The slope of a line parallel to the line whose equation is 10x + 6y = -96 is;
m = - 5/3
Find the slope fully simplify my answer.
10x + 6y =-96
y = - 5/3 x – 16
y = - 5/3 x + (-16)
y = - 5/3 x + (-16), m = - 5/3
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If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age.
The probability that the person is over 40 years of age is 32/51 or 62.75%.
(the table is attached as image)
We know that,
The ratio of the size of the event space to the size of the sample space is the probability of an event.
The total number of possible outcomes is the size of the sample space.
The number of outcomes in the event you are interested in is called the event space.
Using the formula,
P = size of the event space/size of the sample space
⇒The probability that the person is older than 40,
sample size=255
size of the event space=85
P=85/255------> P=1/3
⇒the probability that the person drinks root beer,
sample size=255
size of the event space=75
P=75/255------> P=5/17
⇒the probability that the person is older than 40 of age or that they drink root beer,
P=(1/3)+(5/17)-----> P=(17*1+3*5)/51------> P=32/51-----> 0.6275----> 62.75%
therefore,
the answer is
32/51 or 62.75%
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(complete question)
if one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.
What is the domain and range of the relation shown in the table?
X Y
2 0
-1 4
4 2
-3 0
A. domain:{−3,−1,2,4}, range:{0,2,4}
B. domain:{0,2,4}, range:{−3,−1,2,4}
C. domain:{−3,−1,2,4}, range:{y|y∈R}
D. domain:{x|x∈R}, range:{0,2,4}
The domain and range of the relation shown in the table include the following: A. domain:{−3, −1, 2, 4}, range:{0, 2, 4}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined.
This ultimately implies that, a domain is the set of all possible input values (x-values) to a relation, and the domain of a graph comprises all the input values which are located on the x-coordinate from the least to the greatest.
Additionally, a range is the set of all real numbers that is associated with the elements of a domain i.e all of the y-values shown on the y-coordinate of the graph of a relation, from the least to the greatest.
By critically observing the table of this relation shown, we can reasonably infer and logically deduce the following:
Domain = {−3, −1, 2, 4}.
Range = {0, 2, 4}.
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1/2 of a number is 15 more than 1/7 of the same number. find the number.
Answer:
42
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] x = [tex]\frac{1}{7}[/tex]x + 15 Clear the fraction by multiplying all the way through by 14
7x = 2x + 210 Subtract 2s from both sides
5x = 210 Divide both sides by 5
x = 42
If r(x) = 2x² and w(x) = x-2, what is the range of (wor)(x)?
The given function are
r(x) = 2 - x² and w(x) = x - 2
(w*r)(x) can be obtained by multiplying the both function together
So, (w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)
(w*r)(x) = x (2-x²) - 2(2-x²)
= 2x - x³ - 4 + 2x²
∴ (w*r)(x) = -x³ + 2x² + 2x - 4
It is a polynomial function with a domain equal to R
The range of (w*r)(x) can be obtained by graphing the function
To graph (w*r)(x), we need to make a table between x and (w*r)(x)
See the attached figure which represents the table and the graph of (w*r)(x)
As shown in the graph the range of (w*r)(x) is (-∞,∞)
11. Ryan and Kathy each drew a triangle with an angle of 20 degrees. Under which condition would the
triangles be similar?
a) if both are right triangles
c) if the triangles have the same area
b) if both are obtuse triangles
d) if the triangles have the same perimeter
Answer:
a if both are right triangle
Step-by-step explanation:
if both are right triangles is the correct answer. Three sides and three angles together create a triangle. Here, Ryan and Kathy drew triangles with the same angle. We can say that two triangles are similarly based on certain rules.Ma
how are literal equations similar to and different from equations in one variable
x+a=b x + a = b , where a,b are uncertain values. Although both can be solved similarly, the difference is that, in literal equations, the letters representing the amount of a numerical value do not always change; however, in a single-variable equation, the letters representing these
Answer:
x+a= b , where a,b are uncertain values. Although both can be solved similarly, the difference is that, in literal equations, the letters representing the amount of a numerical value do not always change; however, in a single-variable equation, the letters representing these can/may vary.
Step-by-step explanation:
x+a= b , where a,b are uncertain values. Although both can be solved similarly, the difference is that, in literal equations, the letters representing the amount of a numerical value do not always change; however, in a single-variable equation, the letters representing these can/may vary.
Use a determinant to find the area of the triangle in R^2 with vertices (-4, -4), (0,-2), and (-2, 4) Hint: A triangle is half a parallelogram.
Area of the triangle in R² using determinant for the given vertices (-4, -4) , (0,-2) and (-2,4) is equal to 14 square units.
As given in the question,
Vertices of the triangle are given by:
( x₁ , y₁ ) = (-4,-4)
(x₂ , y₂) = (0, -2)
( x₃ , y₃) = (-2, 4)
Area of triangle using determinant is given by
= [tex]\frac{1}{2} \left|\begin{array}{ccc}-4&-4&1\\0&-2&1\\-2&4&1\end{array}\right|[/tex]
= (1/2) [-4(-2 -4) + 4(0+2) +1(0-4)]
=(1/2) ( 24 + 8 - 4)
= (1/2) ( 28)
= 14
Therefore, area of the triangle in R² using determinant for the given vertices (-4, -4) , (0,-2) and (-2,4) is equal to 14 square units.
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A boat is heading towards a lighthouse, where Yaritza is watching from a vertical distance of 139 feet above the water. Yaritza measures an angle of depression to the boat at point AA to be 21^{\circ}
∘
. At some later time, Yaritza takes another measurement and finds the angle of depression to the boat (now at point BB) to be 50^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
The distance from an angle of depression to the boat at 21° to angle of depression of 50° is 112 feet
How to determine the required distanceInformation from the question
A boat is heading towards a lighthouse, where Yaritza is watching from a vertical distance of 139 feet
Yaritza measures an angle of depression to the boat at point AA to be 21°
Yaritza takes another measurement and finds the angle of depression to the boat (now at point BB) to be 50°
the distance from point AA to point BB = ?
The direction of movements describes a right triangle of
opposite = ?
adjacent = 139 feet
The distance is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
for x = 21 point AA is solved
tan 21 = ? / 139
? = 139 * tan 21
? = 53.357
for x = 50 point BB is solved
? = 139 * tan 50
? = 165.654
the distance from point AA to point BB
= 165.654 - 53.357
= 112.297
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scot is picking out a pumpkin to buy at the local pumpkin farm. Each pumpkin costs $5.00 plus $0.35 per pound. Which equation represents the price of a pumpkin, p, that is x pounds
The equation represents the price of a pumpkin is p = 5 + 0.35x
The cost of each pumpkin = $5.00
The cost of the pumpkin per pound = $0.35
Consider the price of the pumpkin = p
Consider the number of pounds = x
The equation is the mathematical statement that shows the relationship between two expression with an equal sign. In equation the inequality will not be a part. The expression is the combination of two expression and an equal sign
Then the equation will be
p = 5 + 0.35x
Hence, the equation represents the price of a pumpkin is p = 5 + 0.35x
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how much for 19.35 to get to 25 ill give brainliest whoever answers first <3
The number remaining for 19.35 to get to 25 is 5.65.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both
In this case, the number remaining for 19.35 to get to 25 will be:
= New number - Old number
= 25 - 19.35
= 5.65
The number is 5.65.
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18. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the pair of triangles?
Answer:
HL
Step-by-step explanation:
Since the two triangles are right triangles and have 2 sets of congruent sides, you can use the HL congruence theorem to prove that they are congruent.
**HL only works with right triangles
Zach loves to compete in triathlons. At a race a few months ago, he finished in 280 minutes. Yesterday, he completed another triathlon and finished in 294 minutes. What was the percent of increase in Zach's finishing time?
The percent of increase in Zach's finishing time is 5%.
How to calculate the percentage?From the information, at a race a few months ago, he finished in 280 minutes and yesterday, he completed another triathlon and finished in 294 minutes.
The increase in time will be:
= New time - Old time
= 294 - 280
= 14 minutes
The percentage increase will be:
= Increase in time / Original time × 100
= 14 / 280 × 100
= 1/20 × 100
= 5%
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Which graph has a domain of all real numbers greater or equal to 6?
Answer:
Step-by-step explanation
C
Line A is represented by the equation y=4x−6. How do these equations compare to line A?
The comparison of the linear functions to line A are given as follows:
y = 4x ± constant: parallel.y = -x/4 ± constant: perpendicular.y = x/4 ± constant: neither parallel nor perpendicular.When are lines parallel, perpendicular or neither?A linear function is defined as follows:
y = mx + b.
In which the coefficients are listed as follows:
m is the slope.b is the intercept.The slope determines if the lines are parallel, perpendicular, or neither, as follows:
If the slopes for both lines are equal, the lines are parallel.If the multiplication of the slopes of both lines is of -1, they are perpendicular.Otherwise, they are neither.In this problem, the function is:
y = 4x - 6.
Hence the slope is of:
m = 4.
Then the functions, relative to y = 4x - 6, are classified as follows:
Parallel: slope of 4.Perpendicular: slope of -1/4, as 4 x (-1/4) = -1.Neither: any slope different of 4 and of -1/4.Missing InformationThe problem gives three lines with different slopes, and you have to define if they are parallel, perpendicular or neither parallel nor perpendicular.
The intercepts are not relevant and I couldn't find the problem on the internet, hence I say that they are constants.
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Please help! I don’t understand and this is due asap!
I need help from 39-53!!
Answer: -14
Step-by-step explanation:
The surface area of a square pyramid is 96 square feet. The height is two-thirds of the length of the base edge.
What is the length of the base edge?
The length of the base edge of the pyramid is 1.71 feet
What is surface area of a pyramid?In order to find the total surface area, we will need to add up the areas of the base and the three other sides. SA=B+12(P×h), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid.
If l is the length of the square base and h is the height of the pyramid, then h =2/3l
from the formula, SA= B+12(P×h)
the perimeter of a square is 4l
the base area of square is l^2
therefore 96= l^2+ 12(4l×2/3l)
96= l^2+ 12×8/3l^2
96=l^2+32l^2
96= 33l^2
divide both sides by 33
l^2= 96/33
l=√2.91
l=1.71 feet
therefore the length of the base edge is 1.71 feet
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(b) Work out y when C = 88 and x = 0.5
Answer:
x+y=73, 1.5x+2y=1−8
lazyuser30
What’s the answer someone please help
Answer:
Step-by-step explanation:
Ok:
1. This is a percent problem!
45/100*15=
675/100=
6.75
2. Subtract:
15-6.75=
8.25$
Answer: 8.25$
Deon, Jerome, Lamar, and Terell are practicing for the meter relay race. The school record for the race is 49.6 seconds. The fastest time that each boy ran a 100-meter sprint in practice is shown in the table. If each of the boys can run their best 100-meter sprint during the race, can they beat the school record?
Answer: Yes
Step-by-step explanation:
Add all of their best times.
11.9 + 12.6 + 12.52 + 11.95 = 48.97
48.97 < 49.6
Please helppp please help
Answer:
a. parallel b. neither c. neither d. perpendicular
Step-by-step explanation:
Find the gradient of the line in the graph
Choose 2 coordinates, I choose (0,1) and (3,3)
Use the formula
(y2 - y1)/(x2 - x1)
(3 - 1) / (3 - 0)
2/3
Gradient of a parallel line is the same
Gradient of a perpendicular line formula m1m2 = -1
(2/3)m2 = -1
m2 = -3/2
The gradient of the perpendicular line will be -3/2
The gradient of the parallel line will be 2/3
Any other gradient will be neither parallel nor perpendicular.
how do you estimate the product of 5 1/3 and 4 7/8
what is the functional for seven less than 3/5 of B is A
The mathematical expression is 3/5b -7 = a.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
7 less than three fifths of b is a
So, the mathematical expression for the above statement is
(3/5)b - 7 = a
3b - 35 = 5a
3b- 5a= 35
Hence, the mathematical expression is 3/5b -7 = a.
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What characteristics of something that is cyclical
Answer: regularly patterned or that occur in regular intervals.
Step-by-step explanation: took it
For each number, determine if it can be written as a fraction. Then state the reason.
Answer:
las fórmulas de 3 dividir por r te va a dar igual a 1.862
A train left Sheffield station at 6.30 am and
arrived at Tiverton station at 11.00 am.
The train travelled 243 miles in total.
What was the average speed of the train in
miles per hour (mph)?
If your answer is a decimal, give it to 1 d.p.
Which theorem or postulate could be used to prove the congruence of the triangles?
Which function has a greater constant rate of change? Use the drop-down menus to show your answer.
y
1.5
5
Function A
2.5
10 15
3.5 45 5.5
Function A has a rate of change of Choose...
change of Choose...
So, Function
Function B
y=-4.5x + 15
Function B has a rate of
Choose...
has a greater rate of change.
HELPPP PLS
Function A has a rate of change of 5 & function B has a rate of change of -4.5. so, function A has a greater rate of change.
What is the rate of change?
The rate at which a variable changes over a given time period. It is frequently used when discussing momentum, and it can be expressed as a ratio of a change in one variable to a corresponding change in another. This ratio is represented graphically by the slope of a line.
For the first function, we can use the equation of the slope
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
take any two points,
m = (25-15)/5.5-3.5 = 10/2 = 5
The general equation of a straight line is;
y = mx + c
where m is the slope
Therefore, in the case of the second equation, -4.5 is the slope
Hence, function A has a rate of change of 5 & function B has a rate of change of -4.5. so, function A has a greater rate of change.
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julia rides her bike at a rate of 1/2 mile per 1/9 of an hour. how far does she ride in one hour
Answer:
4.5 miles
Step-by-step explanation:
0.5 of a mile per 1/9 of an hour.
rate x time=distance and you need to find distance for one hour not 1/9 so multiply it by 9 so
0.5*9=4.5, 1/9*9=1
rate time distance
4.5 * 1 = d
4.5*1=d
4.5=d
so the distance traveled in one hour is 4.5 miles
Answer:
4.5 miles
Step-by-step explanation:
Given:
Julia rides her bike at a rate of 1/2 mile per 1/9 of an hour.Let x be the distance Julia rides in one hour.
Create an equivalent ratio of miles to hours:
[tex]\implies \dfrac{1}{2}:\dfrac{1}{9}=x:1[/tex]
[tex]\implies \dfrac{\frac{1}{2}}{\frac{1}{9}}=\dfrac{x}{1}[/tex]
[tex]\implies \dfrac{1}{2}\times \dfrac{9}{1}}=x[/tex]
[tex]\implies \dfrac{9}{2}=x[/tex]
[tex]\implies x=4.5[/tex]
Therefore, Julia rides 4.5 miles in one hour.
I WILL NAME YOU THE BRAINLIEST IF YOU PLEASE HELP ME!
solve the system by graphing.
y = x + 2
2x - y = -1
Answer:
y = x + 2y = 2x + 1Set the two functions equal to each other to find the point where they intersect:
[tex]x+2=2x+1\\\\x-2x=1-2\\\\-x=-1\\\\x=1[/tex]
Plug the x-value in to find the corresponding y-value. It should be the same for both functions:
[tex]y=x+2=1+2=3\\\\y=2x+1=2(1)+1=2+1=3[/tex]
So, they intersect on (1, 3), as shown on the graph below.
Help Pls Help I need it in 10 mins!!!!!!!!!!!!!!PLS
The point (6,2) is reflected over the -axis and then the image is translated 4 units right and 3 units down. What is the absolute difference between the coordinates of the final image?
Answer:
When we reflect over the x-axis the answer will be (6, -2)
Then when we go 4 units right it will turn into (10,-2)
And lastly, when we go 3 units down, it will be (10,-5)
The Answer is (10,-2)
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