To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.
The number of socks chosen at random will be denoted by the letter "n." Given by: The anticipated number of blue socks in "n" pairs
Expected number of blue socks = n * 1/4
In order for there to be four blue socks as expected, we need to determine the value of "n." Thus, we can construct the equation:
n * 1/4 = 4
And solving for n:
n = 4 / (1/4) = 4 * 4 = 16
So, To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.
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Which two equations form a system of linear equations that has no solution
The two equations form a system of linear equations that has no solution are
y=3x+2
y=3x+(1/2)
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
y=3x+2
y=3x+(1/2)
Equate both the equations to find x
3x+2 =3x+(1/2)
same term 3x cancels out
2=(1/2)
This is not true
So, two equations form a system of linear equations that has no solution are
y=3x+2
y=3x+(1/2)
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Simplify. Express your answer as a single term, without a denominator.
j^-5k^-5 x jk^-7
The simplified expression is j^-4k^-12
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
j^-5k^-5 x jk^-7
Rewrite as
j^-5k^-5 x jk^-7 = j^-5 * j * k^-5k^-7
Apply the law of indices in the products
j^-5k^-5 x jk^-7 = j^-4 * k^-12
So, we have
j^-5k^-5 x jk^-7 = j^-4k^-12
Hence, the expression is j^-4k^-12
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consider a little league team that has 15 players on its roster. (a) how many ways are there to select 9 players for the starting lineup? incorrect: your answer is incorrect. ways
The number of ways to select 9 players for the starting lineup from a team of 15 players is 4862 ways.
The number of ways to select 9 players for the starting lineup from a team of 15 players can be calculated using the formula for combinations, which is given by:
C(n,k) = n! / (k! (n-k)!)
Where n is the total number of items, k is the number of items being selected, ! means factorial, and C(n,k) represents the number of combinations of k items from n.
Using this formula, the number of ways to select 9 players from a team of 15 players is:
C(15,9) = 15! / (9! (15-9)!) = 15! / (9! 6!) = 4,862
So, there are 4,862 ways to select 9 players for the starting lineup from a team of 15 players.
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100 Points!!
Will mark brainliest
A cake recipe says to bake the cake until the center is 180 degrees F, then let the cake cool to 100 degrees F. The table shows temperature readings for the cake.
a. Given a room temperature of 69 degrees F, what is an exponential model for this data set?
b. How long does it take the cake to cool to the desired temperature?
Please don't answer just for the points
The exponential model is [tex]T(t)=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex] and It takes the cake 9.32 minutes to cool to the desired temperature
We can solve this by using Newton's Law of cooling,
[tex]T(t)=C+(T_o-C)e^k^t[/tex]
where
T(t) is the temperature at any given time
C is the surrounding temperature
T₀ is the initial temperature
k is a negative constant
t is the time
A cake recipe is baked until the center is 180 °F
T₀=180 ⇒ initial temperature
The room temperature is 69 °F
C = 69 ⇒ surrounding temperature
By using the table, substitute t and T to find the constant k
At t = 5 minutes, T = 125 °F
[tex]125=69+(180-69)e^k^t[/tex]
By subtracting 69 on both sides
[tex]56=(111)e^k^t[/tex]
Dividing both sides by 111
[tex]\frac{56}{111} =e^k^t[/tex]
Add ㏑ for both sides
[tex]ln(\frac{56}{111} )=ln(e^k^t)[/tex]
Dividing both sides by 5
k=- 0.1368357021
The exponential model is [tex]T(t)=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
The cake cools at 100 °F and the desired temperature is 100°
T(t) = 100 ⇒ cake's temperature at t minute
Using the model above to find t
[tex]T(t)=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t\\\\100=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
Subtract 69 from both sides
[tex]39=(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
Divide both sides by 111
[tex]\frac{39}{111} =e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
Applying ㏑ for both sides
[tex]ln(\frac{39}{111}) =e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]
Dividing both sides by - 0.136835702
t=9.321711938
t ≅ 9.32 minutes
It takes the cake 9.32 minutes to cool to the desired temperature.
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For positive acute angles A and B, it is known that sun A=40/41 and tan B= 20/21. Find the value of sin(A+B) in simplest form
The exact value of the trigonometric function sin (A + B) is equal to 1020 / 1189.
How to find the exact value of a trigonometric function of a sum of angles
In this problem we must determine the exact value of the sine of the sum of two acute angles. There are acute angles in the first quadrant, thus:
sin θ > 0
cos θ > 0
tan θ = sin θ / cos θ
In addition, by trigonometric formulas:
cos θ = √(1 - sin² θ)
cos θ = 1 / √(tan² θ + 1)
Where θ is the angle, in degrees.
sin (α + β) = sin α · cos β + cos α · sin β
If we know that sin A = 40 / 41 and tan B = 20 / 21, then the exact value of sin (A + B) is:
cos A = √[1 - (40 / 41)²]
cos A = 9 / 41
cos B = 1 / √[1 + (20 / 21)²]
cos B = 21 / 29
sin B = √[1 - (21 / 29)²]
sin B = 20 / 29
sin (A + B) = (40 / 41) · (21 / 29) + (9 / 41) · (20 / 29)
sin (A + B) = 1020 / 1189
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Nolan had 20 dollars to spend on 3 gifts. He spent 9 34 dollars on gift A and 3 12
dollars on gift B. How much money did he have left for gift C?
Therefore, Nolan has 8 dollars left to spend on gift C.
Nolan spent 9 dollars and 34 cents on gift A,
and 3 dollars and 12 cents on gift B,
for a total of
9 + 3 = 12 dollars and
34 + 12 = 46 cents spent so far.
Nolan started with 20 dollars, so he has 20 - 12 = 8 dollars remaining for gift C.
By using wildcards (such as "x" and "y") that are replaced with random values when the quiz is taken, simple calculated questions provide a technique to build individual numerical questions whose response is the result of a numerical formula that contains changeable numerical values.
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£200 is invested for 10 years at 9 compound interest per annum
After 10 years at 9% compound interest per annum, The amount will be £393.57.
The amount of money you will have after 10 years can be calculated using the formula for compound interest:
[tex]A = P * (1 + r/n)^{nt}[/tex]
where:
A is the final amount,
P is the initial amount (principal),
r is the interest rate as a decimal,
n is the number of times the interest is compounded per year,
t is the number of years the money is invested.
In this case:
P = £200
r = 9% = 0.09
n = 1 (because interest is compounded annually)
t = 10
So, plugging in the values, we get:
[tex]A = 200 * (1 + 0.09/1)^{1 * 10)} = 200 * (1.09)^{10}[/tex]
[tex]A = 200 * 1.96787 = 393.57[/tex]
So, after 10 years at 9% compound interest per annum, you will have £393.57.
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Help ASAP please !!!!!!!!,,
The exponential function shown in the graph is f(x) = 2ˣ
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
The standard form of an exponential function is:
y = abˣ
where a is the initial value and b is the multiplication factor.
The graph shown is an exponential function.
At the point (0, 1):
y = abˣ
substituting:
1 = ab⁰
a = 1
At the point (2, 4):
y = abˣ
substituting x = 2, y = 4 and a = 1:
4 = b²
b = 2
The exponential function is y = 2ˣ
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find the minimum value c=x+3y
Answer: To find the minimum value of c = x + 3y, you need to solve the optimization problem with a constraint or without any constraint.
Without a constraint:
The minimum value of c = x + 3y without a constraint is achieved when the partial derivatives of c with respect to x and y are equal to zero.
Let's take the partial derivative of c with respect to x:
dc/dx = 1
And with respect to y:
dc/dy = 3
Setting these equal to zero, we have:
1 = 0 and 3 = 0
Since the partial derivatives are not equal to zero, there is no minimum value of c without a constraint.
With a constraint:
If there is a constraint, such as a limit on x or y, then the minimum value of c can be found by using optimization techniques, such as the method of Lagrange multipliers.
Step-by-step explanation:
What is the most simplified expression for 4 c squared d + 3 d c minus 2 (d c squared + c d) + 6 c squared d squared?
2 c squared d + d c + 6 c squared d squared
2 c squared d + 5 d c + 6 c squared d squared
3 c squared d + 3 d c + 6 c squared d squared + c d
3 c squared d + 2 d c + 6 c squared d squared minus 2 cd
Answer: 2 c squared d + d c + 6 c squared d squared
Step-by-step explanation: I looked it up
or
Rudy has run many marathons and keeps track of all of his finishing times. At a race last month, he finished in 260 minutes. At his next race, he finished with a time that was 20% longer. What was his finishing time at the most recent race?
Rudy's timing in the most recent race is 312 minutes.
What are algebraic expressions?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 Rudy has run many marathons and keeps track of all of his finishing times. At a race last month, he finished in 260 minutes. At his next race, he finished with a time that was 20% longer.
Rudy's timing in the most recent race can be calculated as -
{x} = 260 + 20% of 260
{x} = 260 + (20/100) x 260
{x} = 260 + 20 x 2.6
{x} = 260 + 52
{x} = 312
Therefore, Rudy's timing in the most recent race is 312 minutes.
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The town of Valley View conducted a census this year, which showed that it has a population
of 1,800 people. Based on the census data, it is estimated that the population of Valley View
will grow by 12% each decade.
Write an exponential equation in the form y = a(b) that can model the town population, y, x
decades after this census was taken.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential function to model the population of Valley View is [tex]y = 1800(1.012)^t[/tex].
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
An exponential function is written in the form -
[tex]y=ab^t[/tex]
Here, y is the function, a is the base value b is the rate and t is time period.
The number of people in Valley view is 1800. So, the base is a = 1800.
The function y depicts the towns population.
Each decade the population grows by 12%.
The growth rate per year is = 12 / 10
The growth rate is 1.2%
The value for b will be = 1 + r
b = 1 + 1.2/100
b = 1 + 0.012
b = 1.012
So, the exponential equation will be -
[tex]y = 1800(1.012)^t[/tex]
Therefore, the exponential equation is [tex]y = 1800(1.012)^t[/tex].
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The points (-8, -3) and (-1, -2) fall on a particular line. What is its equation in point-slope form?
Answer: y+3= 1/7 * (x+8)
Step-by-step explanation:
What is −12 + |−3| − |−14|?
−26
−23
−11
−5
Step-by-step explanation:
The expression can be simplified as follows:
-12 + |-3| - |-14| = -12 + 3 - 14 = -23
So, the answer is -23.
Answer: -23
Step-by-step explanation: The absolute value symbols turn the numbers inside to positive. The subtraction symbols outside dont change. When doing this conversion the simplified version will be -12+3-14 which equals -23.
The ordered pair (a,b) satisfies the inequality y < x+5
(-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is y < x+5
First, we have to find the x-intercept which occurs at y = 0
0 < x + 5
x<-5
For y-intercept,
y < 0+ 5
y <5
As a result, the obtained ordered pair is (-5, 0 ) and (0, 5).
Hence, (-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5
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write each equation in slope-intercept form. Identify the slope and y-intercept. Then graph the line described by the equation.
-4x+2y=10
Answer:
y = 2x + 5
The slope: 2
Y-intercept: 5
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = the slope
b = y-intercept
Our equation
-4x+2y=10
2y = 4x + 10
y = 2x + 5
The slope: 2
Y-intercept: 5
x^2-6x=55 complete the square
Answer: X= 5 ; -11
To solve our problem lets work backwards.
x^2-6x=55. First we must subtract 55 from both sides our equation. That leaves us with x^2-6x-55=0.
We next need to cancel out the number six. We also need to find two numbers that can be multiplied by one another to equal 55.
This would be 5 and -11. 5 and -11 can be added together to make -6, which is the negative integer for 6. They can also be multiplied together to make the negative integer of 55, which is -55.
This means that our X has two possible solutions.
Hence, X= 5 & -11
I hope this helps & Good Luck <3 !
Help please:
Eliza loves ferris wheels and she was super excited to ride one at the state fair. Unfortunately, the ferris wheel broke halfway through her ride (180 degrees) so she was stuck at the op! If the sector area of the half of the wheel is 5618 pi ft^2, how far up is Eliza from the ground? Hint: find diameter. Round, if necessary, to the nearest whole number
Eliza is 212 feet above the ground as the given sector area of the half of the wheel is 5618 pi ft^2 and ride is stuck at 180 degrees.
Ferris wheel has a shape of a circle
So, we can use this formula
Area = πr²
Sector area of half the circle = πr²/2
From Eliza to the ground is the diameter of the wheel
5618 π ft² = πr²/2
r² = √2×5618ft²
r = 106 feet
The diameter of the wheel is twice the radius
= 2 × 106 feet = 212 feet
Therefore, Eliza is 212 feet above the ground.
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find the product 5^56 × 5^22 × 5^-96
Answer:
5^-18
Step-by-step explanation:
here is the answer please mark me as the brainliest
If the loss made on selling an article is 25
of the cost price, then find the loss percentage.
The loss percentage on selling an article is, 75%.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The loss made on selling an article is 25% of the cost price.
Let the cost price = 100
Hence, Selling price is,
⇒ 25% of cost price
⇒ 25% of 100
⇒ 25
Thus, The loss is,
⇒ Loss = cost price - selling price / cost price × 100
= (100 - 25) / 100 × 100
= 75%
Thus, The loss percentage on selling an article is, 75%.
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Evaluate the expression for the given value of the variable.
41 + 5/7t =
t= -1/2
41 + 5.7t= Answer?
The value of the expression is 40.64.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
41 + (5/7)t
When t = -1/2
41 + (5/7)t
= 41 + 5/7 x (-1/2)
= 41 - 5/14
= (574 - 5) / 14
= 569/14
= 40.64
Thus,
The value is 40.64.
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the value of a car that depreciates over time can be modeled by the function J(t)=27000(0.9)^2t+2. Write an equivalent function of the form J(t)=ab^t.
The value of a car that depreciates over time can be modeled by the function [tex]J(t)=27000(0.9)^{2t+2}[/tex] has an equivalent form of [tex]J(t) = 21870(0.81)^t[/tex].
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
The value of the car is given as:
[tex]J(t)=27000(0.9)^{2t+2}[/tex]
The equation can be written as:
[tex]J(t)=27000(0.9)^{2t} (0.9)^2\\\\J(t) = 27000(0.81)^t(0.81)\\\\J(t) = 21870(0.81)^t[/tex]
Hence, the value of a car that depreciates over time can be modeled by the function [tex]J(t)=27000(0.9)^{2t+2}[/tex] has an equivalent form of [tex]J(t) = 21870(0.81)^t[/tex].
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solve these simultaneous equations
4a+3b=-9
2a+5b=-1
The two equations can be rearranged to get two equations with one variable on each side. The equations become 4a = -9 - 3b and 2a = -1 - 5b. By dividing both sides of the first equation by 4, the equation becomes a = -2.25 - 0.75b. Substituting this value of a into the second equation gives -4.5 - 3.75b = -1. Solving this equation for b gives b = 1.2.
4a + 3b = -9
2a + 5b = -1
4a = -9 - 3b
2a = -1 - 5b
a = -2.25 - 0.75b
-4.5 - 3.75b = -1
b = 1.2
a = -2.25 - 0.75(1.2)
a = -1.95
The given set of equations is a simultaneous equation. This means that both equations have the same two variables, a and b. To solve for a and b, we must rearrange the equations so that each equation has only one variable on one side. We can do this by subtracting 3b from the first equation and 5b from the second equation. This gives us the equation 4a = -9 - 3b and 2a = -1 - 5b.
Next, we divide both sides of the first equation by 4 to get a = -2.25 - 0.75b. We can then substitute this into the second equation to get -4.5 - 3.75b = -1. Solving this equation for b gives us b = 1.2. Finally, we can substitute this value of b back into the first equation to get a = -1.95. This means that the solutions for a and b are a = -1.95 and b = 1.2.
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Which function is the inverse of g(x)=^3√2x-6+4
g⁻¹(x) = ∛(x²/2 + 3) is the inverse of the function g(x)= √(2x³-6)
How to find the inverse of a function?In mathematics, the inverse function of a function g (also called the inverse of g) is a function that undoes the operation of g.
g(x)= √(2x³-6)
Let g(x) = y
So we can say y = √(2x³-6)
We will then make x the subject:
y = √(2x³-6)
y² = 2x³-6
y² + 6 = 2x³
2x³ = y² + 6
x³ = y²/2 + 6/2
x³ = y²/2 + 3
x = ∛(y²/2 + 3)
since x = g⁻¹(y) = ∛(y²/2 + 3)
Thus, g⁻¹(x) = ∛(x²/2 + 3) (Replace y with x)
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9.
Hanif makes green paint by mixing blue paint and
yellow paint in the ratio
blue: yellow = 7:3
He buys blue paint in 50 litre containers, each costing £225
He buys yellow paint in 20 litre containers, each costing £80
He wants to sell the green paint in 5 litre tins.
Make 40% profit on each tin.
How much should he sell each tin for?
Answer:
your profit is 400
Step-by-step explanation:
50×225
Line M goes through the points (-2,-8) and (1,1). Which pair of points
lies on a straight line that intersects Line M?
(-3,-2), (2,6)
(-2,-1), (3,14)
(0,2), (1,5)
(2,1), (-5,-20)
The equation of line m passing through the points (-2,-8) and (1,1) is y = 3x - 2
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept.
Line M goes through the points (-2,-8) and (1,1). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-8)=\frac{1-(-8)}{1-(-2)} (x-(-2))\\\\y=3x-2[/tex]
The equation of line m is y = 3x - 2
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On a given day, the temperature in a pool increases with both the work of a heater modeled by the function h(t) and the sun, s(t), depending on the amount of time that passes,t, in minutes.
Which graph best shows the combination of both functions, c(t)?
Option C) is the correct graph that best represents the combination of both functions.
The graph, which plots time on the x-axis and temperature on the y-axis, displays an increasing function that depicts the temperature. The graph is divided into two sections: one shows a straight line with a positive slope to reflect the heater's contribution, and the other shows a curve to show the sun's contribution.
Option A) depicts a straight line that illustrates the rise in temperature brought on by the heater, but it omits the sun's influence. The intersection of these two functions is not depicted in this graph.
Option B) displays a curve that depicts the rise in temperature brought on by the sun, but it omits the impact of the heater. The intersection of these two functions is not depicted in this graph.
The sum of the two functions h(t) and s(t), which model the rise in pool temperature, can be written as follows:
c(t) = h(t) + s (t)
The specific functions h(t) and s(t) and their values at various times t would affect the graph of c(t).
Both the function h(t) and the function s(t) model the rise in temperature brought on by the sun and the heater, respectively.
As a result, Option C) is the correct graph that accurately depicts the union of the two functions.
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Answer:
Its A.
Step-by-step explanation:
it just looks like a combination of the other 2
Given right triangle A B C ABC with altitude B D ‾ BD drawn to hypotenuse A C ‾ AC . If A D = 11 AD=11 and A C = 21 , AC=21, what is the length of A B ‾ AB in simplest radical form?
The length of AB is [tex]2\sqrt{105}[/tex].
What is an altitude?An altitude is a line which passes through the vertex of the triangle and meets the opposite side at the right angle. A triangle has three altitudes.
Consider the triangle ABC, with right angle at B,
Let AB = x, BC = y, BD = z.
By pythagoras theorem,
[tex]AC^{2} =AB^{2} +BC^{2}[/tex]⇒[tex]x^{2} +y^{2} = 21^{2}[/tex]----------(1)
From triangle ADB,
[tex]z^{2} +11^{2} =x^{2}[/tex]-------(2)
[tex]z^{2} +10^{2} =y^{2}[/tex]--------(3)
(2)-(3), we get, [tex]x^{2} -y^{2} =21[/tex]-----(4)
subtract (1) and (4) we get,
[tex]x^{2} =420[/tex]
⇒[tex]x=2\sqrt{105}[/tex]
Hence, the length of AB is [tex]2\sqrt{105}[/tex] in simplest radical forms.
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what are the relative minimum and relative maximum values over the interval [1, 5] for the function shown in the graph?
The relative minimum and the relative maximum for the attached graph over the interval [ 1, 5 ] of the function given in graph is equal to -14 and -3 respectively.
Graph is attached.
Function shown in the attached graph over the interval [ 1, 5 ] is :
Representing the parabola function.
Vertex representing lowest point of the graph in the interval [ 1, 5 ] is given by :
( 4.5 , -14 )
Vertex representing highest point of the graph in the interval [ 1, 5 ] is given by :
( 1.5 , -3)
Relative minimum and maximum is represented by the y -coordinate of the graph.
Lowest point gives relative minimum = -14
Highest point gives relative maximum = -3
Therefore, for the function in the graph the relative minimum = -14 and relative maximum= -3.
The above question is incomplete , the complete question is:
what are the relative minimum and relative maximum values over the interval [1, 5] for the function shown in the graph?
Graph is attached.
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each side of the base of a square pyramid measures 10 inches. the height of each lateral face of the pyramid is also 10 inches. what is the surface area of the pyramid?
The total surface area of the pyramid is 100 + 4 x 50 = 100 + 200 = 300 square inches.
A square pyramid's surface area is calculated by summing the areas of its four lateral sides and base.
Since each side of the base of the pyramid measures 10 inches, the base has an area of 10 x 10 = 100 square inches.
Due to the fact that each lateral face is a triangle with a base of 10 inches and a height of 10 inches each, they each have an area of (1/2) x 10 x 10 = 50 square inches.
Therefore, the total surface area of the pyramid is 100 + 4 x 50 = 100 + 200 = 300 square inches.
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