circle.
The length of the arc of a quarter circle is given by (πr)/2, where r is the radius of the quarter circle and π is approximately 3.142 (as given in the question).
So, for a quarter circle with a radius of 7 cm, the length of the arc would be:
(πr)/2 = (3.142 x 7)/2 = 10.997 cm (rounded to 3 decimal places)
The two radii that make up the quarter circle are each equal to the radius of the quarter circle, so the total length of the two radii would be:
2r = 2 x 7 = 14 cm
Therefore, the perimeter of the quarter circle would be:
10.997 cm + 14 cm = 24.997 cm (rounded to 3 decimal places)
So the perimeter of the quarter circle is approximately 24.997 cm. The digits given by the calculator will depend on the specific calculator used.
A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $350 each, and the desktop computers cost $375 each. How many total computers would someone buy if they get 10 notebooks and 19 desktop computers? How many total computers would someone buy if they get � n notebooks and � d desktop computers? Total computers, 10 notebooks and 19 desktop computers: Total computers, � n notebooks and � d desktop computers:
1) The total number of computers they would buy if they get 10 notebooks and 19 desktop computers is: 54 computers
2) The total number of computers they would buy if they get n notebooks and d desktop computers is: (350/n) + (375/n)
How to solve Algebraic expressions?The parameters given are:
Cost of notebook Computers = $350
Cost of Desktop desktop = $375
Thus, if they get 10 notebooks and 19 desktop computers, then:
Total number of computers is:
(350/10) + (375/19) = 35 + 19
= 54 computers
(375/19) was approximated to 19 because we must use a whole number and not a decimal.
If they buy n notebooks and d desktop computers, then total computers will be:
(350/n) + (375/n)
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For the formula = − , what is the value of x when y = 3 and z = 1?
Answer:
The formula is: x = -y + z
We are given that y = 3 and z = 1. Substituting these values in the formula, we get:
x = -y + z
x = -(3) + 1
x = -3 + 1
x = -2
Therefore, when y = 3 and z = 1, the value of x is -2.
Step-by-step explanation:
The given formula is: x = -y + z
We are given that y = 3 and z = 1.
Substitute the values of y and z into the formula.
x = -y + z
x = -(3) + 1
x = -3 + 1
Simplify the expression.
x = -2
Therefore, when y = 3 and z = 1, the value of x is -2.
Mass ( mg)
0 < x < 14
14 ≤ x ≤ 18
18 < x < 20
20 ≤ x ≤ 25
25 ≤ x ≤ 40
Frequency
21
28
17
22
33
The information in this table is being
drawn on a histogram.
What is the smallest integer value that
frequency density axis needs to reach,
in order to plot all of the data?
Answer:
To find the smallest integer value that the frequency density axis needs to reach, we need to first calculate the frequency density for each class interval. The frequency density is calculated by dividing the frequency of each interval by its corresponding class width.
The class widths are:
14 - 0 = 14
18 - 14 = 4
20 - 18 = 2
25 - 20 = 5
40 - 25 = 15
The frequency densities are:
21 / 14 = 1.5
28 / 4 = 7
17 / 2 = 8.5
22 / 5 = 4.4
33 / 15 = 2.2
To plot all of the data, we need to find the maximum frequency density and round it up to the nearest integer. In this case, the maximum frequency density is 8.5, so we need to round it up to 9. Therefore, the smallest integer value that the frequency density axis needs to reach is 9.
A supplier must create metal rods that are 18. 1 inches long to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are correct length or an incorrect length?
No, a binomial experiment cannot be used to determine the probability that the rods are the correct length or an incorrect length.
A binomial experiment has the following characteristics:
1. It consists of a fixed number of trials.
2. Each trial has only two possible outcomes: success or failure.
3. The trials are independent.
4. The probability of success is constant for each trial.
In the case of metal rods, the length can vary continuously, so it is not a binary outcome. Therefore, a binomial experiment cannot be used to determine the probability of the rods being the correct length or an incorrect length. Instead, a probability distribution such as a normal distribution could be used to model the distribution of rod lengths and calculate the probability of a rod being the correct length.
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A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound. But at the end of the month
the peanuts had not sold well, so, in order to sell 30 pounds of peanuts, the manager decided to mix the 30 pounds of
peanuts with some cashews and sell the mixture for $3.50 per pound. How many pounds of cashews should be
mixed with the peanuts to ensure no change in the revenue?
The manager should mix
pounds of cashews with the peanuts.
Therefore, the manager should not mix any cashews with the peanuts to ensure no change in revenue.
What is revenue?Revenue is the total amount of money a business or organization earns from selling goods or services during a specific period. It is calculated by multiplying the price of each unit sold by the total number of units sold. Revenue represents the income generated by a company's normal business activities and is used to pay for expenses, invest in future growth, and distribute profits to shareholders or owners. It is an important metric for measuring the financial health and performance of a business.
by the question.
Let's assume that x pounds of cashews are mixed with the 30 pounds of peanuts.
The total weight of the mixture would then be 30 + x pounds.
To ensure no change in revenue, the amount earned by selling the peanuts and cashews separately should be equal to the amount earned by selling the mixture.
The revenue earned by selling 30 pounds of peanuts is 30 x $1.50 = $45.
If y pounds of cashews are sold separately, the revenue earned would be y x $4.00 = $4y.
The total revenue earned by selling the peanuts and cashews separately would be $45 + $4y.
When the 30 pounds of peanuts and x pounds of cashews are mixed together and sold for $3.50 per pound, the total revenue earned would be (30 + x) x $3.50 = $105 + $3.50x.
Since the revenues from selling the mixture and selling the peanuts and cashews separately are equal, we can set the equations equal to each other and solve for x:
$45 + $4y = $105 + $3.50x
$3.50x - $4y = -$60
x - 4/7y = -60/7
We still have one unknown variable y, so we need another equation to solve for both x and y.
We know that the total weight of the mixture is 30 + x pounds. If we add y pounds of cashews to the mixture, the total weight becomes:
30 + x + y
We can set this equal to the total weight of the peanuts and cashews sold separately:
30 + y
Solving for y:
30 + x + y = 30 + y
x = 0
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Part 1
A company packages colored wax to make homemade candles in cube-shaped containers. The production line needs to plan sizes of the containers based on the associated costs. Write a cube root function that tells the side lengths of the container, x, in inches for a given cost, C
The cube root function that tells the side lengths of the container, x, in inches for a given cost, C is x = (C^(1/3))^3.
We can use the formula for the volume of a cube, which is V = x^3, where x is the side length of the cube. If the cost of producing one cube-shaped container is C dollars, then the cost of producing one unit of volume is C/V = C/x^3 dollars per cubic inch. Solving for x, we get:
x = (C/V)^(1/3)
Substituting V = x^3, we get:
x = (C/x^3)^(1/3)
Simplifying, we get:
x = (C^(1/3)) / (x^(1/3))
Multiplying both sides by x^(1/3), we get:
x^(2/3) = C^(1/3)
Taking the cube of both sides, we finally get:
x = (C^(1/3))^3
Therefore, the cube root function for a given cost, C, is x = (C^(1/3))^3.
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# 10: The circle graph below displays the percentage of
students who choose various drinks at a cafeteria. If 110
students chose milk, how many students did not choose
soda?
Percentage of Students Who Chose
Various Drinks
35%
14%
229
2996
Mik
Water
-Tea
Soda
After answering the provided question, we can conclude that As a result, equation 315 kids did not select soda.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
According to the circle graph, 14% of pupils preferred soda. As a result, 100% - 14% = 86% of pupils did not select soda.
We know that 35% of students, or 110 kids, chose milk. Hence we may calculate the fraction of pupils that did not drink soda as follows:
35/100 = 110/x
When we solve for x, we get:
x = (110*100)/35 = 314.29
x = 315
As a result, 315 kids did not select soda.
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Set up a system of equation and solve for x and y;Michelle finds some dimes and nickels, total 20 coins in her change purse. She counts $1.40 altogether. How many (x) dimes and (y) nickels does she have?
Therefore , the solution of the given problem of equation comes out to be Michelle has 12 nickels and 8 dime in her coin purse.
What is equation?Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. Consider the information provided by y + 7, when combined with generate y + 7, raising instead produces b + 7 within this situation, as opposed to another technique that could divide 12 into two parts.
Here,
Permit x and y to represent the amount of dimes and nickels, respectively.
Since there are 20 pieces in total, the following is true:
=> x + y = 20 ...(1)
=> 10x + 5y = 140 ...(2)
We can now solve for x in terms of y using equation (1):
=> x = 20 - y
When we enter this formula in place of x in equation (2), we obtain:
=> 10(20 - y) + 5y = 140
By enlarging the parentheses and streamlining, we obtain:
=> 200 - 10y + 5y = 140
Further simplification results in:
=> -5y = -60
When we multiply both parts by -5, we get:
=> y = 12
To find x, we can solve equation (1) by substituting this number of y. The result is:
=> x + 12 = 20
=> x = 8
Michelle has 12 nickels and 8 dime in her coin purse.
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If all other quantities remain the? same, how does the indicated change affect the width of a confidence? interval?
(a) Increase in the level of confidence
(b) Increase in the sample size
(c) Increase in the population standard deviation
Increase in the level of confidence and increase in the population standard deviation will increase the width of a confidence interval and increasing the sample size will decrease the width of a confidence interval.
(a) Increasing the level of confidence will increase the width of a confidence interval. This is because a higher level of confidence requires a larger margin of error, which in turn increases the width of the interval.
(b) Increasing the sample size will decrease the width of a confidence interval. This is because a larger sample size leads to a more precise estimate of the population parameter, which reduces the amount of uncertainty and therefore narrows the interval.
(c) Increasing the population standard deviation will increase the width of a confidence interval. This is because a larger standard deviation indicates greater variability in the population, which in turn requires a larger margin of error and therefore widens the interval.
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1. What is the asymptotic slope of the best fit line for the equation, y = 5x^4+3, when plotted on log-log plot?
2. What is the maximum number of inversions in a list of 100 distinct elements?
3. What is the minimum number of inversions in a list of 100 distinct elements?
1. Asymptotic slope of the best line for the equation y = 5x⁴ + 3 plotted on a log-log plot is 4. To find this, first note that the dominant term in the equation is 5x⁴. On a log-log plot, the slope corresponds to the exponent of the dominant term. In this case, the exponent is 4.
2. The maximum number of inversions in a list of 100 distinct elements is 4,950. This occurs when the list is sorted in descending order.
To calculate the maximum number of inversions, use the formula n * (n - 1) / 2, where n is the number of elements. In this case, n = 100, so the maximum number of inversions is 100 * 99 / 2 = 4,950.
3. The minimum number of inversions in a list of 100 distinct elements is 0. This occurs when the list is already sorted in ascending order, meaning no inversions are present.
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In triangle rst, m∠r > m∠s m∠t. which must be true of triangle rst? check all that apply. m∠r > 90° m∠s m∠t < 90° m∠s = m∠t m∠r > m∠t m∠r > m∠s m∠s > m∠t
Only two options are necessarily true for the triangle,
m∠r > 90°
m∠s + m∠t < 90°
In any triangle, the sum of the three angles is 180 degrees. If m∠r > m∠s + m∠t, then angle r must be the largest angle in the triangle. Additionally, the sum of the other two angles (s and t) must be less than 90 degrees.
Option m∠s = m∠t is not necessarily true because the two angles could be different and still add up to be less than m∠r. Options m∠r > m∠t, m∠r > m∠s, and m∠s > m∠t are not necessarily true and depend on the specific values of the angles in triangle RST.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
slope= 1/4
Step-by-step explanation:
This table shows the average cost of a gallon of gas each year for the past 8 years.
Use the data from the table to create a scatter plot.
Whoever answers this with a screenshot of the answer gets 100 pts + brainliest
The scatter plot for the table shows the average cost of a gallon of gas each year for the past 8 years is attached.
What is a scatter plot and why is it important?A scatter plot is a graphical representation of a collection of data points in a two-dimensional coordinate system. It is important because it allows us to visualize the relationship between two variables and identify any patterns or trends in the data, which can help us to make informed decisions and predictions.
Based on the given data, we can deduce that the average cost of gas remained relatively stable between years 1 to 2, and then increased from years 2 to 5. However, there was a sharp decrease in the average cost of gas in year 6, and it remained constant in years 7 and 8.
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Which of the following equations will produce the graph shown below?
A. X^2- y^2/4= 1
B. Y^2/9 - x^2/4=1
C. Y^2- x^2/9= 1
D. Y^2/2 - x^2/4= 1
From following equations option B will produce the hyperbola graph shown in the figure
what is hyperbola ?
A hyperbola is a type of conic section, which is a curve that is formed by the intersection of a plane and a double cone. A hyperbola can also be defined as the set of all points in a plane, the difference of whose distances from two fixed points (called the foci) is a constant.
In the given question,
Based on the shape of the hyperbola shown on the y-axis graph, we can tell that the hyperbola has a vertical transverse axis, which means that its equation must have the form:
(y - k)² / a² - (x - h)²/ b² = 1
where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices.
Option A is not correct because it produces a hyperbola with a horizontal transverse axis, whereas the given graph has a hyperbola with a vertical transverse axis.
We can eliminate option D since its equation has a transverse axis that is not vertical.
Next, we can eliminate option A since the coefficient of x² is positive, which means that the transverse axis is horizontal.
Option C has a transverse axis that is also horizontal, so we can eliminate it as well.
That leaves us with option B, which has a vertical transverse axis and its equation fits the form we determined earlier. Therefore, the equation Y²/9 - x²/4=1 will produce the hyperbola shown on the y-axis graph
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please help i have until saturday
Considering the Pythagorean Theorem, we have that:
The length of the rectangular plot is of 264 ft.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.For this problem, we have that:
The sides are the length and 170 ft.The hypotenuse is of 314 ft.Hence the length is obtained as follows:
l² + 170² = 314²
l = sqrt(314² - 170²)
l = 264 ft.
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