The area of the shaded region in the first quadrant is: 0.75 units
What is area under a curve?The area under a curve between two points can be found by doing a definite integral between the two points.
Now,
Given:
x = 0, y = 2Curve: y = 3x - x²To find: area bounded by the given lines and curve in the first quadrant.
Finding:
Now, according to the question, the lines x = 0 and y = 2 intersect at the point (0,2).
Point of Intersection of y = 2 and y = 3x - x²:
2 = 3x - x²
=> x² - 3x + 2 = 0
=> (x - 2)(x - 1) = 0
That is, the line and the curve intersect at two points: ( 1 , 2) and (2,2). But the point that is of our importance is only (1,2).
Thus, area shaded = [tex]\int\limits^1_0 {2 - 3x +x^{2}} \, dx[/tex] = 0.75 square units.
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(COMPLETE QUESTION:
What is the area in the first quadrant bounded by y=3x-x³ and the lines x=0, y=2?)
please help will give brainlist
A scale drawing of a rectangular park is 6 cm wide and 10 cm long. The actual park is 180 meters wide. What is the area of the actual park in square meters?
The area of the actual park in square meters will be 54000m².
How to calculate the area?The length of the actual park will be:
= 180/6 × 10
= 300m
Width = 180m
Therefore, the area will be:
= Length × Width
= 300 × 180
= 54000 m²
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What did I do wrong ? Question is 7x + 5 = 6x
Answer: Look at the explanation.
Step-by-step explanation: So first you move the 6x to the left side of the equal sign, then u turn it into a negative number. Next, you do 7x-6x=5. Which is 2x=5. And to find x you do 5÷2. Which is 2.5.
Hope this helps!
Answer:
x = -5
Step-by-step explanation:
Let's solve the problem,
→ 7x + 5 = 6x
→ 7x - 6x = -5
→ [ x = -5 ]
Hence, the answer is -5.
3. In Mrs. Middleton's math class, there are 7 more boys than girls. If there are 29 total students in the class, how many boys are there?
Convert the word problem into an equation as follows:
Let's use the variable 'x' for girls and 'x+7' for boys.
x + x + 7 = 29
Combine like terms
2x + 7 = 29
Subtract 7 from both sides
2x = 22
Divide 2 into 22 to get x
x=11 girls
x+7 = 18 Boys
phone numbers consist of 10 digits. how many phone numbers are possible in wilmington? 10000000 how many phone numbers are possible in wilmington if the number 7 cannot be used? 4782969 how many phone numbers are possible in wilmington if they must be divisible by 2 or 5? how many phone numbers are possible in wilmington if there are no repeated digits?
The phone numbers that are possible in Wilmington are 10000000. The phone numbers possible in Wilmington if the number cannot be used is 4782969. The phone numbers are possible in Wilmington if they must be divisible by 2 or 5 are 6000000. The phone numbers are possible in Wilmington if there are no repeated digits are 5040.
What is a digit?A positional numeral system uses a single symbol, a numerical digit, to represent numbers. The word "digit" refers to the ten decimal (old Latin adjective decem meaning "ten") digits, which are the equivalent of the ten symbols used in the conventional base-10 numeral system. The word "digit" comes from the Latin word "digiti," which means "fingers."
The absolute value of the base determines the required number of different digits for a given numeral system with an integer basis. For instance, the base-10 decimal system requires ten digits (0 through 9), whereas the base-2 binary system just needs two digits (0 and 1).
Explanation:
The number after area code is of 7 digits.
a) [tex]10^{7} =10000000[/tex]
b) [tex]9^{7} =4782969[/tex]
c) X X X X X X X
I I I I I I I
10 10 10 10 10 10 0,2,4,6,8,5,i.e,6digits are possible
=[tex]10^{6} x6=6000000[/tex]
d)7!
=5040
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8 + 3 (-s + 2 ) -5s - 1 - 4s
Answer:
13 - 12s
Step-by-step explanation:
= 8 - 3s + 6 - 5s - 1 - 4s
= 13 - 12s
Answer:
8+3=11
(-s + 2) - 5s - 1 - 4s = -10s + 1
I don’t know what to do
Answer:
8 - positive
9- no correlation
10- negative
11- positive
12- No correlation
13- negative
14- no correlation
15- no correlation
Step-by-step explanation:
8- Positive because the more hours a person has driven, the more number of miles he/she drives increases.
9- the number of siblings a student has should not affect the grade they have in math class
10- negative because as a car gets older, the value decreases
11- positive because the longer a cd is out the more sales they get
12- In a logical sense, it could be positive, because someone who dropped out of highschool will get paid less than someone who went to school for 18 years and graduated with a hs diploma. it can also mean no correlation. therefore I think it is positive.
13- negative because the more songs someone downloads, the more the ipods space decreases
14- no correlation, the amount of computers in your house does not change how much you message your friends
15- no correlation, your house can be 3 years old and have 5 people living in it
suppose electric power is supplied from two independent sources which work with probabilities 0.4, 0.5, respectively. if both sources are providing power enough power will be available with probability 1. if exactly one of them works there will be enough power with probability 0.6. of course, if none of them works the probability that there will be sufficient supply is o.
Answer:
What is the question
Step-by-step explanation:
What is the equation for the line that passes through the points (-4,-4) and (8,5)
Answer:
y = 3/4 x - 1
Step-by-step explanation:
We can use the point-slope form of the equation of a line.
y - y_1 = (y_2 - y_1)/(x_2 - x_1)(x - x_1)
y - (-4) = (5 - (-4))/(8 - (-4))(x - (-4))
y + 4 = (9/12)(x + 4)
y + 4 = (3/4)(x + 4)
y + 4 = (3/4)x + 3
y = (3/4)x - 1
What is the sum?I need help right now!!!
Answer:
12
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
BODMAS
start with solving 2^2 which is similar to 2×2 you get 4
2^2=4
4+3 =7
Find The Domain Find the Value
1a) The domain is a set of all real numbers not equal to 5
1b) The domain is a set of all real numbers not equal to 4
What is the domain of the function?
Domain of a function is the set of all possible input values that make the function defined.
1a) We are given the function;
C(x) = -3²/(x - 5)
The domain will be a set of values that makes the denominator not equal to zero. Thus;
The domain is a set of all real numbers not equal to 5
1b) The function is; R(x) = 4x/(3x - 12)
The domain will be a set of values that makes the denominator not equal to zero. Thus;
The domain is a set of all real numbers not equal to 4
2a) Function is;
f(x) = (x + 8)/(2x - 1)
f(2) = (2 + 8)/(2(2) - 1)
f(2) = 10/3
f(0) = (0 + 8)/(2(0) - 1)
f(0) = -8
f(-1/2) = (-1/2 + 8)/(2(-1/2) - 1)
f(-1/2) = -15/4
2b) Function is;
r(t) = (t² + 8)/(t³ - 25t)
r(3) = (3² + 8)/(3³ - 25(3)) = -17/48
r(2) = (2² + 8)/(2³ - 25(2)) = -12/42 = -2/7
r(-1) = ((-1)² + 8)/((-1)³ - 25(-1)) = 9/24 = 3/8
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your cousin has $156.34 in his bank-
account. He withdraws $15.50 one day
and B 6.75 the next day how much
money is in his bank accout now ?
Answer:
$134.09
Step-by-step explanation:
you take 156.34 and minus 15.50, then you take that and minus it by 6.75
Answer $134.09
why 156.34 - 15.50+6.75=134.09
Mike walked 5 blocks in 15 minutes.how many minutes did it take for him to walk one block?
Find the distance between the two points in simplest radical form (0,-7)(-9,5)
Step-by-step explanation:
1111111111111111111111
three friends ate at restaurant. They ordered nachos for S19 95 and jalapeno poppers. Each friend paid $9.73, not including sales tax or tip, which was 1/3 of the total determine the cost of the jalapeno poppers
The total cost of a Jalapeno is $ 9.24
Three friends ate at a restaurant and ate nachos for $19.95 and jalapeno poppers.
Three of them paid $9.73 each
So the total amount of money paid by three friends = 3×9.73
= 29.19
Now we have to calculate the cost of jalapeno poppers
Therefore we have,
Total amount of money paid = cost of nachos + cost of jalapeno poppers
29.19 = 19.95 + cost of jalapeno poppers
The cost of jalapeno poppers =29.19 - 19.95
= $9.24
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Answer: The cost is $9.24 for the peppers.
Step-by-step explanation: Just do math.
Describe the approximate shape of a distribution using the terms approximately
symmetric
bell shaped
screwed Left
screwed right
uniform
bimodal
The type of distributions represented by the given graphs in the question are as follows;
(a) Symmetric
(b) Bimodal
(c) Skewed right
(d) Uniform
(e) Skewed right
What are the types of distributions represented the graphs?The definition and descriptions of the given terms are;
Approximately; The term is used to describe the state of things which is close to an actual thing or situation.
Symmetric; A distribution is symmetric when the area of the side on the left and on the right of the mean are equal and balance each other.
The distribution represented by the first figure, (a), can be described as a symmetric distributionBell shaped; A distribution that has a bell shaped graph, which usually represents a normal distribution, can be described as a bell shaped distribution.
The graph in option (a) can be described as a bell shaped distributionSkewed left; The graph of a distribution is skewed left if it has a tail (smaller values) on the left of the graph
Skewed right; The graph of a distribution is skewed right if the tail is on the right of the graph.
The distributions represented by the graphs in (c) and (e) are right skewedUniform; A distribution is uniform if the shape of the graph is approximately rectangular.
The distribution in graph (d) is a uniform distributionBimodal; A distribution that has two peaks is said to be a bimodal distribution.
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1 3 Given the resting heartrates below, determine the best measure of variability and calculate it. Heartbeats 48 55 60 61 62 63 64 65 66 66 68 70 70 71 71 72 74 74 75 76 77 77 78 79 81 86
The best measure to determine the variability is mean which is equal to 69.48
We are given the data:
48, 55, 60, 61, 62, 63, 64, 65, 66, 66, 68, 70, 70, 71, 71, 72, 74, 74, 75, 76, 77, 77, 78, 79, 81 and 86
The best measure to determine the variability is mean.
Total number of observations = 26
Sum of observations (S) will be:
S = 48 + 55 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 66 + 68 + 70 + 70 + 71 + 71 + 72 + 74 + 74 + 75 + 76 + 77 + 77 + 78 + 79 + 81 + 86
S = 1809
Mean = Sum / total
Mean = 1809 / 26
Mean = 69.58
Therefore, the best measure to determine the variability is mean which is equal to 69.48
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If the average of x and y is 11 and the average of x, and y z is 5 what is the value of z
If the average of x and y is 11 and the average of x, y and z is 5, then the value of z is -7
Given,
The average of x and y = 11
We know average = Sum of the terms / Number of terms
Then, the equation will become
[tex]\frac{x+y}{2}=11[/tex]
x+y =11×2
x+y =22
Average of x, y and z = 5
[tex]\frac{x+y+z}{3}=5[/tex]
x+y+z = 5×3
x+y+z =15
Substitute the value of x+y
22+z=15
z =15-22
x = -7
Hence, If the average of x and y is 11 and the average of x, y and z is 5, then the value of z is -7
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what is the range of the function on the graph? i’m
Answer: y∈(-∞,3]
Step-by-step explanation:
[tex]y=-|x+1|+3[/tex]
Tong draws 5 cards from a deck of 52 cards (which has 13 spades) without replacement. what is the probability of getting at most 2 spades?
As per the question, without replacement draw 5 cards from a deck of 52 playing cards. The probability to draw 5 cards can be written as:
[tex]P(getting2 spades) = \frac{P(E)}{n(E)} = \frac{13X12}{52X51} =\frac{1}{17}[/tex]
Therefore, the probability of getting at most two spades is [tex]\frac{1}{17}[/tex].
What is probability?
Probability is the method to measure the occurred events or the occurrence of the events. It is also used to analyze the outcomes of random events. To calculate the probability of a playing card which is [tex]52[/tex] in numbers. And it is divided into fours cards and each are in the count of [tex]13[/tex].These fours cards are heart, spades, diamond and club.
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Find the total amount given the original price and tax rate. round to the nearest hundredth if necessary. original price: $123.28 tax rate: 7.5% enter the correct answer in the box.
The Total amount to pay including the tax will be $132.52
In the given question, For the Total amount, we know that we have to add the Tax rate to the Principal amount. It is mentioned that the Principal amount P = $123.28 and the Tax rate is 7.5%. Firstly we have to calculate what amount of interest is to be charged upon the Principal amount. To calculate Interest we have the formula :
=> I = (P * R)/100 , where I = Interest, P = Principal Amt, R = Interest Rate
=> I = (123.28 * 7.5)/100 => I = 9.24
We get Interest amount = $9.24
To calculate the Total amount, We have the formula: T = P + I
where, T = Total Amount, P = Principal Amount, and I = Interest Amount
=> T = 123.28 + 9.24 => T = 132.52
Hence, the Total Amount is $132.52
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Venus has switches at the top and bottom of her stairs to control the light for the stairwell. She notices that when the upstairs switch is up and the downstairs switch is down, the light is turned on.
c. If the upstairs switch is in the down position and the downstairs switch is in the up position, will the light be on?
If the upstairs switch is in the down position and the downstairs switch is in the up position, the light will be off
How to determine if the light will be on?The given parameters are
Switches = 2 i.e. top and bottom
Also, we have:
When the upstairs switch is up and the downstairs switch is down, the light is turned on.
This means that the light is only on when the upstairs switch is up and the downstairs switch is down
Any other position of the switches, the light is off
From the question, we have
Upstairs switch is in the down position and the downstairs switch is in the up position
This is different from the required position to on the light
Hence, the light will be off
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jaylon created this stained glass window the upper two coners are quater ciecleseach with a radius of 4 inches. find the area of the window
The area of the window is 305.12 square inches.
How to find the area of the window?given that
jaylon created this stained glass window the upper two coners are quater ciecleseach with a radius of 4 inches.
The window's area is equal to the sum of the areas of a rectangle, two quarter circles, and the smaller square between the two upper corners.
The quantity of space occupied by a flat surface with a specific shape is referred to as the area.
now, find the area of rectangle
A = length x breadth
A = 12 x (26-4)
A = 12 x 22
A = 264 square inches
find the area of the two quarter circle
[tex] A= 2( \frac{1}{4} (3.14) \times {4}^{2} ) \\ A = 25.12 {in}^{2} [/tex]
Find the area of the smaller square between the two upper corners
A = (12-8) (4)
A = 4 x 4
A = 16 sq.in
now, find the total area
A = 264 + 25.12 + 16
A = 305.12 square inches
Hence, the area of the window is 305.12 square inches.
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Translate this sentence into an equation.
48 is the difference of Vidya's height and 19.
Use the variable v to represent Vidya's height.
The answer for the given question is 67.
An equation is a mathematical statement made up of two expressions connected by an equal sign. 2x - 4 = 16 is an example of an equation. We get the value of the variable x as x = 10 after solving this equation.
Coefficients, variables, operators, and constants are all components of an equation.
An equation is formed by joining two expressions with an equal sign ("=").. The two expressions on either side of the equals sign are referred to as the equation's "left-hand side" and "right-hand side" The right-hand side of an equation is usually assumed to be zero. This will not reduce generality because we can balance it by subtracting the right-hand side expression from the expressions on both sides.
Let x be Vidya's height.
The equation will be determined by the given conditions:
x – 19 = 48
move the variable to the equation's left side:
x = 48 + 19
x = 67
Hence, the correct value for the given question is 67
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the probability that a carton of eggs taken from the cooler at a store will have at least one cracked egg is 2.5%.2.5%. what are the odds that a carton of eggs will have at least one cracked egg?
The odds that a carton of eggs will have at least one cracked egg is 97.5 %
The question has to do with probability
What is probability?Probability is the likelihood for an event to occur. It is given by P(event) = number of required outcomes/total number of possible outcomes.
How to find the odds that a carton of eggs will have at least one cracked egg?Given that the probability that a carton of eggs taken from the cooler at a store will have at least one cracked egg is 2.5%. Let the probability of at least one cracked egg be P(egg ≤ 1) = 2.5% = 0.025
Now, since we require the probability of that a carton of eggs will have at least one cracked egg, that is the number of cracked is greater than 1.
Let the probability of cracked eggs greater than 1 be P(egg ≥ 1).
From the law of probability
P(egg ≤ 1) + P(egg ≥ 1) = 1
So, P(egg ≥ 1) = 1 - P(egg ≤ 1)
P(egg ≥ 1) = 1 - 0.025
P(egg ≥ 1) = 0.975
P(egg ≥ 1) = 0.975 × 100 %
P(egg ≥ 1) = 97.5 %
So, the odds that a carton of eggs will have at least one cracked egg is 97.5 %
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Keisha read 8 pages in her book each day for 5 days. Then, she r How many total pages did Keisha read?
Answer:
40
Step-by-step explanation:
Solve for c.
a(c- b) = d
a. c = ab-d/a
b. c = d+ab/a
c. c = d-ab/b
d. c = d-ab/a
Answer:
a(c-b)=d
we open the bracket i.e expand it
ac-ab=d
make c the subject formula to get your answer
ac=d+ab
c=d+ab/a
If a number is "squared" that means it
is raised to the
______ power.
1. 1st
2. 2nd
3. 3rd
4. square root
5. none of the above
Answer:
2nd power
Step-by-step explanation:
3rd is cubed and 1st is: example 3^1 = 3
square root is √
AAah! This is my third time aaasking pleeease. Why am I being ignored.
The value of x in the figure is 4
How to determine the value of x in the figure?From the attached figure, we have the following parameters:
DE = x + 1
BC = 4x - 6
The triangles ADX and ABC are similar triangles
Based on the representation of the sides, we have:
BC = 2 * DE
So, we have
2 * (x + 1) = 4x - 6
Expand
2x + 2 = 4x - 6
Evaluate the like terms
2x = 8
Divide by 2
x = 4
Hence, the value of x in the figure is 4
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Solve. 4n - 6 (n + 1) > 12 (first blank is the inequality sign, second blank is the value) n
The solution to the inequality is: n < -9.
How to Solve an Inequality?Given the inequality statement, 4n - 6 (n + 1) > 12, to solve for the value of n, we would isolate the n to one side of the inequality as shown below:
4n - 6 (n + 1) > 12
Distribute
4n - 6n - 6 > 12
Combine like terms
-2n - 6 > 12
-2n - 6 + 6 > 12 + 6
-2n > 18
Divide both sides by -2
-2n/-2 < 18/-2
n < -9
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