how many square units are in the region satisfying the inequalities and ? express your answer as a decimal.
Answers
Therefore, the total area of the region that satisfies the two inequalities is 14.5 square units.
The two inequalities given are:
y >= x
y <= |x - 3|
The region that satisfies both inequalities is the shaded area in the graph.
We can find the area of this region by splitting it into two parts: the triangle formed by the points (0, 0), (3, 0), and (3, 3), and the trapezoid formed by the points (3, 3), (2, 1), (-1, 3), and (-3, 3).
The area of the triangle is (1/2)33 = 4.5 square units.
To find the area of the trapezoid, we need to find the lengths of its two bases and its height. The height is the distance between the x-axis and the line y = |x - 3|. This line intersects the x-axis at x = 3 and at x = -1. At x = 3, the height is 0. At x = -1, the height is |-1 - 3| = 4. So the height of the trapezoid is 4 units.
The lengths of the two bases of the trapezoid are the distances between the y-axis and the lines x = 2 and x = -3. These distances are 2 and 3 units, respectively. So the area of the trapezoid is (1/2)*(2 + 3)*4 = 10 square units.
Therefore, the total area of the region that satisfies the two inequalities is 4.5 + 10 = 14.5 square units.
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Complete question:
How many square units are in the region satisfying the inequalities y>=(x) and y<=-(x)+3? Express your answer as a decimal. * the () are absolute value signs.
Related Questions
◄)) Divide:
4) 8,567
R
Submit
Answers
The Remainder is 3 and the Quotient is 2141.
What is meant by long term division?Long division is a mathematical technique for breaking down large numbers into smaller groups or parts. It is beneficial to divide a problem into simple and easy steps. Dividends, divisors, quotients, and remainders are all part of the long divisions.The layout of short division and long division is similar, but there are two major differences. Long division is used when dividing multi-digit numbers by two-digit numbers, whereas short division is used when dividing multi-digit numbers by one-digit numbers. Follow the steps below to find the square root of 5 using the long division method. As a result, the value of root 5 is 5 = 2.2360... Long division can be used to calculate the value of the square root of any non-perfect square number.Therefore,
The given Divisor = 4 and Dividend = 8567
4 ÷ 8567
= 2141.75
The Quotient is 2141 and the Remainder is 3
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A motorcycle drives on a ramp in order to enter the parking garage. The ramp has a height of 4 feet and a horizontal length of 20 feet. What is the angle of the ramp?
Answers
Sam wantds to put a fence around his garden. two sides are already near a fence and the other sides are 15 and 23 feet. how many feet of fencing does he ned
Answers
We cannot determine the exact amount of fencing Sam needs.
To find out how many feet of fencing Sam needs, we need to calculate the total perimeter of his garden.
First, let's find the length of the two sides that are already near a fence. Since these sides are already taken care of, we don't need to include them in our calculation.
Now, let's focus on the other two sides that are 15 and 23 feet long. To find the total perimeter, we need to add the lengths of all four sides together.
So, the total perimeter is 15 + 23 + (length of the two sides near the fence) + (length of the other side near the fence).
Since we don't know the length of the sides near the fence, we cannot calculate the exact length of the total perimeter.
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I need help in this question please
Answers
Ross's profit percentage is 17%.
How to calculate the percentages?
To calculate a percentage, you need to divide the part by the whole and then multiply the result by 100. The formula is:
Percentage = (part/whole) x 100
Let's work through the problem step by step:
Ross bought the chair for 1000.
1. He marked it up by 30%, which means he added 30% of 1000 to the original price:
\(1000 + 0.3 * 1000 = 1300\)
2. He gave a discount of 10%, which means he subtracted 10% of the marked-up price:
\(1300 - 0.1 * 1300 = 1170\)
3. The customer paid 1228.50 inclusive of a 5% tax, which means the original price before tax was:
1228.50 / 1.05 = 1170
4. Ross's profit was the difference between the price he sold the chair for and the price he bought it for:
1170 - 1000 = 170
5. To find the profit percentage, we divide the profit by the cost and multiply by 100:
\((170 / 1000) * 100 = 17%\)
Hence, Ross's profit percentage is 17%.
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The perimeter around a dog's running space is 20x2 + 283 + 8. The length of the dog's running space is
10x+4.
What is the width of the dog's running space? Show why your answer is correct.
Answers
Answer:
You need to add all of the number together
Step-by-step explanation:
Find the volume of the cylinder in terms of pie
Answers
Pi x 3.8^2 x 8
= 115.52pi cm^3
(-5, -4) and (-13,2)
Answers
The slope of the line passing through the points (-5, -4) and (-13, 2) is -3/4.
What is the slope of the line through the given points?Slope is simply expressed as a change in y over the change in x.
It is expressed as
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Given the points:
(-5, -4) and (-13,2)
Point (-5, -4):
x₁ = -5
y₁ = -4
Point (-13,2):
x₂ = -13
y₂ = 2
Plug the given x and y values into the slope formula and simplify.
\(m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{2 - (-4)}{-13 - (-5)}\\\\m = \frac{2 + 4}{-13 + 5}\\\\m = \frac{6}{-8}\\\\m = -\frac{3}{4}\)
Therefore, the slope of the line is -3/4.
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find the missing number 87(M)
= 28.71
Answers
There are 10 boys in a class of 15 people. create a ratio of boys to girls simplify
Answers
Answer:
10:5
Step-by-step explanation:
Answeer
2 to 3. ... On many GMAT questions, you will be given a ratio, and you will solve by setting up a ... We set up a proportion by finding something that we can set the ratio equal to:.
Step-by-step explanation:
Which hill is the steepest
Answers
Answer:
Liberty Hill
Step-by-step explanation:
To determine which hill is the steepest, calculate the absolute value of m for each hill and compare them:
|m|= |Slope (or gradient)|
= |\(\frac{VerticalDistance}{HotizontalDistance}\)|
The hill with the greatest absolute value of m is the steepest:
|\(m_{Dixie} = |\frac{40}{80}|\)
= 0.5
\(|m_{Bell}| =|\frac{20}{80}|\)
= 0.25
\(|m_{Liberty}| = |\frac{60}{80}|\)
= 0.75
Liberty Hill has the greatest absolute value of m of 0.75, therefore it is the steepest
What does it mean to have 2 equal roots?
Answers
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
What is square root ?A number's root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as or as 3 x 3.
Here,
If an equation have 2 roots , it means it is a quadratic function
If D=0, a quadratic function has two roots that are equal.
D (discriminant) = 0
=>b24ac=0 is required for a polynomial function to have equal roots.
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
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A stock has an expected return (μ) of 17% per annum and a standard deviation (volatility, σ) of 37% per annum. Under the probability distribution assumptions of the BSM model:
A) Compute the mean and standard deviation of the continuously compounded rate of return earned over a one-year period (answer in % and round to the nearest tenth).
Mean is: %; Standard deviation is: %
B) Construct a 95% confidence interval for the continuously compounded rate of return earned over a one-year period (answer in % and round to the nearest tenth).
95% confidence interval is from: % to: %
Answers
A) The mean of the continuously compounded rate of return earned over a one-year period can be calculated using the formula: μ = ln(1 + R), where R is the annual rate of return.
Solving for R, we get: R = e^μ - 1
Substituting the given values, we get: R = e^0.17 - 1 = 0.1876 or 18.8% (rounded to the nearest tenth)
The standard deviation of the continuously compounded rate of return can be calculated using the formula:
σ_R = σ * sqrt(t), where t is the time period (in years).
Substituting the given values, we get: σ_R = 0.37 * sqrt(1) = 0.37 or 37% (rounded to the nearest tenth)
B) To construct a 95% confidence interval for the continuously compounded rate of return, we can use the formula:
CI = R ± z * (σ_R / sqrt(n)), where CI is the confidence interval, z is the critical value from the standard normal distribution for a 95% confidence level (which is 1.96), and n is the sample size (which is assumed to be large in the BSM model).
Substituting the given values, we get: CI = 0.188 ± 1.96 * (0.37 / sqrt(1)) = 0.188 ± 0.724
The 95% confidence interval is from 11.6% (0.188 - 0.724) to 24.0% (0.188 + 0.724), rounded to the nearest tenth.
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use a maclaurin series derived in this section to obtain the maclaurin series for the given functions. enter the first 3 non-zero terms only.
f(x) = cos (8x³) = ... + ...
Answers
The first three non-zero terms of the Maclaurin series for f(x) = cos(8x³) are cos(8x³) = 1 - 32x⁶ + 512x¹²/4!
The Maclaurin series for f(x) = cos(8x³) is not provided in the context. However, we can use the Maclaurin series for cos(x) to obtain the Maclaurin series for f(x) = cos(8x³).
The Maclaurin series for cos(x) is:
cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...
To obtain the Maclaurin series for f(x) = cos(8x³), we substitute 8x³ for x in the Maclaurin series for cos(x):
cos(8x³) = 1 - (8x³)²/2! + (8x³)⁴/4! - (8x³)⁶/6! + ...
Simplifying, we get:
cos(8x³) = 1 - 32x⁶ + 512x¹²/4! - 32768x¹⁸/6! + ...
Therefore, the first three non-zero terms of the Maclaurin series for f(x) = cos(8x³) are:
cos(8x³) = 1 - 32x⁶ + 512x¹²/4!
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Kate has 48 softballs. She wants to divide them evenly among b softball bags. Which expression represents how many softballs she should put into each bag?
Answers
Answer:
Softballs = (48/b)
Step-by-step explanation:
Given that,
Total number of softballs = 48
She wants to divide them evenly among b softball bags.
We need to find an expression that represents how many softballs she should put into each bag.
As it is dividing among b softball, it means we divide 48 and b. So,
\(s=\dfrac{48}{b}\)
Hence, the required expression is (48/b).
Find the area under the standard normal curve for the following using the z-table.
Between z=0 and z=.68
Between z= -0.46 and z=0
Between z= -0.34 and z=0.68
Answers
1. The area between z=0 and z=0.68 is: 0.7517 - 0.5000 = 0.2517.
2. The area between z=-0.46 and z=0 is: 0.5000 - 0.3222 = 0.1778.
3. The area between z=-0.34 and z=0.68 is: 0.7517 - 0.3669 = 0.3848.
To find the area under the standard normal curve using the z-table, you need to locate the corresponding z-scores and subtract the areas.
Between z=0 and z=0.68:
From the z-table, the area to the left of z=0 is 0.5000, and the area to the left of z=0.68 is 0.7517.
Therefore, the area between z=0 and z=0.68 is: 0.7517 - 0.5000 = 0.2517.
Between z=-0.46 and z=0:
From the z-table, the area to the left of z=-0.46 is 0.3222, and the area to the left of z=0 is 0.5000.
Therefore, the area between z=-0.46 and z=0 is: 0.5000 - 0.3222 = 0.1778.
Between z=-0.34 and z=0.68:
From the z-table, the area to the left of z=-0.34 is 0.3669, and the area to the left of z=0.68 is 0.7517.
Therefore, the area between z=-0.34 and z=0.68 is: 0.7517 - 0.3669 = 0.3848.
Note: The z-table provides the area to the left of the given z-score. To find the area between two z-scores, you need to subtract the areas corresponding to those z-scores.
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A class of 65 students is going on a field trip. They will take 12 busses.How many students will be on each bus?
Answers
Which is greater |-2| or-2
Answers
To Find :
Which is the greater |-2| or -2 .
Solution :
Value of |x| for any value of x ( real number ) is always positive .
\(|x| = \left \{ {x , \ for \ x >= 0 \atop { -x, \ for \ x < 0 }} \right.\)
So, |-2| = 2 > -2
Therefore, the value of |-2| is greater than -2 .
Hence, this is the required solution.
What is the CIV of each of the customers? Amber Jung Joe Ashley Lauren Maria Jose Customer Amber Ashley Joe Lauren Jung Maria Jose CLV 10 20 10 25 10 15 CIV Hint. CIVAshley = [CLVMaria + 0.5CLV Josel + [CIVMaria + 0.5CIV Josel 20
Answers
The CIV of each customer is:
- Amber: 20 - Ashley: 20 - Joe: 20 - Lauren: 30 - Jung: 20 - Maria: 30 - Jose: 30
To calculate the CIV (customer lifetime value) of each customer, we can use the formula provided in the hint for Ashley and then apply the same formula for the rest of the customers:
CIVAshley = [CLVMaria + 0.5CLVJose] + [CIVMaria + 0.5CIVJose]
Plugging in the values given in the table:
CIVAshley = [10 + 0.5(15)] + [10 + 0.5(10)] = 20
Therefore, the CIV of Ashley is 20.
Using the same formula for the other customers:
CIVAmber = [10 + 0.5(15)] + [10 + 0.5(10)] = 20
CIVJoe = [10 + 0.5(15)] + [10 + 0.5(10)] = 20
CIVLauren = [25 + 0.5(10)] + [10 + 0.5(15)] = 30
CIVJung = [10 + 0.5(15)] + [10 + 0.5(10)] = 20
CIVMaria = [10 + 0.5(15)] + [20 + 0.5(10)] = 30
CIVJose = [10 + 0.5(15)] + [20 + 0.5(10)] = 30
Therefore, the CIV of each customer is:
- Amber: 20
- Ashley: 20
- Joe: 20
- Lauren: 30
- Jung: 20
- Maria: 30
- Jose: 30
Note that the CIV represents the total value a customer is expected to bring to a company over the course of their relationship, taking into account the frequency and monetary value of their purchases.
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ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
(4x - 2).
Step-by-step explanation:
12x^2 + 20x - 6x - 10
= 12x^2 + 14x - 10
= 2(6x^2 + 7x - 5)
= 2(2x - 1)(3x + 5)
= (4x - 2)(3x + 5)
= 12x^2 + 20x - 6x - 10
Hope this helps!
Answer:
(4x - 2)
Step-by-step explanation:
choice A
15x + 5y = 20 y = 8 - 3x
Answers
Answer:
Step-by-step explanation:
15x+5y=8-3x
18x+5y=8⇒eqn 1
15x+5y=20y
15x-15y=0⇒eqn 2
eqn 1 * 3
54x + 15y=24⇒eqn 3
eqn 3 + eqn 2
69x=24
x=24/69=0.3478
eqn 1⇒
5y=8-18(24/69)
y=1.7391/5
y=0.3478
The solution to the system of equations is (10/3, -2).
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equations are 15x + 5y = 20 and y = 8-3x.
15x + 15y = 20
Substitute y = 8-3x into the above equation:
15x + 15(8-3x) = 20
15x + 120 - 45x = 20
45x - 15x = 120 - 20
30x = 100
x = 10/3
Substitute x = 10/3 in y = 8 - 3x:
y = 8 - 3 (10/3)
y = 8 - 10
y = -2
Hence, the solution to the system of equations is (10/3, -2).
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Evaluate each expression. Enter the correct answers in the boxes. (60−6)×(13)3+27÷3= ( 60 − 6 ) × ( 1 3 ) 3 + 27 ÷ 3 = 82÷4×(2+3)−9= 8 2 ÷ 4 × ( 2 + 3 ) − 9 = Ʃ 789+Plus456-Minus123×Multiplied by0.,÷Divided byemptyemptyBackspace=Equals
Answers
Answer:
2115
Explanation:
To evaluate the expression (60−6)×(13)3+27÷3 we use BODMAS
BODMAS is an acronym/rule in mathematics that dictates the order we should solve mathematical operations such as the above.
BODMAS stands for bracket first, order or of, division, multiplication, addition and then lastly subtraction
To solve the expression using BODMAS, we solve the brackets first
(60−6)×(13)3+27÷3 =54×39+27/3
Then division
=54×39+9
=2106+9
Then addition
=2106+9=2115
Answer=2115
Refer to the Venn diagram to the right for events A and B in an equally likely sample space S. Find the indicated probability P{(ANB)') s Pranay 1030 P((ANB)')- Pranay) - Type a decimal (Type a decimal.) DE
Answers
the probability of the complement of the intersection, P((A ∩ B)'), is 40.
What is probability ?
Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
P(A ∩ B) = 40 + 30 - 10 = 60
Next, we can find the probability of the complement of the intersection:
P((A ∩ B)') = 1 - P(A ∩ B)
P((A ∩ B)') = 1 - 60 = 40
Therefore, the probability of the complement of the intersection, P((A ∩ B)'), is 40.
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5 people are meeting for the first time and shake each others hand once. determine the number of handshakes
Answers
Step-by-step explanation:
5
Answer:
10 B
Step-by-step explanation:
you would just start with 4 and each time count down.which gives you 10
The scatter plot below suggests which of the following types of data relationship?
A. Weak positive correlation
B. Weak negative correlation
C. Strong negative correlation
D. Strong positive correlation
Answers
Answer:
Strong negative maybe
Step-by-step explanation:
They dots are mostly all together and the dots are going down from left to right indicating it’s negative
Someone Smart Help With Math!
Answers
Answer:
-48. You multiply the figures
Answer:
B. -48
Explanation:
Simply -16 multiplied by 3. When one negative number is multiplied, the product is a negative. When two negative numbers are multiplied together, the product is positive.
Find the area of the circle. Use 3.14 for π.
Answers
Answer:
1256 yd²
Step-by-step explanation:
\(A=\pi r^2 \approx (3.14)(40/2)^2=1256\) yd²
Jessie uses 20 liters of gasoline to travel 200 kilometers, how many liters of gasoline will he use on a trip of 700 kilometers?.
Answers
Trip of 700 km required 70 liter gasoline
For go 200 km Distance total gasoline required = 20 liter
For go 1 km Distance total gasoline required = 20÷200
= 0.1 liter
Total trip distance =700 km
Total gasoline required for going 700 km = Total distance×Gasoline required for 1 km
Total gasoline required for going 700 km = 700×0.01
= 70 liters
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70 liters of gasoline will be used on a trip of 700 kilometers.
Given that,
200 kilometer is covered by 20 liters of gasoline.
For go 1 km Distance total gasoline required = 20÷200
= 0.1 liter
Now,
Let x be the liters of gasoline required for a 700-km trip.
⇒ 20/200 = x/700
⇒ (200) (x) = (20) (700)
⇒ 200x = 14,000
⇒ 200x/200 = 14,000/200
or, x = 70
Therefore, the answer is :
70 liters of gasoline will be needed for a 700 kilometer of trip.
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What is the last step when finding the area of a compound shape?
Answers
Using the formula then calculator to get the ans and we must never forget to write the unit in squared form.
Find the length of the hypotenuse
on a right triangle with legs of 15
Inches and 7 Inches. NEED ANSWER NOW!!!
Answers
How much would a man who weighs 50 pounds on the moon weigh on Earth?