Answer:
0.5152
Step-by-step explanation:
Point A is at (5, 6) on the coordinate plane. It is reflected over the y-axis to create point B. Point A is then reflected over both axes to create point C. What is the area of the triangle that results from connecting the three points?
The area of the triangle which is formed as described is; 60.
What is the area of the triangle formed?According to the task content, when Point A(5,6) is reflected over the y-axis, the point B formed is; (-5,6) and when reflected over both axis, the point C formed is; (-5,-6).
It therefore follows that the length of segments AB and BC which represents the base and height of the triangle formed are; 10 and 12 respectively.
Therefore, the area of the triangle is; (1/2) × 10 × 12 = 60.
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The function f and g are given by [tex]f(x)=x^2[/tex] and [tex]g(x)=-^1_2 x+5[/tex].
Let R be the region bounded by the x-axis and the graphs f and g as shown at the bottom. Also, I only need you to answer part b, I've already finished part a.
a) Describe how you would find the area of R.
[tex]R=18 \frac{2}{3}[/tex]
b) The region R is the base of a solid. For each y, where
0 < y < 4, the cross-section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 3y. Explain how you would write an expression that gives the volume of the solid.
As you've pointed out, R is a different region that I originally thought. The area of R can be computed using either
[tex]\displaystyle \int_0^2 x^2 \, dx + \int_2^{10} -\frac x2 + 5 \, dx[/tex]
or
[tex]\displaystyle \int_0^4 (10-2y)-\sqrt y \, dy[/tex]
Either way, you've gotten the correct area for part (a).
For part (b), we can use part of the integral with respect to [tex]y[/tex] above. The horizontal distance between the curves [tex]y=x^2[/tex] and [tex]y=-\frac x2+5[/tex] is obtained by first solving for [tex]x[/tex],
[tex]y=x^2 \implies x=\sqrt y[/tex]
[tex]y=-\dfrac x2+5 \implies x = 10-2y[/tex]
so the length of each cross section is [tex]10-2y-\sqrt y[/tex].
The height of each cross section is [tex]3y[/tex].
Then the volume of the solid is
[tex]\displaystyle \int_0^4 3y \left(10-2y-\sqrt y\right) \, dy = \boxed{\int_0^4 -6y^2 + 30y - 3y^{3/2} \, dy}[/tex]
The instructions don't say to evaluate, but if you're looking for practice the volume ends up being 368/5, or 73 3/5.
Calculate the probability for the following situation, then select the correct answer:
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a head AND an odd number on the die AND a card greater than 6 (assume the ace is equal to 1) from the deck?
The probability is P = 0.135
How to find the probability?
First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.
P(head) = 1/2P(odd number) = 3/6 (there are 3 odd numbers on the dice)P(card greater than 6) = 28/52 (28 cards with numbers larger than 6).The joint probability is given by the product between the individual probabilities, so we get:
P = (1/2)*(3/6)*(28/52) = 0.135
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x+11=35 solve on algebraic equation
Answer:
x = 24
Step-by-step explanation:
x + 11 = 35
x = 35 - 11
x = 24
x+11=35
Subtract 11 on both sides.
x=35−11Subtract 11 from 35 to get 24.
x=24 === AnswerI need help with this geometry problem see the image
The coordinate of each point is just the number it corresponds to.
a) 6
b) -5
c) 9
d) 0
How many pounds are in112 ounces? Enter only the number. Do not include units.
There are 7 pounds in 112 ounces
How to determine the number of pounds?There is 1 pound in 16 ounces
So, the number of pounds in 112 ounces is
Pounds = 116 ounces/16 ounces
Remove the unit
Pounds = 112/16
Evaluate the quotient
Pounds = 7
Hence, there are 7 pounds in 112 ounces
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Please help me with this problem literally so desperate right now.
Answer: 13 inches by 2 inches
Step-by-step explanation:
26 can be made by:
1 x 26
2 x 13
There are only 2 possibilities for the dimensions.
2 x 3 + 7 is 13, which fits the requirements.
Which means, the length is 13 and the width is 2.
Which point is on the graph of f(x) = 5*?
O A. (0, 5)
O B. (0, 0)
• C. (5, 1)
O D. (1, 5)
Answer is (1,5)
The point that is on the graph of the function [tex]F(x) = 5^x[/tex] is given by:
D. (1,5).
Which points are on the graph of the function?The function is defined by:
[tex]F(x) = 5^x[/tex]
When x = 0, [tex]F(x) = 5^0 = 1[/tex], hence point (0,1) is on the graph of the function.
When x = 1, [tex]F(x) = 5^1 = 5[/tex], hence point (1,5) is on the graph of the function, which means that option D is correct.
When x = 5, [tex]F(x) = 5^5 = 3125[/tex], hence point (5,3125) is on the graph of the function.
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Micheal solved this inequality as shown: step 1: -6(x + 3) + 10 < -2 step 2: -6x - 18 + 10 < -2 step 3: -6x - 8 < -2 step 4: -6x < 6 step 5: x > -1. what property justifies the work shown between step 3 and 4?
================================================
Explanation:
These are the steps to focus on
step 3: -6x - 8 < -2
step 4: -6x < 6
The move from the third step to the fourth step has us adding 8 to both sides. Therefore, we use the addition property of inequality.
That property has four forms
If [tex]a > b[/tex] then [tex]a + c > b+c[/tex]If [tex]a < b[/tex] then [tex]a+c < b+c[/tex]If [tex]a \ge b[/tex] then [tex]a + c \ge b+c[/tex]If [tex]a \le b[/tex] then [tex]a+c \le b+c[/tex]It's similar to the idea of starting with a = b, then adding c to both sides to get a+c = b+c
We add the same thing to both sides to keep things balanced.
A truack Cars a load of 50 boxes 50 men are 20kg boxes and the rest and 25 ка Boxes. Is the Total weight of all Boxes is 1175 kg. How many of each type are there? X = 50kg Y=20kg 2= 25kg then sum of that is 1175 kg
The number of boxes with 20kg = 15
The number of boxes with 25 kg = 35.
How to estimate the value of X and Y?
To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Total weight of all boxes = 1175kg
Total number of boxes = 50
X + Y = 50........................(1)
20X + 25Y = 1175 .............(2)
(1) [tex]\times[/tex] 20
20 (X + Y = 50)
20X + 20Y = 1000 .............(3)
Subtracting (3) from (2), we get
20X + 25Y = 1175 -
20X + 20Y = 1000
--------------------
5Y = 175
Y = 175/5
Y = 35
Substitute the value of y in (1), then we get
X + Y = 50
X + 35 = 50
X = 50 - 35
X = 15
The value of X = 15 and Y = 35
Number of boxes with 20kg = 15
Number of boxes with 25 kg = 35.
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simplify (2+3)2 + 8/2
Answer
[tex]2 \times 2 + 6 \times 2 + \frac{8}{2 } [/tex]
[tex]4 + 12 + 4[/tex]
[tex]16 + 4[/tex]
[tex]20[/tex]
Factor f(x) =3x^2+23x^2-35x+9 into linear factors given that -9 is a zero of f(x).
Using the Factor Theorem, the function factored into linear factors is given as follows:
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
-9 is a zero of f(x), hence [tex]x_1 = -9[/tex] and:
3x³ + 23x² - 35x + 9 = (x + 9)(ax² + bx + c)
ax³ + (b + 9a)x² + (9b + c)x + 9c = 3x³ + 23x² - 35x + 9
The coefficients are given as follows:
a = 3.9c = 9 -> c = 1.b + 9a = 23 -> b = -4.Hence:
3x³ + 23x² - 35x + 9 = (x + 9)(3x² - 4x + 1)
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
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There are 32 orange flavoured and a few grape flavoured candies in a jar. The probability of getting a grape flavoured candy randomly from the jar is. Determine the numbers of candies in the jar.
According to Jaxs pedometer, he walked 2.783 km while taking care of the livestock in the morning and 3.124 km taking care of the livestock in the evening.
How far did Jax walk while taking care of the livestock today?
Answer:
5.907 km
Step-by-step explanation:
2.783 km + 3.124 km = 5.907 km
1. Pretend that in a certain city the number of new cases of a virus was reported to be 800 new cases on Sunday. Let’s pretend that the number of new cases grows by 15% on Monday, grows by 5% on Tuesday, and then falls 10% on Wednesday, and finally falls again 10% on Thursday.
a. What will the number of new cases be on Thursday after all of this growth and falling?
The number of new cases be on Thursday after all of this growth and falling is 956.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
There are initially 800 cases, hence:
Number of cases on Monday = 1.15 * 800 = 920
Number of cases on Tuesday = 1.05 * 920 = 966
Number of cases on Wednesday = 0.9 * 966 = 869.4
Number of cases on Thursday = 1.1 * 869.4 = 956.34
The number of new cases be on Thursday after all of this growth and falling is 956.
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What is the equation of the line that is perpendicular to the line defined by the equation 2y=3x+2 and goes through the point (3,2)
The equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]
Equation of perpendicular linesThe equation is defined by 2y = 3x + 2
Rewrite the equation in the form y = mx + c
[tex]y=\frac{3}{2}x + 1[/tex]
The slope, m = 3/2
The y-intercept, c = 1
The equation perpendicular to the given line will be of the form:
[tex]y-y_1=\frac{-1}{m}(x-x_1 )[/tex]
Substitute [tex]x_1=3, y_1=2, and m=\frac{3}{2}[/tex] into the equation above
[tex]y-2=\frac{-2}{3} (x-3)\\\\y-2=-\frac{2}{3}x+2\\\\y=-\frac{2}{3}x+4[/tex]
Therefore, the equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]
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Chandra invests $75 every month at 4.8%/a compounded monthly for 8 years. What is the total amount of
Chandra's investments after 8 years?
The total amount of Chandra's investments after 8 years exists at $110.03 Compound interest.
How to estimate the total amount of Chandra's investments after 8 years?The formula for calculating the compound interest exists described as;
[tex]A = P(1+r/n)^{nt[/tex]
where, P is the amount invested = $75
r be the rate. = 0.048
t be the time = 8 years
n = 12 (monthly)
Substitute, the values in the above equation, then we get
[tex]$A = 75(1+0.048/12)^{96[/tex]
A = 75(1.467)
A = 110.03
Hence the total amount of Chandra's investments after 8 years is $110.03 Compound interest.
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which equation is represented by the graph below a. y=1/8ex b.y=1/2ex c.y=2ex. d.y=8ex
Todd and his friends are painting 5 equal sections of a wall. The wall is 10 feet tall, but its length is unknown.
Each section will be a different color, so they need to know the area of each section
1. Write an expression for the total area of the wall. Explain how you came up with your expression
The expression for the total area of the wall is 10x.
What is area of rectangle?
Let l be length and b be breadth of the rectangle.
Then the area is the product of length and breadth of the rectangle.
That is area = l* b
We can find the expression for the total area of the wall as shown below:
Let the total length of the wall be x.
Height=10 ft
Total area = Height*Length
Putting the value of length and breadth in the above formula.
Total area = 10*x
Total area = 10x
Hence, the expression for the total area of the wall is 10x.
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What is the value of x when (f o g)(x) =-8
Answer:
I think the answer is 3.
Step-by-step explanation:
First make arrow diagram of function f and g.
Then show it as composite function of fog(x) in arrow diagram.
Then in range you find -8 whose domain as x is 3.
The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?
(4, −7)
(−4, −7)
(4, 7)
(−4, 7)
Using translation concepts, it is found that the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Considering the translations, the equivalent point is found as follows:
x - 4 = 0 -> x = 4.y = 0 - 7 -> y = -7.Hence the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).
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A stairway rises 6 feet 4 inches over a horizontal distance of 8 feet 6 inches. What is the diagonal length of the stairway
Answer:
10.6 ft
Step-by-step explanation:
to find the diagonal length of the stairway we can use the pythagorean theorem or a^2 + b^2 = c^2
6'4" is also 6 1/3' or 19/3'
8'6" is also 8 1/2' or 17/2'
now square them both
361/9 + 289/4
make them have the same denominator
1444/36 + 2601/36
add them
4045/36
take the square root
10.6000524 is your answer
10.6 ft
Find the area of a triangle with legs that are: 16 m, 12 m, and 8 m.
Answer: 46.48 m²
Step-by-step explanation:
this question was answered already, go search it up
how many 150-pound gas cylinders are uesd each year at a 500 gpm well that fequires a chlorine dosage of 1.5 mg/L?
The number of 150-pound gas cylinders are used each year for the well is 22.
Total volume of gallons used per year
V = 500 gal/min x 1 year x 525600 min/year
V = 262,800,000 gallons = 994,806,216.835 liters
Mass of the gas cylindersmass = density x volume
mass = 1.5 mg/L x 994,806,216.835 L
mass = 1,492,209,325 mg = 3289.75 lb
number of gas cylinders usedn = 3289.75 lb/150 lb
n = 21.9
n ≈ 22 gas cylinders
Thus, the number of 150-pound gas cylinders are used each year for the well is 22.
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in fact, the cleanup will consist of ripping out all the walls and ceilings of an
The percentage discount from the base price result is 2.16%.
How to compute the value?Discount percent will be:
= (Base price - New price)/Base price × 100
= (9.40 - 9.20)/9.40 × 100
= 0.20/9.40 × 100
= 2.16%
The new price will be:
= Base price - (2.16% of base price)
= 9.40 - (2.16% × 9.40)
= 9.20
Therefore, the percentage discount from the base price result is 2.16%.
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Complete question:
A rodent infestation has left a landlord with a major cleanup job; in fact, the cleanup will consist of ripping out all the walls and ceilings of an 1860-square-foot house to replace them. A trip to the local home improvement store reveals that 4'x8' sheets of drywall have three price points as indicated in the table. Another consideration for the landlord is that he is equipped with only a humble half-ton pickup truck, that can hold at most 20 sheets. His truck sips fuel, so he considers only wear and tear on his vehicle at $5 to haul all the sheets he will use for the job. The holding percentage is 20%. The landlord believes the entire job - all walls and ceiling - will require 10,080 square feet of drywall.
Consider the $9.40 per sheet figure as the base price and use the information in Scenario 11.4 to answer the following question. What percentage discount from the base price results in an optimal order quantity of 101 sheets?
1.42%
2.16%
2.03%
1.86%
If you randomly selected a British Columbia ski resort, what is the probability that it will have an annual snowfall greater than 170 inches?
The probability that it will have an annual snowfall greater than 170 inches is 0.4.
How to compute the probability?The information is incomplete and the complete question wasn't found. An overview will be given. It should be noted that a probability means the likelihood of the occurence of an event.
Probability is calculated as:
= Number of ways of achieving success/Total number of possible outcomes
Let's assume that the total number of resort is 10 and those that have more than 170 inches are 4.
In this case, the probability will be:
= 4/10
= 0.4
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What is the equation of the rational function g(x) and its corresponding slant asymptote?
Rational function with one piece increasing from the left in quadrant 3 and passing through the point negative 3 comma 0 and going to the right asymptotic to the line x equals 2 and another piece increasing from the left in quadrant 3 asymptotic to the line x equals 2 and passing through the point 3 comma 0 and going to the right
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x plus 2 end quantity with a slant asymptote at y = x + 2
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x minus 2 end quantity with a slant asymptote at y = x + 2
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x plus 2 end quantity with a slant asymptote at y = x – 2
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x minus 2 end quantity with a slant asymptote at y = x – 2
The solution to the Questions are
The alternate hypothesis demonstrates that there are two possible outcomes for the test.Decision rule: If z > 2.05 or z<-2.05, reject H0z=2.59The two-tailed nature of the test is shown by the alternative hypothesis.The result of the test yields the following P-value: 0.0096What is the alternate hypothesis?(a)
The alternate hypothesis demonstrates that there are two possible outcomes for the test.
(b)
Here we have
[tex]n_{1}=40,\\\\ \bar{x}_{1}=102,\sigma_{1}=5,n_{2}=50,\bar{x}_{2}=99,\sigma_{2}=6[/tex]
(b)
Here the test is two-tailed. So for [tex]\alpha =0.04[/tex], the critical values of the z-test are -2.05 and 2.05.
Decision rule: If z > 2.05 or z<-2.05, reject H0
(c)
Test statistics will be
[tex]z=\frac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}} \\\\\\z=\frac{(102-99)-(0)}{\sqrt{\frac{5^{2}}{40}+\frac{6^{2}}{50}}}[/tex]
z=2.59
(d)
The two-tailed nature of the test is shown by the alternative hypothesis.
(e)
The result of the test yields the following P-value: 0.0096
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Theo solved the following problem correctly for homework.
2 x + y = 7. Negative 3 x + y = 2.
What is the y-coordinate of his solution?
y = negative 3
y = negative 1
y = 1
y = 5
Answer:
y=5
Step-by-step explanation:
OK, let see, 2x+y=7, –3x+y=2:
[tex]2x + y = 7 \\ - 3x + y = 2 \\ we \: need \: to \: solve \: the \: equation \: so \\ - 2x - y = - 7 \\ - 3x + y = 2 \\ - 5x = - 5 = = > x = 1 \\ 2(1) + y = 7 = = = > y = 5[/tex]
Someone help me with this question!
Answer: [tex]160^{\circ}[/tex]
Step-by-step explanation:
By the exterior angle theorem,
[tex]4x-14+5x-182=5x-100\\\\9x-196=5x-100\\\\4x=96\\\\x=24\\\\\implies m\angle BCD=20^{\circ}\\\\\implies m\angle BCA=160^{\circ}[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Angle BCA = 160°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
By Exterior angle property :
[tex]\qquad❖ \: \sf \:4x - 114 + 5x - 182 = 5x - 100[/tex]
[tex]\qquad❖ \: \sf \:9x -29 6 = 5x - 100[/tex]
[tex]\qquad❖ \: \sf \:9x - 5x = - 100 + 296[/tex]
[tex]\qquad❖ \: \sf \:4x = 96[/tex]
[tex]\qquad❖ \: \sf \:x = 24 \degree[/tex]
Next, Angle BCA = 180° - Angle BCD
( linear pair )
[ let angle BCA = y ]
[tex]\qquad❖ \: \sf \:y = 180 - (5x- 100)[/tex]
[tex]\qquad❖ \: \sf \:y = 180 - (5(24) - 100)[/tex]
[tex]\qquad❖ \: \sf \:y = 180 - (120 - 100)[/tex]
[tex]\qquad❖ \: \sf \:y = 180 - 20[/tex]
[tex]\qquad❖ \: \sf \:y = 160 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Angle BCA = 160°This table shows how many students from two high schools attended a
football game
Attended the game
Total
Did not attend
the game
90
Westville
60
150
North Beach
110
90
200
Total
170
180
350
A student is randomly selected.
What is the probability that a student attended the game, given that the
student is from North Beach? Round your answer to two decimal places,
O A. 0.57
B. 0.48
C. 0.55
OD. 0.65
The probability that a student attended the game, given that the student is from North Beach is 0.65.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a student attended the game, given that the student is from North Beach = number of North beach students that attended the game / total number of students who attended the game
110 / 170 = 0.65
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