Answer:
To find an ordered pair (x, y) that is a solution to the equation -x + 2y = 7, we can substitute any values of x and y that satisfy the equation. For example, let x = 3, then we can solve for y:
-3 + 2y = 7
2y = 10
y = 5
So (3, 5) is an ordered pair that is a solution to the equation.
(x^2 + 7x) / (9 - x^2)
The simplified form of the expression (x² + 7x) / (9 - x²) is x(x + 7) / ( 3 + x )( 3 - x ).
What is the simplified form of the expression?Given the expression in the question;
(x² + 7x) / (9 - x²)
To simplify, first factor out x form x² + 7x
(x × x + 7 × x) / (9 - x²)
Factor out x
x (x + 7) / (9 - x²)
Next, simplify the denominator
x (x + 7) / (9 - x²)
Rewrite 9 as 3²
x (x + 7) / (3² - x²)
Now, since both terms are perfect squares
a² - b² = (a + b)(a - b)
Hence,
x(x + 7) / ( 3 + x )( 3 - x )
Therefore, the simplified form is x(x + 7) / ( 3 + x )( 3 - x ).
Learn more about perfect squares here: https://brainly.com/question/29056294
#SPJ1
Find the product and conjugate of (-12+4i).
Answer:
The product of (-12 + 4i) and its conjugate is (-12 - 4i).
The conjugate of (-12 + 4i) is (-12 - 4i).
In the diagram below of triangle DEF, G is the midpoint of DF and H is the midpoint of EF. If GH = 3x + 2, and DE = 18 + 4x, what is the measure of GH?
Answer:
23.
Step-by-step explanation:
1) if 'G is the midpoint of DF and H is the midpoint of EF', then 0.5*DE=GH, and
2) it is possible to write: 0.5(18+4x)=3x+2, where x=7.
3) if x=7, then GH=3*7+2=23.
Random variables x; and Xz have the following distribution: . x2 f(x1,x2) 0.00 10.00 20.00
x1 5.00 0.20 0.14 0.06
10.00 0.11 0.07 0.12
20.00 0.08 0.02 0.20
Find P(X; < 20,X2 > 10) (write up to second decimal place)
After using the distribution, the value of P(X(1) < 20, X(2) > 10) is 0.18.
The distribution of random variables x(1) and X(2) have given below:
We have to determine P(X(1) < 20, X(2) > 10).
We have to determine the joint probability.
From the table we can see that the value of x(1) is less than 20 is (5, 10) and x(2) greater than the (10, 20).
P(X(1) < 20, X(2) > 10) = P(5, 10) + P(10, 20)
From the table
P(X(1) < 20, X(2) > 10) = 0.06 + 0.12
P(X(1) < 20, X(2) > 10) = 0.18
To learn more about random variables link is here
brainly.com/question/17238189
#SPJ4
The complete question is:
Random variables x(1) and X(2) have the following distribution:
Find P(X(1) < 20, X(2) > 10) (write up to second decimal place)
Suppose that Julie's preference over study (s) and leisure (1) is given by the following cobb-Douglas preferences u(s. 1) = S^(1/3)I^(2/3). If she needs to allocate her waking time of 15 hours between these two activities, how much studying is she going to do per day?
For the hours is she going to do studying per day is 10 hours.
Describe Lagrangian method?The Lagrangian method is a mathematical technique used to find the maximum or minimum value of a function subject to constraints. It is used in optimization problems where the objective is to maximize or minimize a function, but there are some constraints that limit the possible values of the inputs.
The Lagrangian method works by combining the objective function and the constraints into a single function, called the Lagrangian, which is then optimized. The Lagrangian is defined as the original objective function minus the product of the constraints and a set of Lagrange multipliers, which represent the trade-off between the objective and the constraints.
To maximize Julie's utility subject to the constraint of 15 hours of waking time, we need to find the optimal level of s (study time) that satisfies the constraint and maximizes the utility function.
We can start by using the Lagrangian method to find the optimal solution. The Lagrangian is given by:
L(s,λ) = S^(1/3)I^(2/3) + λ(15 - s - I)
Where λ is the Lagrange multiplier, representing the marginal rate of substitution between s and I. To find the optimal solution, we need to find the values of s and λ that satisfy the first-order conditions:
∂L/∂s = (1/3)S^(-2/3)I^(2/3) - λ = 0
∂L/∂λ = 15 - s - I = 0
Solving the first-order conditions for s and λ, we get:
s = (15 * (2/3)) / (1 + (2/3)) = 10 hours
I = 15 - s = 5 hours
So, Julie will spend 10 hours per day studying.
To know more about function visit:
https://brainly.com/question/10500042
#SPJ1
The manager of Jerry’s Barbershop recently asked 15 customers to punch in a time card when first arrive at the shop and to punch out right after they paid for their haircut, and used the data on the cards to measure how long (in minutes ) it took Jerry and his barbers to cut hair. He also recorded the amount of money spent by each of the 15 customers as well as the customers stage of life (Child, Teen, or Adult).
Identify the population in the above scenario. (2 pts.)
Identify the variables and their units (if any). (6 pts.)
Variable 1: Unit:
Variable 2: Unit:
Variable 3: Unit:
Population: The customers of Jerry's Barbershop. Time is taken to cut hair: Minutes. Amount of money spent: Currency (e.g. dollars).
Stage of life: Categorical (Child, Teen, or Adult)
What is a population?A population is a discrete group of people, animals, or things that can be recognized by at least one common trait for the purposes of data collection and analysis in statistics and other fields of mathematics.
As per the given information, the required solution would be as:
Population: The customers of Jerry's Barbershop.
Variables and their units are, as follows:
Time taken to cut hair: Minutes
Amount of money spent: Currency (e.g. dollars)
Stage of life: Categorical (Child, Teen, or Adult)
Learn about the population here:
https://brainly.com/question/27991860
#SPJ1
Not sure about this answer
Answer:
B
Step-by-step explanation:
All that they were asking for is what is given to you, so B would be right
Solve the quadratic equation by completing the square: x^2 + 16x +51 = 0
Answer:
x = ±√13 - 8
Step-by-step explanation:
Move the constant term to the right side of the equation.
x² + 16x + 51 = 0
x² + 16x = -51
We complete the square by taking half of the coefficient, squaring it, and adding it to both sides of the equation. The formula is (b/2)².
x² + 16x = -51
here the formula would be (16/2)² = 64
x² + 16x + 64 = -51 + 64
Now just simplify by factoring the left side and adding up the right side.
(x + 8)² = 13
You have to isolate x to find what it equals. Here start by taking the square root of both sides
x + 8 = √13
Subtract 8 to both sides
x = ±√13 - 8
The taxes on a house assessed at 108,000 are $2700 a year if assessment is raised to 128,000 and tax rate didn't change how much is the taxes now
Answer:
The new taxes would be $3300.
Step-by-step explanation:
The assessment value and tax rate determine how much a house will cost in taxes. The amount of taxes would increase if the assessment is raised from $108,000 to $128,000.
To find the new amount of taxes, you need to multiply the increased assessment value by the same tax rate:
$128,000 - $108,000 = $20,000 increase in assessment value
$20,000 * ($2700/$108,000) = $600 increase in taxes
Therefore, the new taxes would be $2700 + $600 = $3300.
1. Explain IKEA's brand image. The video mentions how the brand at one point had French influence but then decision. 2. Describe IKEA's sustainability initiatives. What impact has Gen Z had on holding retailers accountable to act 3. Some businesses use sustainability as a marketing tactic as opposed to a mission true to its core. Do you be
1. KEA's brand image is centered around affordability, simplicity, and modern design.
2. IKEA has a strong commitment to sustainability, with initiatives that include reducing waste, using sustainable materials in its products, and investing in renewable energy.
3. Sustainability is an increasingly important issue for consumers, and many businesses use it as a marketing tactic to appeal to environmentally-conscious consumers. l IKEA is one such company, and its commitment to sustainability is reflected in its long-term goals and initiatives, as well as its focus on sustainable product design and operations.
How to explain the brand imageThe company's "Democratic Design" philosophy reflects this, emphasizing the importance of quality, sustainability, and affordability in its products.
The company has set ambitious goals to become more environmentally friendly, such as producing as much renewable energy as it consumes by 2020 and becoming climate positive (i.e., reducing its net greenhouse gas emissions) by 2030.
In recent years, Gen Z has been a major driving force behind holding retailers accountable for their environmental impact, and IKEA has responded to this by continuing to focus on sustainability and transparency in its operations.
Learn more about brand on:
https://brainly.com/question/24456504
#SPJ1
Abby squeezed the juice from 4 oranges and made 1 cup of orange juice. Each orange provides the same amount of juice.
PART A.
Complete the table below to show the relationship between the number of cups orange juice that are made by squeezing the juice from different numbers of oranges.
Answer:
The table can't be completed as I can't see the table.
However, I can give you the values:
4 Oranges for every 1 Cup of Orange Juice
4, 1
8, 2
12, 3
16, 4
20, 5
Step-by-step explanation:
Jon walked 98 feet in 11.5 seconds. What is his speed in miles per hour? (1 mi = 5280 ft)
Answer:To convert this to miles per hour, we need to first convert the distance to miles. We know that 1 mi = 5280 ft, so 98 ft = 98 / 5280 mi = 0.0184 mi.
Now we can use the formula speed = distance / time again, but this time using miles and hours as the units. So, speed = 0.0184 mi / (11.5 s / 3600 s/hr) = 0.0184 mi / 0.003194 hr = 5.8 mi/hr.
Step-by-step explanation:
Answer:
5.81 mph
Step-by-step explanation:
We want to first convert the number of feet to miles and then divide by the number of hours. Since we know that 5280 feet is one mile, we essentially want to find how many "groups" of 5280 are in some distance and that's the number of miles. We can do this by dividing.
[tex]\frac{98}{5280}\approx0.018561[/tex]
Now we want to find how many hours 11.5 seconds is. It's basically the same process as we divide this by the number of seconds in an hour 3600.
11.5/3600 = 0.00319
Now divide the distance over the time and this gives us approximately: 5.81 mph
Isabella bought a T-shirt for $85, after sales tax is added is added the final cost was $97.75. what was the percent of sales tax?
97.75 - 85 = 12.75
This means the amount of tax was $12.75.
If we divide the amount of tax by the original price of the shirt, it gives us the percent of the tax:
12.75 ÷ 85 = 0.15 = 15%
Sales tax is 15%.
The key in the calculation is to divide by the original price of the shirt.
Two investments totaling $56,500 produce an annual income of $2480. One investment yields 8 % per year, while the other yields 2 % per year. How much is
invested at each rate?
The first investment is $22500 and second investment is $34000.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Two investments totaling $56,500 produce an annual income of $2480.
let the two investments be x and y.
So, x + y = 56500.........(1)
and, One investment yields 8 % per year, while the other yields 2 % per year then
0.08x+0.02y=2480.......(2)
Solving equation (1) and (2) we get
0.08(56500-y)+0.02y=2480
4520-0.08y+0.02*y=2480
-0.06y=-2040
y= 34000
and, x=56500-y =22500
Hence, the investments were $22500and $34000.
Learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ1
Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the 30 of the lower 48 states, the percentage loss of wetlands per state is as follows. 42 89 38 27 60 67 73 9 27 38 59 50 87 54 48 20 33 85 52 90 50 50 52 35 46 35 35 46 37 46 Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) Percent of Wetlands Lost COVOU AWN NONE 377 3555788 22666 000 26 99 07 >XXXXX 5 77 How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.) These data are strongly skewed left. The percentages are concentrated from 20% to 60%. These data are fairly symmetric, perhaps slightly skewed right. There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands. There are no gaps in the data. There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands. The percentages are concentrated from 60% to 90%.Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the 30 of the lower 48 states, the percentage loss of wetlands per state is as follows. 42 89 38 27 60 67 73 9 27 38 59 50 87 54 48 20 33 85 52 90 50 50 52 35 46 35 35 46 37 46 Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) Percent of Wetlands Lost COVOU AWN NONE 377 3555788 22666 000 26 99 07 >XXXXX 5 77 How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.) These data are strongly skewed left. The percentages are concentrated from 20% to 60%. These data are fairly symmetric, perhaps slightly skewed right. There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands. There are no gaps in the data. There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands. The percentages are concentrated from 60% to 90%.
The stem-and-leaf plot of the given data is attached.
A stem-and-leaf plot refers to a device used to present quantitative data in a graphical format to help in visualizing the shape of a distribution. It is a table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).
From the given options, the statements that describe the percentages distributed, distribution skewness and whether there are any gaps are:
The percentages are concentrated from 20% to 60% as these concentrations have more than one values. These data are fairly symmetric, perhaps slightly skewed right, considering the midpoint, 4.5, there are fairly equal number of values on each side, perhaps a little more on the right side.There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands, as there are no values corresponding to 1, or no values between 10 and 19 percent.Learn more about Stem-and-leaf plot:
https://brainly.com/question/26678606
#SPJ4
Given the table of values below, find the average rate of change of the function f(x) on the interval [4,9].
x 3 4 5 6 7 8 9 10
f(x) 77 97 131 155 160 177 212 245
Enter your answer as a reduced improper fraction, if necessary.
The average rate of change of the function f(x) on the interval [4,9] is equal to 23.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [4, 9]:
a = 4; f(a) = 97
b = 9; f(b) = 212
Substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (212 - 97)/(9 - 4)
Average rate of change = 115/5
Average rate of change = 23.
Read more on average rate of change here: brainly.com/question/23715190
#SPJ1
A map used a scale of 1/2 cm = 75 kilometers. The actual distances between various cities are given below. Find the distance Between the cities on the map.
The distance between the cities on the map is given by the equations
a) The distance of 50km = ( 1/3 ) cm
b) The distance of 280km = ( 1 13/15 ) cm
c) The distance of 142 1/2 km = ( 19/20 ) cm
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the distance on the map be represented as A
Now , the equation will be
The scale on the map is given by 1/2 cm = 75 km
So , 1 km = ( 1/2 ) / 75 cm
1 km = ( 1/150 ) cm
a)
when the distance = 50 km
The distance on the map = 50 x ( 1/150 ) cm
The distance on the map = ( 1/3 ) cm
b)
when the distance = 280 km
The distance on the map = 280 x ( 1/150 ) cm
The distance on the map = ( 1 13/15 ) cm
c)
when the distance = 142 1/2 km
The distance on the map = 142 1/2 x ( 1/150 ) cm
The distance on the map = ( 19/20 ) cm
Hence , the equation is solved
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
Yolanda invests $6,000. Some of the money is invested in stocks paying 6% a year and some in bonds paying 11% a year. If she receives $580 each year., how much is invested in stocks?
The amount of money that Yolanda invested in the stock is x = $1600
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
To solve this problem we will only formulate two equations:
(a) The sum of the amount to invest in stocks and bonds will be $6000:
x + y = 6000
(b) The percentage of stocks 6% and bonds 11% for a profit of $580.
0.06x + 0.11y = 580
x + y = 6000 ----⇒ x = 6000 - y
0.06(6000 - y) + 0.11y = 580
360 - 0.06y + 0.11y = 580
0.05y = 220
y = $4400
x = 6000 - 4400
x = $1600
Learn more about equations at:
brainly.com/question/8806877
#SPJ4
What is the domain of the table below?
Input|Output
-3
6
12
585
The domain of the table below is {-3, 6, 12}
How to determine the domain of the tableFrom the question, we have the following parameters that can be used in our computation:
The table of values
The domain of a function is the set of the input values
This means that the domain is
Domain = {-3, 6, 12}
Read more about domain at
https://brainly.com/question/2264373
#SPJ1
A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $38. The total cost to rent 2 chairs and 12 tables is $107. What is the cost to rent each chair and each table?
Answer:
Chair: $2.50
Table: $8.50
Step-by-step explanation:
First, let's create equations with the information given to us:
x= cost of a chair
y= cost of a table
5x + 3y = $38
2x + 12y = $107
The next step is to solve for x in terms of y. To do this, I will be using the equation 5x + 3y = $38.
5x + 3y = $38 [Subtract 3y from both sides]
5x = -3y + 38 [Divide by 5]
x =(-3/5)y + 38/5
Now that we have found the value of x in terms of y, we will plug it into the equation 2x + 12y = $107.
2x + 12y = $107
2 ((-3/5)y + 38/5) + 12y = 107 [Distribute]
(-6/5)y + 76/5 + 12y = 107 [Combine like terms]
(54/5)y + 76/5 = 107 [Subtract 76/5 from both sides]
(54/5)y = 459/5 [Multiply both sides by 5/54]
y = 17/2 or 8.5
So, the cost of a table is $8.50.
Now that we have found the price of the table, let's plug it into the equation 5x + 3y = $38 to find the price of the chair.
5x + 3y = $38
5x + 3 ( 17/2 ) = 38 [Distribute]
5x + 51/2 = 38 [Subtract 51/2 from both sides]
5x = 25/2 [Divide both sides by 5]
x = 5/2 or 2.5
So, the cost of a chair is $2.50.
So, the chair costs $2.50 while the table costs $8.50.
If this answer helped you, please leave a thanks or a Brainliest!!!
Have a GREAT day!!!
Find the equation of the linear function represented by the table below in slope-intercept form. x y -1 -5 1 3 3 11 5 19
The equation of the linear function represented by the table below in slope intercept form is f(x) = 4x - 1.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
General equation of a linear function in slope intercept form is,
y = f(x) = mx + c
Here c is the y intercept and m is the slope.
y intercept is the point on the line when x coordinate equals zero.
Given four points on the line (-1, -5), (1, 3), (3, 11) and (5, 19).
Consider two points (1, 3) and (3, 11).
Slope, m = (11 - 3) / (3 - 1) = 8 / 2 = 4
So the equation is y = 4x + c.
Substitute (1, 3) in the above equation.
3 = (4 × 1) + c
c = 3 - 4
c = -1
So the equation is y = 4x - 1.
Hence the given function can be represented as f(x) = 4x - 1.
Learn more about Slope here :
https://brainly.com/question/3605446
#SPJ1
Please help me with this question.
The solution of given trigonometric equation, 6sin²θ-13sinθ+7 = 0 is θ = π/2
What are trigonometric equations?A trigonometric equation is one that contains a trigonometric function with a variable.
Given is a trigonometric equation,
6sin²θ-13sinθ+7 = 0
Solving for θ
6sin²θ-6sinθ-7sinθ+7 = 0
6sinθ(sinθ-1)-7(sinθ-1) = 0
(6sinθ-7)(sinθ-1) = 0
sinθ = 1
θ = π/2
or,
6sinθ-7 = 0
sinθ = 7/6 [no solution]
Hence, the solution of given trigonometric equation, 6sin²θ-13sinθ+7 = 0 is θ = π/2
Learn more about trigonometric equation, click;
https://brainly.com/question/30043209
#SPJ1
Factor the expression using GCF
32y - 48
Answer:
2y-3
Step-by-step explanation:
GCF of 32 and 48=16
(32y-48)/16=2y-3
Which point represents the origin? (2 points)
Part B: Starting from the origin, explain how to plot the following three points accurately:
(2, −2)
(−2, 1.5)
(−1, fraction 2 over 4 )
Answer:
The origin is the point (0,0)
(2,-2) Start at the origin and move 2 unit right along the x axis, from there move down 2 units. Place a point at that location.
(-2, 1.5) Start at the origin and move 2 units left along the x axis, from there move up 1.5 space and place a point.
(-1, 2/4) Start at the origin and move left 1 unit along the x axis, from there move up 1/2 a unit and place a point. 2/4 is the same as 1/2
Step-by-step explanation:
4. Mark wants to find the area of a circle with a diameter of 8 cm. Which expressions can he use to find the area of
the circle in square centimeters? Choose all the correct answers.
A 2•4• (pi)
B 8• (pi)
C 4•4•(pi)
D 8²• (pi)
E 4² •(pi)
Answer:
B. the area is d x pi its the solution
someone help me asap
The function that has the average rate of change of -4 over the interval [-2, 2] is (D) p(x).
What is the Average Rate of Change?
The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.The formula for calculating the average rate of change can be given as [tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex]Here, average rate of change of the function must be calculated over the interval [-2, 2].
(A) The average rate of change of the function m(x):
Here, a = -2, m(a) = -12, and b = 2, m(b) = 4
Substituting the values in the formula for average rate of change, we get
[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{4-(-12)}{2-(-2)} \\\implies A(x)=4[/tex]
(B) The average rate of change of the function q(x):
Here, a = -2, q(a) = -4, and b = 2, q(b) = -12
Substituting the values in the formula for average rate of change, we get
[tex]A(x)=\frac{q(b)-q(a)}{b-a}\\\implies A(x)=\frac{-12-(-4)}{2-(-2)} \\\implies A(x)=-2[/tex]
(C) The average rate of change of the function n(x):
Here, a = -2, n(a) = -6, and b = 2, n(b) = 6
Substituting the values in the formula for average rate of change, we get
[tex]A(x)=\frac{n(b)-n(a)}{b-a}\\\implies A(x)=\frac{6-(-6)}{2-(-2)} \\\implies A(x)=3[/tex]
(D) The average rate of change of the function p(x):
Here, a = -2, p(a) = 12, and b = 2, p(b) = -4
Substituting the values in the formula for average rate of change, we get
[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{-4-12}{2-(-2)} \\\implies A(x)=-4[/tex]
Therefore, the function that has the average rate of change of -4 over the interval [-2, 2] is (D) p(x).
To learn more about Average Rate of Change from the given link
https://brainly.com/question/11627203
#SPJ1
What number is 301% of 82?
Answer:
269
Step-by-step explanation:
big × square root 05 is Justin Beiber
Answer:
301/8200
Step-by-step explanation:
82 x (X) = 301/100
82x/1 = 301/100
now we cross multiply.
8200x = 301
x = 301/8200
it may be wrong, sorry if it is :(
1. [1/4 Points] DETAILS PREVIOUS ANSWERS For each absolute value inequality, write an equivalent compound inequality. (a) (x +31 < 1 is equivalent to ____ < x+3< ______
b) |x-6|≥ 2 is equivalent to x-6≤ ______
or x-6≥
The inequalities are :
x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27
|x - 6| ≥ 2 ⇒x- 6 ≥ 2 and 6 - x ≤ 2
What are inequalities ?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two integers on a number line.
The occurrence of an unfair and/or uneven distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different individuals and in various settings, the word "inequality" may indicate different things.
Inequality is a connection between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
The inequalities are :
x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27
|x - 6| ≥ 2 ⇒x- 6 ≥ 2 and 6 - x ≤ 2
To learn more about Inequality refer to :
https://brainly.com/question/13589585
#SPJ1
In a right triangle, sin (4x-5)^\circ(4x−5) ∘ = cos (3x+4)^\circ(3x+4) ∘ . Find the smaller of the triangle’s two acute angles.
The smaller of the triangle’s two acute angles is 65 degrees
What is acute Angle?Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.
Given:
Angles in a triangle
[tex]sin (4x-5)^\circ= cos (3x+4)^\cir[/tex]
Since, sin [tex]\theta[/tex]= cos(90 - [tex]\theta[/tex]),
cos(90 - (4x - 5 )) = cos(3x +4)
cos(85 - 4x) = cos (3x+4)
Cancel out the cosine functions to have:
85- 4x = 3x+ 4
81 = 7x
x= 11.57
Hence, the smaller of two acute angles is 11.57 degrees
Learn more on acute angles here;
brainly.com/question/6979153
#SPJ1
Answer:
27
Step-by-step explanation:
in a recent year, male students and female students were enrolled as undergraduates. receiving aid were of the male students and of the female students. of those receiving aid, of the males got federal aid and of the females got federal aid. choose student at random. (hint: make a tree diagram.) find the probability of selecting a student from the following.
To make a tree diagram, start by writing out the given information and drawing a box around it. Then draw two branches off of the box representing the two possible outcomes of selecting a student, male or female. Then draw two more branches off of each of the first two branches, representing the two possible outcomes of receiving aid.
Then draw two more branches off of each of the second two branches, representing the two possible outcomes of receiving federal aid. This will create a tree diagram that looks like this (see the image).
From the tree diagram, we can calculate the probability of selecting a student from the given information as follows:
P(selecting a student) = P(selecting a male) + P(selecting a female) = (of male students/total students) + (of female students/total students) = (of male students + of female students)/total students =
Therefore, the probability of selecting a student from the given information is .
Learn more about probability
https://brainly.com/question/13604758
#SPJ4
