A carpenter is assigned a job of installing a spa into a pre-existing deck. The dimensions of the deck are (6x + 1) wide by (4x - 3) long. The dimensions of the spa are (4x + 5) wide by (x + 6) long.
Write the polynomial that represents the remaining area of the deck after the carpenter cut the hole out for the spa.
A prism measures base 15cm. Height 100mm. Length 40cm. Calculate volume of prism cm3
is 5 a solution to the equation 2x^2 + 10 = 60 yes or no
Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. 2, 9, 16, 23
The rarest form of dichromatism is _____.?
a. ?protanopia
b. ?deuteranopia
c. ?tritanopia
d. ?fruitopia
The rarest form of dichromatism is tritanopia. This condition affects the perception of blue and yellow colors and is less common than protanopia and deuteranopia which affect red and green perception respectively.
Explanation:The rarest form of dichromatism is tritanopia. The term dichromatism refers to an abnormality in color vision where an individual can only perceive two of the three primary colors. This question is related to the broader topic of color vision deficiencies, a study within biology. Among the options listed, protanopia and deuteranopia tend to be the most common color vision deficiencies, both affecting the perception of red and green respectively. Tritanopia is a condition that impacts the ability to perceive blue and yellow and is the least common form, while 'Fruitopia' is not related to this topic as it's a brand of fruit drinks.
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Hydraulicists often express rainfall in acre-feet. this is the amount of water required to cover an area of one acre to a depth of one foot. there are 640.0 acres in a square mile, and 5280 feet in one mile. how many cubic feet are there in one acre-foot?
Answer:
1 acre foot = 43560 ft³
Step-by-step explanation:
1 square mile = 640 acres.
5280 feet = 1 mile
5280 x 5280 ft² = 640 acres.
1 acre = 43560 ft².
1 acre foot = 43560 x 1 ft³ = 43560 ft³
1 acre foot = 43560 ft³
A continuous random variable is a random variable that can: ?assume any value in one or more intervals ?assume no continuous random frequency ?have no random sample ?assume only a countable set of values
A continuous random variable can assume any value within one or more intervals and result from measurements, providing an uncountable range of possibilities. Continuous random variables are commonly used in many fields, including reliability engineering and standardized testing, to assess continuous data.
A continuous random variable is a type of random variable that can assume any value within one or more intervals. Unlike discrete random variables, which take on countable values, continuous random variables result from measurements rather than counts. For instance, the temperature of a day measured by a thermometer or the height of students measured by a ruler are examples of continuous random variables. The values are uncountable as they lie on a continuum, like the speed of an automobile or the duration of a telephone call.
Two main characteristics of a discrete probability distribution function include the fact that each probability must be between zero and one, inclusive, and the sum of the probabilities should equal one. These rules do not apply to continuous random variables, which instead use probability density functions to describe their distributions.
Continuous random variables play significant roles in numerous applications such as assessing baseball batting averages, calculating IQ scores, and evaluating SAT scores. In the field of reliability engineering, a variety of continuous random variables are essential for analyzing the life expectancy of components.
Ray and lilli are designing their own shoes. They have 4 color options for the base and 6 color options for the accent. They can also pick 2 fonts for the embroidery. What is the probability that ray and lilli design identical shoes?
To solve this problem, let us first calculate the probability of designing one shoe out of all the combinations.
Probability of designing one shoe = (probability of choosing 1 color for the base) * (probability of choosing 1 color for the accent) * (probability of choosing 1 font for the embroidery)
We know that probability is:
Probability = number of chosen event / number of total events
Therefore:
Probability of designing one shoe = (1 / 4) * (1 / 6) * (1 / 2)
Probability of designing one shoe = 1 / 48
This means that either Ray or Lilli has this probability of designing a specific shoe. Since we are asked for the probability that they will both design this specific shoe, so we multiply:
Probability they will design the same shoe = (1 / 48) * (1 / 48)
Probability they will design the same shoe = 1 / 2304 = 4.34 * 10^-4
The probability is around 0.043% that they will design the same shoe.
a squared + b - c ÷ m , if a=6 , b= 8 ,c = 5 and m = 3. Is it 12 , 13, 14, or 15?
What is the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice?
The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The total number of probability is given as,
Total event = 6 x 6
Total event = 36
The samples are given as,
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Then the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be given as,
P = (4/36) + (11/36)
P = 15/36
P = 5/12
The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.
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Use the slope formula to find the missing coordinate. m =3/5 , P(3, 2) and Q(8,_)
Answer:
The missing coordinate is 5
Step-by-step explanation:
PLEASE HELP
If AD is median in triangle ABC and BD=24, then CD is:
24.
12.
6.
None of the choices are correct.
To solve this problem, let us first define what a median is. A median is a line segment that connects a vertex and the midpoint of the side opposite to that vertex.
In this case, the vertex is point A while the opposing side is side CB. Since it connects to the midpoint of CB, therefore this means that the median AD equally divides side CB into 2 parts. Since the length side CB is the sum of the lengths side CD and side BD. Therefore this means that:
length of CD = length of BD
length of CD = 24
Answer:
24
N a poisson probability problem, the rate of errors is one every two hours. what is the probability of at most three defects in four hours
The probability of having at most three defects in a four-hour period is approximately 0.8572.
The Poisson probability distribution is used to model the number of events that occur in a fixed interval of time or space, given the average rate at which the events occur. In this problem, the rate of errors is given as one error every two hours. We need to find the probability of having at most three defects in a four-hour period.
To solve this problem, we can use the Poisson probability formula, which is:
P(x; λ) = (e^(-λ) * λ^x) / x!
where P(x; λ) is the probability of having exactly x events occur in the given interval, λ is the average rate of events, e is the base of the natural logarithm, and x! is the factorial of x.
First, we need to calculate the average rate of events in a four-hour period. Since the rate is given as one error every two hours, we can calculate the rate for a four-hour period as follows:
Average rate = (4 hours) / (2 hours/error) = 2 errors
Now, we can plug this average rate (λ = 2) into the Poisson probability formula for x = 0, 1, 2, and 3 to find the probabilities of having at most three defects:
P(0; 2) = [tex](e^{(-2)} * 2^0)[/tex] / 0! ≈ 0.1353
P(1; 2) = ([tex]e^{(-2)} * 2^1[/tex]) / 1! ≈ 0.2707
P(2; 2) = [tex](e^{(-2)} * 2^2)[/tex] / 2! ≈ 0.2707
P(3; 2) = [tex](e^{(-2)} * 2^3)[/tex] / 3! ≈ 0.1805
To find the probability of at most three defects, we sum up these individual probabilities:
P(at most 3 defects) = P(0; 2) + P(1; 2) + P(2; 2) + P(3; 2) ≈ 0.8572
So, the probability of having at most three defects in a four-hour period is approximately 0.8572.
There are 65 people who want to go on a tea cups ride at an amusement park. There are 10 tea cups that each seat 4 people. How many people need to wait before they get to go on the ride?
Find the point on the line y = 3x + 2 that is closest to the origin.
The point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].
Given, [tex]y=3x+2[/tex], whose slope is [tex]3[/tex].
Let [tex]m[/tex] is the slope of the line perpendicular to the above line.
So,
[tex]3\times m=-1\\m=-1/3[/tex]
Then, the general equation of a line perpendicular line will be [tex]y=-1/3x+k[/tex].
So the equation line passing through the origin [tex](0,0)[/tex] and perpendicular to the line [tex]y=3x+2[/tex] is [tex]y=-1/3x[/tex] , [tex](k=0)[/tex].
Then the closest point will be the intersection point of these two lines, i.e.
[tex]3x+2=-1/3x\\9x+6=-x\\10x+6=0\\x=-0.6[/tex]
and
[tex]y=\dfrac{-0.6}{3} \\y=0.2[/tex]
Therefore, the point on the line [tex]y=3x+2[/tex] that is closest to the origin is [tex](-0.6, 0.2)[/tex].
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To avoid distortion of extreme values, a good indicator would be the A. mean. B. weighted-mean. C. mode. D. median
To avoid distortion of extreme values, a good indicator would be the
B. median.
42 out of 96 support a candidate in an office election what percent of the vote is that
divide
42/96 = 0.4375
0.4375*100 = 43.75 percent
round the answer as needed.
Patricia pays $1.19 each to download songs to her MP3 player,if n is the number of downloaded songs, which equation represents the cost C in dollars?
A.C=1.19n
B.n=1.19c
C.C=1.19/n
D.C=n+1.1
The net of a pyramid is shown below. The net of a square based pyramid, with base edges labeled 4 inches and the height of the triangle labeled 8 inches. The surface area of the solid is ____ square inches.
what is 795840000 in a scientific notation
The median for the given set of six ordered data values is 26.5. what is the missing value? 7 12 21 ____ 41 50
Answer:
The missing term is x=32.
Step-by-step explanation:
Given : The median for the given set of six ordered data values is 26.5.
To find : What is the missing value?
Solution :
The data set is 7 12 21 ?41 50
let the missing term or 4th term be x.
We know, The median of an even number is sum of nth term by 2 and nth+1 term by 2.
So, Applying median formula for even terms is
Term, [tex](\frac{n}{2},\frac{n}{2}+1)[/tex]
[tex](\frac{6}{2},\frac{6}{2}+1)=3^{rd},4^{th}[/tex]
The median is sum of 3rd and 4th term.
[tex]26.5=\frac{21+x}{2}[/tex]
[tex]53=21+x[/tex]
[tex]53-21=x[/tex]
[tex]32=x[/tex]
Therefore, The missing term is x=32.
If the median for the given set of six ordered data values is 26.5 then the missing value is 32.
The ordered set of data values is:
7, 12, 21,x, 41, 50
Given that the median is 26.5, it represents the middle value of the data set.
Since the set has six values, the median should be the average of the two middle values.
Let's assume the missing value is 'x':
7, 12, 21, x, 41, 50
We can see that 'x' should be the fourth value to maintain the ascending order.
Now, we need to find the value of 'x' that makes the median equal to 26.5.
To calculate 'x', we can set up the equation:
(21 + x) / 2 = 26.5
Multiply both sides by 2:
21 + x = 53
Subtract 21 from both sides:
x = 32
Therefore, the missing value in the set is 32.
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Kholdy enterprises' outstanding bonds mature in 6 years, have a par value of $1,000, and make an annual coupon payment of $60. the market yield on the bond is currently 10%. what is the bond's price?
Consider the equation y=2x+5 . Create a table of five ordered pairs that satify the equation. What is the y-intercept of the equation? What is the x-intercept of the equation?
Answer:
five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)
y intercept is (0,5)
x intercept is (-2.5, 0)
Step-by-step explanation:
y=2x+5
To get 5 ordered pairs , plug in some random number for x and find out y
x y= 2x+5
-2 2(-2) + 5= 1
-1 2(-1) + 5= 3
0 2(0) + 5= 5
1 2(1) + 5= 7
2 2(2) + 5= 9
five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)
When x=0 , the value of y = 5
So y intercept is (0,5)
To find x intercept we plug in 0 for y
y=2x+5
0 = 2x +5
subtract 5 from both sides
-5 = 2x
divide by 2 on both sides
x= -5/2
so x intercept is (-2.5, 0)
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager?
Answer:
3181 yards.
Step-by-step explanation:
All the given information can be used to draw a simple diagram. The diagram shows a triangle which is formed by the ships. There are two angles given and one side is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:
sin V / v = sin G / g.
It can be observed that the angle V is unknown, however, it can be calculated very easily. Simply use the law of triangle in which all the 3 angles sum up to 180 degrees. So V = 180 degrees - 44 degrees - 36 degrees = 100 degrees. So plugging in v = 4510 yards, V = 100 degrees, G = 44 degrees, and g = x yards into the sine rule gives:
sin 100 / 4510 = sin 44 / x.
Cross multiplying gives:
x*sin 100 = 4510*sin 44
Making x the subject gives:
x = (4510*sin 44)/sin 100.
x = 3181 yards (to the nearest yard).
Therefore, Norman and Voyager are 3181 yards apart from each other!!!
The required distance between the Norman and the Voyager is 3181 yards.
Given that,
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager is to be determined.
These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
Here,
The measure of the angle between Gladstone and the norman,
= 180 - 44 + 36
= 100°
sin(100) / 4510 = sin(44) / x.
x = 3181.12
x ≈ 3181 yards
Thus, the required distance between the Norman and the Voyager is 3181 yards.
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Ace Hardware sells boxes of wrenches ($ 100) and hammers ($300). Howard ordered 40 boxes of wrenches and hammers for $ 8,400. How many boxes of each are in the order.
Answer:
18 boxes of wrenches and 22 boxes of hammers.
Step-by-step explanation:
A house is 51.0 ft long and 44 ft wide, and has 8.0-ft-high ceilings. what is the volume of the interior of the house in cubic meters and cubic centimeters?
volume = l x w x h
51 x 44 x 8 = 17952 cubic feet
1 cubic foot = 0.0283168 cubic meters
17952 x 0.0283168 = 508.343 cubic meters
1 cubic meter = 1,000,000 cubic centimeters
508.343 x 1000000 = 508,343,000 cubic centimeters
What is the greatest angle measure in the diagram?
95˚
105˚
119˚
180˚
The solution is, The greatest angle measure is angle F which is 119°
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
The sum of all the angles of a quadrilateral is 360°
(15x-10)°+(15x+14)°+(9x-4)°+(11x+10)° = 360°
Open up the brackets and rearrange the expression
15x-10°+15x+14°+9x-4°+11x+10°=360°
15x+15x+9x+11x-10°+14°-4°+10° = 360°
50x+10°=360°
Collect like terms
50x=360°-10°
50x=350°
Divide by the coefficient of x
x= 350/50
X=7°
Substitute the value of x into the various angles
15x-10°=(15×7)-10= 105-10=95°
15x+14°=(15×7)+14=105+14=119°
9x-4°=(9×7)-4=63-4=59°
11x+10°=(11×7)+10=77+10=87°
The greatest angle measure is angle F which is 119°
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Which of the following methods would be easiest to use to solve 2x^2 + 5x - 11 = 0
A) factoring
B) isolating the x^2 term and finding the square root of both sides
C) using quadratic formula
D) all three methods would be easy and effective
It takes Sam 3 hours to do all of the yard work, but it takes his brother Carl only 2 hours. How long, in hours, would take them to do the yard work if they work together?
A.
5/6
B.
2/3
C.
6/5
D.
3/2
At the swim club, what is the ratio of men to all members?
A
1:3
B
3:4
C
1:2
D
4:1
Due to the lack of numerical details, a precise ratio of men to all members at the swim club cannot be determined. The ratio would be based on the exact number of men verses total members. Ratios offer a method to compare quantities.
Explanation:Unfortunately, without more information, it's impossible to definitively say what the precise ratio of men to all members at the swim club is. To determine the correct ratio, we would need to know the total number of members at the club, and the number of those members who are men. A ratio is a way to compare quantities or numbers, and in this case, the quantity of men compared to the quantity of all members.
For example, if there were 20 members total in the club, and 10 of those members were men, the ratio would be 1:2 (choice C), because for every one man, there are two total members. However, if there were 4 members and 3 of them were men, then the ratio would be 3:4 (choice B). Without the specific numbers, we cannot determine the correct answer from choices A, B, C, or D.
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