The solution to the given statement "75 less than a number x is greater than or equal to 420" is written as 75 - x ≥ 420 where x ≤ -345
How to write inequality?75 less than a number x is greater than or equal to 420
75 - x ≥ 420
Subtract 75 from both sides
- x ≥ 420 - 75
- x ≥ 345
divide both sides by -1
x ≤ 345/-1
x ≤ -345
Therefore, the expression is given by 75 - x ≥ 420 where, x ≤ -345
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Problem 1 What is meant by the term 'Decision Analysis'? - Decision Analysis: The term decision analysis originated in 1964 by ROnald A. Howard, professor of Management Science and Engineering at Stanford University. - The objective of a decision analysis is to choose the most advantageous alternative from various alternative solutions of decision problems. - Decision analysis is systematic, quantitative and visual approach to addressing and evaluating important choices confronted by businesses. - Systematic approach means creating a constructive environment, investigating the situation, generating good solutions or alternatives, choosing the best solution and taking action. - Quantitative approach means to convert the problem into a mathematical model or formula to find the best solution. By using common quantitative tools. Decision tree, payback analysis and simulation. - Visual approach means to convert the problem into graphical charts to find the best solution.
Decision Analysis is a mathematical method for making decisions in uncertain environment.
What is environment ?
Environment refers to the surrounding conditions, resources and factors that can have an impact on an organism, community, or system. This can include physical factors such as weather, terrain, and pollution, as well as biological factors such as other living organisms, and social or economic factors such as culture, laws and economic conditions.
The process of Decision Analysis can be broken down into several steps:
1) Define the decision problem: Clearly state the problem and the decision maker's objectives.
2) Identify the decision alternatives: List all the feasible options available to the decision maker.
3) Specify the probability distribution of the uncertain parameters: Assign probabilities to the possible outcomes of the uncertain parameters.
4) Evaluate the expected value or expected loss for each alternative: Compute the expected value or expected loss for each alternative, using the probability distribution of the uncertain parameters.
5) Choose the alternative with the highest expected value or the lowest expected loss: Select the alternative that maximizes the expected value or minimizes the expected loss.
6) Sensitivity analysis: Check the robustness of the decision by studying the effect of small changes in the model's assumptions.
Decision Analysis is a mathematical method for making decisions in uncertain environment.
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Volume of a cone and cylinder
the volume of a cone will be 201.06 in³.
What is volume of cone?
The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.
So the
V = (1/3)πr²h.
Given, data r = 5yards
h = 8 yards
Volume = 1/3 * π * r ²* h
V = 1/3 * π * 4 ²* 12 =201.06 in³.
Hence, the volume of a cone will be 201.06 in³.
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Which line segment is a radius of Circle S?
Answer:
SQ
Step-by-step explanation:
radius is half the circumference, which is a line from one side to the other. Half of that is a line to the middle.
Identify the triangle as scalene isosceles or equilateral A(0,-4) B(0,-9) C(-2,-5)
Answer:
Step-by-step explanation:
it c
What is the HCF of 12 and 18 and 48?
The Highest Common Factor (HCF) of 12, 18, and 48 is 6. This means that 6 is the greatest number that can be evenly divided into all three numbers without leaving a remainder.
1. List out the factors of each number:
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
2. Find the common factors of all three numbers:
1, 2, 3, 6
3. The greatest number of these common factors is 6, so 6 is the HCF of 12, 18, and 48.
The Highest Common Factor (HCF) is the greatest number that can be evenly divided into all the numbers in a set. To find the HCF of a set of numbers, we must first list out the factors for each number. The factors are the numbers that can be evenly divided into the original number. For instance, 1, 2, 3, 4, 6, and 12 are the factors of 12. We then compare the lists of factors of all the numbers and find the common factors. The greatest number of these common factors is the HCF. For example, the HCF of 12, 18, and 48 is 6, because 6 is the greatest number that can be evenly divided into all three numbers without leaving a remainder
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*image is attached*
Please help on this!!!!!
I’ll give Brainly
And points
(x,y) = (2,0) trust me substitution is easy
Is 3 a an algebraic expression?
No, 3 is not an algebraic expression.
In mathematics, an algebraic expression is a combination of numbers, variables and arithmetic operations (such as addition, subtraction, multiplication and division) that can be evaluated to a specific value when the variables are assigned specific numerical values.
For example, 3x + 2 is an algebraic expression. Here, x is the variable and 3, 2 are constants. We can substitute any numerical value for x and evaluate the expression for that specific value.
On the other hand, 3 is a numerical value, not an expression. It doesn't contain any variables or operators that can be evaluated for different values. It is a constant value, it doesn't change with the change of x or any other variable.
In summary, an algebraic expression is a combination of numbers, variables and arithmetic operations, whereas 3 is just a numerical value, not an algebraic expression.
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Please write word answer that I can use
The type of triangle that Kevin drew based on the information is a scalene triangle.
What is a scalene triangle?A scalene triangle is a triangle with different lengths for each of its three sides and different measures for each of its three angles. A scalene triangle's angles adhere to the angle sum property and always add up to 180 degrees.
A scalene triangle has three sides, each of which is measured differently. Each of a triangle's three interior angles has a different measurement. Scalene triangles don't have a symmetry line.
In this case, the sides are all different as illustrated in Kevin's case.
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what is 52.085 rounded to the nearest tenth
Answer:
52.1
Step-by-step explanation:
have great day!!!
Answer:
OK so
The 10th is the one right after the decimal. We are basically rounding that 0.
5 and above rounds up
below 5 rounds down
the next number is an 8,
so we would round it as
52.1
Step-by-step explanation:
What is the answer for 7 to the power of zero?
No matter what the number is, the answer when raised to the power of zero is always 1.
No matter what the number is, the answer when raised to the power of zero is always 1
7 to the power of zero is written as 7^0.
The answer is 1, since any number raised to the power of zero is equal to 1.
Any number raised to the power of zero is equal to 1. This is true regardless of the number. For example, 7 to the power of 0 is written as 7^0. The answer is 1. This can be seen from the equation 7^0 = 7 x 1 = 1. Similarly, 8^0 = 8 x 1 = 1, and 9^0 = 9 x 1 = 1. This concept can be applied to any number, positive, negative, whole, fractional, or decimal. No matter what the number is, the answer when raised to the power of zero is always 1.
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please answer this its a maths question attached below this task
My answer's in screenshot format since Brainly bot is suspicious of long answers:
If you run at an average speed of 10 mi/h, how long will it take you to run 2.5 miles? (Write the answer with minutes at the end. e.g. 10 minutes)
It will take 15 minutes to run 2.5 miles at an average speed of 10 miles per hour.
What is Speed?speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.
Given, you run at an average speed of 10 mi/h.
Since,
Average speed = 10 mi/h
or in minutes
Average speed = 10/60 = 1/6 miles per minutes
Thus,
to run 2.5 miles it will take:
time = distance/ speed
time taken to run 2.5 miles = 2.5 * 6 =15 minutes
therefore, to run 2.5 miles at the average speed of 10mi/h it will take 15 minutes.
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Liczba o 8 mniejsza od iloczynu liczb w i 3
Answer: 3w-8
Step-by-step explanation: I don't quite understand you because I speak English but it's 3w-8
An angle measures 28° more than the measure of its supplementary angle. What is the measure of each angle?
The measure of each angle is 104° and 76°.
What are Supplementary Angles?Supplementary refers to angles that come together to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles. If two angles Supplementary one another if,
It has an acute angle on one side and an obtuse angle on the other.
The angles are both right angles.
Given An angle that measures 28° more than the measure of its supplementary angle,
let the angle be x
and supplementary angle of x = 180 - x
according to condition
x = 28 + 180 - x
2x = 208
x = 208/2
x = 104°
and supplementary angle of x = 180 - x
supplementary angle of x = 180 - 104
supplementary angle of x = 76°
Hence the angles are 104° and 76°.
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prove that any nonzero rational number may be written as the product of two irrational numbers.
If r is a nonzero rational number, then r is a product of two irrational numbers.
If q≠0 is rational and y is irrational, then qy is irrational.
: You know that if G
is a group and H≠G
is one of its subgroups then h∈H
and y∈G∖H
implies that hy∈G∖H
Proof: suppose hy∈H
You know that h−1∈H, and therefore y=h−1(hy)∈H
Contradiction
In our case, we have the group (R∗,⋅) and its proper subgroup (Q∗,⋅). By the arguments above q∈Q∗ and y∈R∖Q implies qy∈R∖Q
.
Simply multiply it by the square root of two to obtain an irrational number. A product of two irrational numbers, your original number is obtained by multiplying this irrational number by the square root of two, which is itself irrational.
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I got stuck, does anyone know how to do this?
Nothing can be done to this it is in its simplest form.
For what value of k has real and equal roots?
For [tex]$\mathrm{k}=2$[/tex] and[tex]$\mathrm{k}=-\frac{10}{9}$[/tex]given equation will have real and equal roots.
What are real and equal roots?If D=0, a quadratic equation has two roots that are equal. D (discriminant) = 0 b24ac=0 is required for a quadratic equation to have equal roots.If the discriminant of a quadratic equation is 0, then its roots are equal. A quadratic equation has equal roots if both of these roots are equal to the derivative's root. A quadratic function has no real roots and does not intersect the x-axis if the discriminant of the function is less than zeroOn comparing given equation with [tex]$\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0$[/tex]we get,[tex]$a=1, b=-2(1+3 \mathrm{k})$[/tex] and [tex]$c=7(3+2 \mathrm{k})$[/tex]
For the roots to be real and equation D must be equal to zero,
[tex]\mathrm{D} & =\mathrm{b}^2-4 \mathrm{ac} \\[/tex]
[tex]0 & =4(1+3 \mathrm{k})^2-4 \times[7(3+2 \mathrm{k})] \\[/tex]
[tex]& =9 \mathrm{k}^2+6 \mathrm{k}+1-21-14 \mathrm{k} \\[/tex]
[tex]9 \mathrm{k}^2-8 \mathrm{k}-20 & =0[/tex]
The given equation will have equal roots, if
[tex]9 k^2-8 k-20 & =0 \\[/tex]
[tex](k-2)(9 k+10) & =0 \\[/tex]
[tex]k-2=0 \text[/tex] and [tex]9 k+10 & =0 \\[/tex]
[tex]k=2 \text[/tex] and [tex]k & =-\frac{10}{9}[/tex]
Hence, for [tex]$\mathrm{k}=2$[/tex] and[tex]$\mathrm{k}=-\frac{10}{9}$[/tex]given equation will have real and equal roots.
The complete question is,
Find the values of [tex]$\mathrm{k}$[/tex] for which the given equation has real and equal roots
[tex]$$\mathrm{x}^2-2 \mathrm{x}(1+3 \mathrm{k})+7(3+2 \mathrm{k})=0$$[/tex]
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Point
(-3,5),
Line
x+6=0
Equation of line passing through the point and having slope m=1
y=mx+C
In this question, m=tan45°=1
So the equation becomes y=x+C
New line passes through (3,5)
Putting the values in the equation,5=3+c
C=2
New equation of line becomes y=x+2
Another line x+y−6=0
These two lines intersect at Q
y=x+2
y=−x+6
2y=8
y=4
Put the value of y=4 in line equation,
y=x+2
x=2
Q(2,4)
P(3,5)
O(0,0)
Distance between two points
=9×PQ² +14×O ² +10×OQ²
=9×2+14×34+10×20
=18+476+200
=694
What is slope?The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.
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Question 4 of 9
Triangle EFG has vertices E(-4, 1), F(-3,-2), and G(2, 1). Find the coordinates of the image of points E
F, and G'after a translation 2 units down.
The coordinates of the image of point E after a translation 2 units down are (-4, -1).
The coordinates of the image of point F after a translation 2 units down are (-3, -4).
The coordinates of the image of point G after a translation 2 units down are (2, -1).
How to translate coordinates?To translate coordinates in a two-dimensional plane, you need to know the translation vector. A translation vector is a pair of numbers (a, b) that indicates the amount of movement in the x-direction and y-direction.
To translate a point (x, y) by the translation vector (a, b), you can use the following formulas:
x' = x + a
y' = y + b
Where x' and y' are the new coordinates of the point after the translation.
A translation is a transformation that moves a figure a certain distance in a certain direction without rotating or reflecting it. In this case, we are asked to translate the triangle EFG 2 units down. This means that we need to move the triangle down 2 units on the y-axis.
To translate a point (x, y) down 2 units, we can add -2 to the y-coordinate. The new coordinates of the point will be (x, y - 2).
The coordinates of E are (-4, 1), so the coordinates of E' after the translation are (-4, 1-2) = (-4,-1)
The coordinates of F are (-3,-2), so the coordinates of F' after the translation are (-3,-2-2) = (-3,-4)
The coordinates of G are (2, 1), so the coordinates of G' after the translation are (2,1-2) = (2,-1)
So the new coordinates for the triangle EFG' after the translation are:
E'(-4,-1)
F'(-3,-4)
G'(2,-1)
It's important to notice that the x-coordinates didn't change because we are only translating the triangle down, on the y-axis.
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I need the work and the answer
Answer: 70
Step-by-step explanation: 14 + 6 = 20, 20 time 5 is 100, so 14 times 5 is the answer
I need help with this please
a = 15, b = -14, c = -5, d = 25
What is identities values? How to solve it?Identity values are equations that are true no matter what value is assigned to the variable. In mathematics, identity values (sometimes referred to as identity equations) are equations that are true regardless of the value of the variables. For example, the identity value for addition is a + 0 = a. This is true for any value of a.To solve an identity value, first identify the equation. Then, substitute a value for the variable. If the equation is still true, then it is an identity value. For example, if a = 4 and we plug that into the equation a + 0 = a, we get 4 + 0 = 4. This is still true, so it is an identity value.In summary, identity values are equations that are true regardless of the value of the variable. To solve an identity value, first identify the equation and then substitute a value for the variable. If the equation is still true, then it is an identity value.
Solution:
The equation 8(x+5)+8(x-9) = ax + b can be rewritten as 8x + 40 + 8x - 72 = ax + b, which simplifies to 16x - 32 = ax + b. Since 16x - 32 = ax + b, we can solve for a and b to get a = 15 and b = -14. The equation 7(x + c) + 3(x+d) = 10x + 28 can be rewritten as 7x + 7c + 3x + 3d = 10x + 28, which simplifies to 10x + 7c + 3d = 10x + 28. Since 10x + 7c + 3d = 10x + 28, we can solve for c and d to get c = -5 and d = 25.To learn more about identity values refer to:
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A chef preheats an oven. It starts at room temperature, 68°F, and heats up 23°F per minute. How long does it take for the oven temperature to reach 275°F?
Please help me.
====================================================
Explanation:
x = number of minutes
y = temperature
The equation is
y = 23x+68
The slope 23 tells us how fast the oven is heating up. The 68 is the y intercept, and it's the starting temperature (when x = 0).
We want to find the value of x when y = 275
y = 23x+68
275 = 23x+68
275-68 = 23x
207 = 23x
23x = 207
x = 207/23
x = 9
It takes 9 minutes for the oven to reach a temperature of 275°F
--------
Check:
y = 23x+68
y = 23*9+68
y = 207+68
y = 275
The answer is confirmed.
What is the nearest 100 to 350?
The nearest multiple of 100 to 350 is 400.
We must determine the smallest value of x that comes the closest to the specified number n given two values, n and x. We must identify a k such that x*k is most similar to n. If we use k = n/x, we may not get the maximum value of k. By comparing the values of floor(n/x)*x and ceil(n/x)*x, we may get the nearest.
Rounding off numbers are discussed here, where we need to round a number. Rounding can be done for every place value of a number.
We round off a number to the closest multiple of hundreds when we want to represent it in hundreds. For instance: 300 is farther from 200 than 225. Thus, 225 is reduced to 200.
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This table shows Carter's October budget. How much money does Carter need to earn at the
bike shop to keep his budget balanced? Complete the table.
Carter's October budget
Income
Dog walking: $20
Working at the bike shop: $
Gift from uncle: $50
Pet sitting: $35
Total: $
Save answer
Expenses
Costume: $40
Fixing bike: $25
Corn maze: $15
Saving for college: $170
Total: $
$145 money does Carter need to earn at the bike shop to keep his budget balanced
What is budget?The projection of future income and spending is done using a budget. Simply expressed, a budget accounts for both anticipated income and costs as well as future saving and spending. A budgeting method enables you to prepare for your income and spending over a specific time period. For instance, planning a monthly budget involves considering how much money you'll have coming in and going out each month. Surplus, Balanced, and Deficit Budgets are the three types of yearly government finances based on projections.
Dog walking: $20 Costume: $40
Working at the bike shop: $145 Fixing bike: $25
Gift from uncle: $50 Corn maze: $15
Pet sitting: $35 Saving for college: $170
Total: $250 Total: $250
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f(1)= 10 and f(21)= 2 ; find f(14)
the function value f(14) = 4.8.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function if one were mapped to a single value instead. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
f(1)= 10
f(21)= 2
Let the function f(x) = ax+b
f(1)= 10 = a+b
f(21)= 2 = 21a +b
20a = -8
a=-8/20
b = 208/20
f(14) = 14*(-8/20)+208/20 = 4.8
Hence the function value f(14) = 4.8.
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d dianna are going to drive together to a nearby theme park. the car they are using has seats: driver seat, front passenger seat, and back passenger seat. bonnie and carlo are the only ones who know how to drive the car. how many possible seating arrangements are there?
There are 12 possible seating arrangement that Ali, Bonnie, Carlo, and Dianna can seat in a 4 seated car while visiting to a nearby theme park.
There are in total 4 people so the the possible seating arrangement should be 4! = 4*3*2 = 24.
But only 2 people know how to drive a car that is Bonnie and Carlo,
So the remaining seat can be occupied by any three that are remaining beside the driver.
So 3 remaining people can go in the front passenger seat.
There are 2 people who can go in the first back passenger seat.
The remaining person must go in the last seat.
Thus, there are 2x3x2 or 12 ways that they can be seated.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
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COMBINING LIKE TERMS
9 + 6f - 7
Answer:
6f + 2
Step-by-step explanation:
The 9 and the - 7 are "like terms"
They are both constants. That is, they don't have a variable. The terms will be considered "like terms" if they have the same variables to the same power.
So we can combine 9 and - 7.
9 + - 7 is 2.
9 + 6f - 7
= 6f + 9 - 7
= 6f + 2
HELP!
im doing a state test and i forget exactly how to solve these, and i cant get it wrong
Answer:
46cm
Step-by-step explanation:
Determine the value of each variable for parallelogram INDY That has diagonals that intersect at P. IP equals 3X, DP equals 6X -2, and P equals 3Y, and YP equals 7X -2
Consequently, each variable's value for the parallelogram INDY that's diagonals intersect at P and have values of x = 2/3 and y = 8/9.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. a formula that expresses the connection between two expressions on either side of a sign.
Here,
If a parallelogram INDY has diagonals that intersects at P, then O bisects ID and YN
Hence IP = PD and NP = YP
IP=3x
DP = 6x - 2
NP = 3y and
YP=7x-2,
Substitute
3x = 6x-2
3x-6x = -2
-3x = -2
x = 2/3
x = 0.67
Also NP = YP
3y = 7x-2
3y = 7(2/3) - 2
3y = 14/3 - 2
3y = 14-6/3
3y = 8/3
9y = 8
y = 8/9
Hence the value of each variable for parallelogram INDY That has diagonals that intersect at P is x = 2/3 and y = 8/9.
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You bake 53 lemon cupcakes to take to a homeless shelter. If you keep 2 lemon cupcakes at home, how many boxes of 3 lemon cupcakes do you have to give away
Answer: 17 boxes
Step-by-step explanation: 53-2=51 (subtract 2 from 53 as they are left at home)
51/3=17 ( divide by 3 as one box contains 3 lemon cupcakes)
so the answer is 17 boxes