xplanation:
a b c your way out the picture
The CEO should allocate $144,000 to labor and $216,000 to capital equipment.
How should the CEO allocate the $360, 000 between labor and equipment?Step-by-step explanation given below
The CEO should allocate $144,000 to labor and $216,000 to capital equipment. This allocation maximizes the output of the factory, which can be found by taking the partial derivatives of the function Q with respect to K and L and setting them equal to 0.
Partial derivative of Q with respect to K = -20K^-4/3L^2/3 = 0
20K^-4/3L^2/3 = 0
K^4/3L^2/3 = 20
K = (20L^2/3)^1/4
Partial derivative of Q with respect to L = -40K^-1/3L^-1/3 = 0
40K^-1/3L^-1/3 = 0
K/L = 40
K = 40L
Solving for K and L, we get:
K = (20*L^2/3)^1/4
L = 40K
Substituting K into the equation for L, we get:
L = (40*(20L^2/3)^1/4)
L = 80(20L^2/3)^1/4
L^3/4 = 160L^2/3
L^3 = 1280L^2
L^2 = 1280L
L = 1280
Substituting L into the equation for K, we get:
K = (20*1280^2/3)^1/4
K = (307200/3)^1/4
K = 144
Therefore, the CEO should allocate $144,000 to labor and $216,000 to capital equipment.
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I need to make sure part b is correct
Answer:
no picture is added ill help you if you add it
Step-by-step explanation:
Answer:
Add a picture than I'll tell you if (b) is correct or not :)
Step-by-step explanation:
Find the value of x. 72 Degree x+4
Answer: x = 104
Step-by-step explanation:
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
Answer:
Step-by-step explanation:
Assuming the oatmeal raisin and sugar cookies have an equal probability, it is less likely that a chocolate chip cookie will be picked since the other two cookies have a 37.5% chance of being picked. Despite this, it is still both likely and unlikely since it is only a small difference.
To conclude, it depends on what your teacher or textbook think. If they think a 12.5% difference between the other two cookies means that chocolate chip is unlikely, then it's unlikely. In my opinion, it is not equally but near equally likely and unlikely.
need some help with this third question
Answer:
276.46 in^3
Step-by-step explanation:
See the attached worksheet. The pencil balloon if formed by a cylinder and cone. Use the volume formulas for each of these shapes to calculate that shape's contribution to the total volume, and then add them.
The volume of the cylinder portion is 263.9 in^3.
The volume of the cone portion is 12.56 in^3
The sum is 276.46 in^3, which matches the first answer option.
Answer:
276.46 cubic inches
Step-by-step explanation:
Volume of the cylindrical part = πr²h, r= radius, h = height
Volume of a cone (1/3) πr²h, r= radius, h = height
For given dimensions
cylinder h = 21, cylinder r = 2
Volume of cylindrical part of balloon = π · 2² · 21 = 4 · 21 · π = 84π cubic inches
Volume of conical part of balloon = (1/3) π · 2² · 3 = 4π
Total volume = 84π + 4π = 88π = 276.46 cubic inches
What Is The Answer To This Problem??
calculate the double integral. (y xy^-2) da r = (x y) 0 ≤ x ≤ 2 0 ≤ y ≤ 2 r
The double integral of (xy y^(-2)) over the region R is equal to 0.
What is double integral ?
The term integral in math is defined as a method of adding or summing up the parts to find the whole and it is basically used to find the volume, area and the central values of many things. Double integrals are a two-dimensional integration method.
The given expression is the integrand of a double integral over the region R defined by the constraints 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2. To calculate this double integral, we would evaluate the following expression:
∬(xy y^(-2)) dA = ∬(xy y^(-2)) dx dy over the region R
We can evaluate this double integral using a change of variables, such as polar coordinates, or using rectangular coordinates.
In rectangular coordinates, we can evaluate the double integral using the following steps:
Evaluate the bounds of integration:
x: 0 to 2
y: 0 to 2
Evaluate the integral with respect to y first, keeping x fixed:
∬(xy y^(-2)) dx dy = ∫(x ∫(y y^(-2)) dy) dx, from 0 to 2
Evaluate the inner integral with respect to y:
∫(y y^(-2)) dy = -y^(-1) = -ln(y) + C, where C is an arbitrary constant
Substitute the solution for the inner integral back into the outer integral:
∫(x (-ln(y) + C)) dx = x(-ln(y)) - xC + D, where D is another arbitrary constant
Evaluate the outer integral with respect to x:
∫(x(-ln(y)) - xC + D) dx = (-x^2/2)ln(y) - (x^2/2)C + xD + E, where E is yet another arbitrary constant
Evaluate the constants of integration C, D, and E using the boundaries of integration for x and y:
-ln(2) - 0C + 0D + E = 0
-2ln(2) - 2^2/2 C + 2D + E = 0
Solving the system of equations, we find C = 2ln(2), D = 0, and E = 0
Substitute the values of C, D, and E back into the solution:
(-x^2/2)ln(y) - (x^2/2)C + xD + E = (-x^2/2)ln(y) - x^2ln(2)
Finally, evaluate the integral over the region R by substituting the bounds of integration for x and y:
(-2^2/2)ln(2) - 2^2ln(2) = -4ln(2) + 4ln(2) = 0
So, The double integral of (xy y^(-2)) over the region R is equal to 0.
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What is the solution to the system of equations?
{y=7x+11
y=−3x+1
Enter your answer as an ordered pair, like this: (42, 53)
The solution to the system of equations ordered pair is (-1, 4).
What exactly is an equation system?A simultaneous equation is any one or more equations that can have the same number of unknowns and be solved concurrently. The system of equations is a simultaneous equation.the solution to the system of equations {y=7x+1 , y=−3x+1
Given:
a collection of equations
Equation 1 is y = 7x + 11.
Equation 2: y = 3x + 1.
Equation 1's y value is changed to equation 2's value.
7x + 11 = -3x + 1
10x = -10
x = -1
And y = 4
Consequently, the answer is (-1, 4).
The solution to the system of equations ordered pair is (-1, 4).
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Which one of the following is a statistically valid reason for sampling randomly when choosing subjects for a study?Correct Response- Sampling randomly tends to reduce sampling bias or risk- Sampling randomly (with a large sample) gives a perfect reflection of the population- Sampling randomly is easier than sampling nonrandomly- Actually, there is no statistically valid reason for sampling randomly
Sampling randomly is considered a statistically valid reason for choosing subjects for a study as it reduces the risk of sampling bias. The correct option is a.
Sampling bias refers to a systematic error that occurs in the process of selecting subjects for a study, leading to a sample that is not representative of the population.
By selecting subjects randomly, researchers aim to eliminate any preconceived biases or preferences that may influence the selection process. This leads to a sample that is more representative of the population, providing a more accurate representation of the population's characteristics.
Furthermore, random sampling (with a large sample) has the potential to give a perfect reflection of the population, assuming that the sample size is large enough. This is because, as the sample size increases, the sample becomes more representative of the population and tends to exhibit the same characteristics and distributions as the population.
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A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number less than 5.
8 over 60
10 over 60
27 over 60
42 over 60
The probability of rolling a number less than 5 is 42/60
How to find the experimental probability?It is given by the quotient between the number of times that we got a given outcome and the total times that the experiment was performed.
Here we want to find the experimental probability of landing on a number less than 5 (these are 1, 2, 3, 4)
Outcome Frequency
1 12
2 13
3 11
4 6
These are the tables, adding these we get:
12 + 13 + 11 + 6 = 42
So in 42 out of 60 tosses we got a number less than 5, then the experimental probability is:
42/60
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2x＝ 3 -5√x usind log form find x
2x＝ 3 -5√x using log form, x = log(2x + 5√x) = log(3)
How did we get the value?To convert the equation 2x = 3 - 5√x into logarithmic form, we need to isolate the radical expression on one side of the equation. We can do this by adding 5√x to both sides:
2x + 5√x = 3
Next, we'll take the square root of both sides to eliminate the radical:
√(2x + 5√x)^2 = √(3^2)
Expanding the left side and simplifying:
2x + 5√x = 3
Finally, we'll take the logarithm of both sides to get x in logarithmic form:
log(2x + 5√x) = log(3)
To solve for x, we'll need to use logarithmic properties and/or exponential functions to isolate x on one side of the equation. log(2x + 5√x) = log(3)
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In math, what does ab, a(b+c), and (a+b) (c+d) mean?
Answer:
ab means a multiplied by b, a(b+c) means add b and c together, then multiply by a, and (a+b)(c+d) means first add a and b
Step-by-step explanation:
ab means product, a(b+c) means product of a and sum of b & c and (a+b)(c+d) product of sum of a & b and c & d.
The result of multiplying two or more numbers together is the sum. The product of two or more numbers is what results from multiplication.
In mathematics, "ab" typically represents the product of two numbers, a and b.
"a(b+c)" represents the product of a and the sum of b and c, where a, b, and c are numbers.
"(a+b) (c+d)" represents the product of the sums of a and b and the sums of c and d.
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The position of a particle in the xy-plane at time t is r(t) = (t + 4) i + (t2 + 5) j. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t = 4. The equation for the path of the particle is y = . The velocity vector at t = 4 is v = ( ) i + ( ) j.
The equation in x and y whose graph is the path of the particle is y = (x - 4)2 + 5. The velocity vector at t= 4 is v(4) = i + 8j.
What is vector?A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.
In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.
Given r(t) as r(t) = x(t)i + y(t)j
Thus, this means that:
x = t+ 4 y = t2 + 5
We see that we can solve t as:
t = x - 4, thus:
y = (x - 4)2 + 5
v(t) is given by r'(t).
r'(t) = v(t) = i + 2tj
at t = 4:
v(4) = i + 8j
The acceleration is given by: r"(t).
a(t) = r"(t) = 0i + 2j
The acceleration at t = 4 is:
a(4) = 0i + 2j
Hence, the equation in x and y whose graph is the path of the particle is y = (x - 4)2 + 5. The velocity vector at t= 4 is v(4) = i + 8j.
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What is the Consecutive Interior Angles Theorem?
According to the consecutive interior angles theorem, when two lines are parallel, the consecutive interior angles are supplementary to each other.
How to prove consecutive interior angles theorem?According to the consecutive interior angles theorem, if a transversal passes through two parallel lines, it creates two pairs of supplementary consecutive interior angles. In other words, the sum of the consecutive interior angles formed by two parallel lines intersected by a transversal equals 180°.When a transversal cuts two lines, the pair of angles on one side of the transversal and inside the two lines is known as the consecutive interior angles. Angles 3 and 5 in the diagram are consecutive interior angles. Angles 4 and 6 are also consecutive interior angles.The two lines are parallel if the alternate interior angles produced by the transversal line on two coplanars are congruent. As a result, for example we can write ∠ 2 = ∠ 5, which are corresponding angles. As a result, an is parallel to b.To learn more about Consecutive Interior Angles Theorem refer to :
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the _____ of a square are both congruent and perpendicular.
The diagonals of a square are both congruent and perpendicular.
Because a square is a regular quadrilateral with four equal sides and four equal angles, it is a quadrilateral. A rectangle with two adjacent sides of equal length can also be used to describe it. A chess board, dice, tiles, napkins, etc. are a few examples.
The perpendicular bisectors of a square's diagonals are one another. Each diagonal is divided into two congruent parts as a result, and their intersection creates four right angles. As a result, if a diagonal is given, its length, one segment's length is equal to half of the diagonal's overall length. They are also divided at a 90-degree angle, making them perpendicular, and they are similar in length.
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The quadratic function h(t)=-16. 1t2+150 models a balls height in feet over time in seconds after it is dropped from a 15 story building
f(x) = ax2 + bx + c, where a, b, and c are real values and a = 0, is a quadratic function. A quadratic function's domain is (,). The graph of the simplest quadratic function, f(x) = x2, is shown below. Its shape, a parabola, should be recognizable from Intermediate Algebra.
To find the time at which the ball hits the ground, we need to find the value of t when h(t) = 0.
Solving -16.1t^2 + 150 = 0 gives us:
-16.1t^2 = -150
t^2 = 9.37
t = 3.05 (rounded to the nearest hundredth)
So the ball hits the ground after 3.05 seconds.
The complete question is:-
The quadratic function h(t)=-16.1t^2 + 150 models a balls height, in feet, over time, in seconds, after it is dropped from a 15 story building.
- From what height, in feet, was the ball dropped?
-After how many seconds, rounded to the nearest hundredth, did the ball hit the ground?
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what angle is 6y+2=8y-14
Answer:
y = 8
Step-by-step explanation:
6y+2 = 8y-14
2 = 2y - 14
16 = 2y
y = 8
At the beginning of the party, there were 1 pizzas. By the end of
the party, there were 4/5 pizzas left. How many pizzas were
consumed during the party?
Show your work here
0.2 pizzas were consumed during the party.
What are the arithmatic calculations?
Arithmetic is the branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division, and their properties and applications. Arithmetic calculations are mathematical operations that involve one or more numbers and result in a numerical answer.
To find the number of pizzas consumed during the party, we need to subtract the number of pizzas left at the end of the party from the number of pizzas at the beginning of the party.
At the beginning of the party, there was 1 pizza.
At the end of the party, there were 4/5 pizzas left.
So, the number of pizzas consumed during the party can be calculated as:
1 - 4/5 = 1 - 0.8 = 0.2
Therefore, 0.2 pizzas were consumed during the party.
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i can do this one i am just too lazy
Answer: 7/2
Step-by-step explanation: An easy way to calculate slope with two given points is to count the rise (y) between the points (7). Then count the run (x) between the points (2). Then put the rise over the run. 7/2
68x157 to the nearest 100
Answer:
Below
Step-by-step explanation:
68 x 157 = 10 676 to the nearest 100 would be 10700 ....the '7' next to the 6 in the 100s place dictates that you round the 6 UP to 7
Draw an x-y graph that show the vertical profiles of pressure, density, and temperature in the troposphere. This means the vertical y-axis, which will be height or altitude, going from 0 to 10 km. You can draw three separate graphs, or combine them into one (the axes do not need to be precisely calibrated; you are showing the general trends of each parameter, so the shapes of the plots are important).
The vertical profiles for pressure, density, as well as temperature with in troposphere are displayed in an x-y graph.
Explain the relation of pressure, density, and temperature in the troposphere.Pressure altitude is temperature-adjusted density altitude.
In simple terms, it has a direct impact on an aircraft's performance parameters and is essentially the height at which the aircraft "thinks" it is performing. The performance of an airplane decreases with increasing density altitude and vice versa.Pressure and temperature have a direct and indirect relationship with density.
Density rises as pressure rises and temperature remains constant. Conversely, density falls as temperature rises while maintaining the same pressure. For every 10 hPa decrease in pressure or 3 °C rise in temperature, the air density will drop by around 1%.Thus, the vertical profiles for pressure, density, as well as temperature with in troposphere are displayed in an x-y graph.
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Find the length of each line segment using Pythagorean theorem verify using distance formula. Round the answer to the nearest tenth.
5.385 is the length of each line segment according to the Pythagoras theorem and distance formula.
what is Pythagoras theorem ?The basic Geometric mathematical relationship between one right triangle's three sides is termed as the Pythagorean Theorem, or simply the Pythagorean Theorem. This rule states that the areas with squares with the two parts added together equal the area of the square well with hypotenuse side. The Pythagorean Theorem says that the square that crosses the tangent of a right angled triangle opposite the right angle equals the total of the squares that span the sides of something like a right triangle. It is sometimes written as the generic geometric notation a2 + b2 = c2.
given
A2 + B2 = C2 is a Pythagorean theorem.
Let C be the point (-2,1)
A two-unit line segment AC would be required.
The length of line segment BC would be 5 units.
Incorporate the line segment length into the Pythagorean theorem by adding
2^2 + 562
= 4 + 25
= 29
≅5.385.
5.385 is the length of each line segment according to the Pythagoras theorem and distance formula.
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the numbers, if any, at which f has a relative maximum. what are these relative maxima?
Using the graph of the function f, the relative maxima of function is at x = 3 and is equal to 6.
The graph of the function f is given below:
A relative maximum occurs at an x-coordinated position when the function value is higher than it is compared to nearby places. At that time, the function value is at its relative maximum (y coordinate).
A relative minimum occurs at an x-coordinated location where the function value is the lowest in relation to its neighbors.
The Relative maximum is determined by y's maximum value.
In the graph we can see that;
The greatest value of the y value for x = 3 is 6.
As a result, the function's relative maximum is at x = 3 and is equal to 6.
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The complete question is:
The graph of a function f is given. Use the graph to find each of the following.
The numbers, if any, at which f has a relative maximum. What are these relative maxima?
Just to make sure, what is 0.4x2.5 equal?
Answer:
1
Step-by-step explanation:
You can think of this problem this way:
[tex]0.4*2.5=\frac{2}{5}*\frac{5}{2}=\frac{10}{10}=1[/tex]
Answer: 1
Step-by-step explanation:
there are two decimal places in total, keep that in mind
multiply everything by 10 to make whole numbers and multiply
4x25=100 because 4x5=20 and 4x20=4x10x2=80 and 20+80=100
remember those two decimals we counted, take that number, and move the decimal place over that many in your answer. 100 becomes 1
why not just use a calculator lol, you have internet access
i need help please thanks
The inequality equation is y ≤ -2x + 1 and the graph is plotted
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y ≤ -2x + 1 be equation (1)
when the inequality is solved ,
y = -2x + 1 , where the slope of the line is m = -2
Therefore , the value of A is -2x + 1 and the graph is plotted
Hence , the inequality equation is y ≤ -2x + 1
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1. Here are a few pairs of positive numbers whose sum is 50.
first number
second number
product
1
49
2
48
10
40
a Find the product of each pair of numbers.
b. Find a pair of numbers that have a sum of 50 and
will produce the largest possible product.
c. Explain how you determined which pair of
numbers have the largest product.
Activate Wir
Go to Settings to
The pair of numbers that have a sum of 50 and will produce the largest possible product is 10 and 40, with a product of 400. This was determined by comparing the products of each pair and determining which is the largest.
a. The product of the first pair of numbers is 1 x 49 = 49, the product of the second pair of numbers is 2 x 48 = 96, and the product of the third pair of numbers is 10 x 40 = 400.
b. The pair of numbers that have a sum of 50 and will produce the largest possible product is 10 and 40.
c. To determine which pair of numbers have the largest product, we need to compare the products of each pair and determine which is the largest. In this case, the pair of 10 and 40 have the largest product of 400.The pair of numbers that have a sum of 50 and will produce the largest possible product is 10 and 40, with a product of 400. This was determined by comparing the products of each pair and determining which is the largest.
The complete question is :
What are a few pairs of positive numbers whose sum is 50 and which have the largest possible product?
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3 cylinders have a height of 8 cm cylinder one has a radius of 1 cm cylinder 2 has the radius of 2 cm cylinder 3 has a radius of 3 cm find the volume of each cylinder
The volume of the cylinder 1 = 25.12 cubic centimeters.
The volume of the cylinder 2 = 100.48 cubic centimeters.
The volume of the cylinder 3 = 226.08 cubic centimeters.
What is a cylinder?A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.
Given:
3 cylinders have a height of 8 cm cylinder one has a radius of 1 cm cylinder 2 has the radius of 2 cm cylinder 3 has a radius of 3 cm.
The volume of the cylinder 1,
= πr²h
= (3.14)(1)(8)
= 25.12 cubic centimeters.
The volume of the cylinder 2,
= πr²h
= (3.14)(4)(8)
= 100.48 cubic centimeters.
The volume of the cylinder 3,
= πr²h
= (3.14)(9)(8)
= 226.08 cubic centimeters.
Therefore, the volume of each cylinder is given above.
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pls answer will mark brainliest
what are the domain and range of the function f(x) = √ x-7+9?
Domain : { x ∈ R : x ≥ 7 }
Range: { f ∈ R : f ≥ 9 }
Given function is:
f(x) =
Firstly find the domain of the given function.
Domain is set of all real x's values where given function is defined.
In other words, we exclude all the x's values from all real values where function is undefined.
In case of square root function, inside the square root given expression must be greater or equal to zero.
So,
x - 7 ≥ 0
Solve for x
x ≥ 7
So, domain is all real x when x ≥ 7.
Now find the Range of this function.
Range is set of all output values.
So, lowest value of out put is 9 when x is 7
and maximum value of the function is infinite.
So, Range is all real f's values when f ≥ 9.
Pls help
Beatriz is in charge of setting up a banquet hall. She has five tables that
will seat six people each. If no more than 62 people will attend, how
many tables seating four people each will she need?
The number of tables with a seating of 4 people is 13.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Beatriz is in charge of setting up a banquet hall. She has five tables that will seat six people each. If no more than 62 people.
The number of the tables will be calculated as:-
Number = 62 / 4
Number = 13
Hence, the number of tables with a seating of 4 people is 13.
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What's the answer and how do you solve for the answer?
The solution to the exponential inequality in this problem is given as follows:
x < 1.72.
How to solve the exponential inequality?The exponential inequality for this problem is defined as follows:
3^(4x - 5) < 8.
The number 8 is not a base of 3, hence the way to isolate the variable x is applying the log of base 3 to both sides, as follows:
log3(3^(4x - 5)) = log3(8)
4x - 5 = log3(8)
The logarithm of base 3 of 8 can be obtained applying the change of base property, as follows:
log3(8) = log(8)/log(3)
log3(8) = 1.893.
Hence the inequality is solved as follows:
4x - 5 < 1.895
4x < 6.896
x < 6.896/4
x < 1.72.
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Find The Sample Standard Deviation. Round To One Decimal Place. 1,5, 12, 16, 15, 12, 19, 5, 10 O A. 5.9 OB. 34.8 OC. 5.6 OD. 30.9
The sample standard deviation is A. 5.9
What is Standard Deviation ?
It is a measure of how evenly distributed numbers are. It is the square root of the Variance, which is the average of the squared deviations from the Mean.
To find the sample standard deviation, first, we have to find the mean of the data, then subtract each data point from the mean, square each deviation, sum them, divide by the sample size minus 1, and then take the square root of the result.
Here's the calculation:
Mean = (1 + 5 + 12 + 16 + 15 + 12 + 19 + 5 + 10) / 9 = 11
Deviations = [-10, -6, 1, 5, 4, 1, 8, -6, -1]
Squared deviations = [100, 36, 1, 25, 16, 1, 64, 36, 1]
Sum of Squared deviations = 239
Sample Variance = Sum of Squared deviations / (Sample size - 1) = 239 / (9 - 1) = 239 / 8 = 29.875
[tex]Sample \ Standard\ Deviation=\sqrt{(Sample Variance)} \\\\Sample \ Standard\ Deviation=\sqrt{29.875}\\\\ Sample \ Standard\ Deviation= 5.9[/tex]
So, The sample standard deviation is 5.9 (rounded to one decimal place).
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