The common difference of the arithmetic sequence -13, -22, -31, is -9.
What is an arithmetic sequence?An arithmetic sequence is a set of numbers that are ordered and have a common difference between each consecutive term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.
To find a specific term in an arithmetic sequence, we use the nth term formula. Step 1: An = a + (n - 1)d gives the nth term of an arithmetic sequence.
Some arithmetic sequence examples using this expression are:
1, 5, 9, 13, 17, 21, 25, 29, 33, ...
2, 4, 6, 8, 10, 12, 14, 16, 18,...
In this case, the difference will be:
= 2nd term - 1st term
= -22 - (-13)
= -22 + 13
= -9
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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
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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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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(b) Work out y when C = 88 and x = 0.5
Answer:
x+y=73, 1.5x+2y=1−8
lazyuser30
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.
Emmet michael’s gross pay is $31,700. He takes a single exemption of $2,000. His state income tax rate is 4. 5%. How much will he pay in state income tax?.
The state income tax that should be paid by Emmet Michael's is $1,336.50.
Given,
In the question:
Emmet Michael's gross pay is $31,700.
He takes a single exemption of $2,000.
and, His state income tax rate is 4. 5%.
To find the how much will he pay in state income tax?
Now, According to the question;
The calculation of the state income tax paid by Emmet Michael is as follows:
= (Gross pay - exemption amount) × income tax rate
= ($31,700 - $2,000) × 4.5%
= $29,700 × 4.5%
= $1,336.50
Hence, we can conclude that the state income tax that should be paid by Emmet Michael's is $1,336.50.
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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.
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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evaluate the integral. check your results by differentiation. (remember the constant of integration.) (3x3 1)69x2 dx
After evaluating the integral is [tex]69x^{6}/2 + 23x^{3} +C[/tex].
Given:
(3x3+1)69x2 dx
= 69[tex]x^{2}[/tex]*3[tex]x^{3}[/tex] + [tex]69x^{2}[/tex]
= 207[tex]x^{5}[/tex] + [tex]69x^{2}[/tex]
apply integration
= ∫ 207[tex]x^{5}[/tex] + [tex]69x^{2}[/tex]
= 207∫[tex]x^{5}[/tex] + 69∫[tex]x^{2}[/tex]
= 207*[tex]x^{6} /6[/tex] + 69*[tex]x^{3} /3[/tex]
= 69[tex]x^{6} /2[/tex] + [tex]23x^{3}[/tex] + C
Therefore After evaluating the integral is [tex]69x^{6}/2 + 23x^{3} +C[/tex].
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A rectangle has a height to width ratio of 3:4.5. Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.
Answer:
6:8:10, 9:12:15
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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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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answer pls bc my teacher is going 2 fail me
Answer:
point C
Step-by-step explanation:
Kammi and Alejandro each go to a hardware store to buy wire. The table shows the relationship between the cost and the length of wire.
a. Kammi needs 24 feet of wire. How much will she spend on wire?
b. Alejandro needs 13 yards of wire. How much will he spend on wire?
Answer: i think this is the same thing https://brainly.com/question/28965695?referrer=searchResults
if it is then theres ur answer
Step-by-step explanation:
Find the missing values in the ratio table. Then write the equivalent ratios. Burgers 3 9 hot dogs 5 10 the equivalent ratios are $3:$ , $:10$ , and $:$.
The required ratio for the burger is 3:6:9 and the ratio for the hot dog is 5:10:15.
Let the missing ratio in Burger be x and the ratio in the Hot dogs be y,
Now,
According to the question,
3 / 5 = x / 10
x = 6
Now,
x / 10 = 9 / y
Substitute the value of x,
6 / 10 = 9 / y
y = 90 / 6
y = 15
Thus, the required ratio for the burger is 3;6:9 and the ratio for the hot dog is 5:10:15.
In mathematics, a ratio suggests how commonly one variety consists of another. for example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to 6 (this is, eight:6, that's equal to the ratio four:3). similarly, the ratio of lemons to oranges is 6: 8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7).
The numbers in a ratio may be quantities of any kind, consisting of counts of human beings or items, or which include measurements of lengths, weights, time, and many others. In maximum contexts, each number is constrained to be advantageous.
A ratio may be specified either by way of giving each constituting number, written as "a to b" or "a: b", or through giving simply the price of their quotient a/b. identical quotients correspond to the same ratios.
Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number inside the numerator and the second one in the denominator, or as the price denoted by using this fraction. Ratios of counts, given via (non-zero) herbal numbers, are rational numbers, and might occasionally be natural numbers. while portions are measured with the same unit, as is often the case, their ratio is a dimensionless number. A quotient of quantities that are measured with distinct devices is referred to as a rate.
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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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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
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.
a process used to manufacture paint yields, on the average, 70 tons of paint each day. yields, however , vary from day to day due to changes in raw materials and plant conditions. suppose, it is established that the daily yields are normally distributed, and that the variability from one day to the other is more or less independent , and the standard deviation is 3 tons. because of increasing demand for this type of paint, certain modifications are suggested , and we are interested in estimating the mean yield of this modified process. how many sample observations do we have to obtain if we want to be 98% confident that our estimate is within 1 ton of the true, but unknown mean?
Using the Sample size formula , the sample manufactuer of paints observations or sample size is 22 ton .
Sample size: It is defined as the number of participants or total observations in a study of sample.
we have provided that,
standard deviations of sample (σ)= 3 tons
mean of sample ( X) = 70 tons
confidence level = 98% = 0.98
Margin of error (M.E) = 1 ton
Using the sample size formula,
n = z²(σ)(1-σ) /( M.E)²[1+σ (1-σ)z²/(M.E)²X]
where, X---> population size
s.d --> standard deviations
M.E ---> margin of error
Z-value for confidence level
so, z-value corresponding to 98% of confidence level is 2.32 ..
putting all the values in above formula we get, n = (2.32)²(2)3/(1)²(1+ (2.32)²(6)70×1)
=> n= 32.29/(1+(0.46))= 32.29/ 0.46
= 22.1 ~ 22
Hence, sample size is 22 ton .
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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.
Please help! I don’t understand and this is due asap!
I need help from 39-53!!
Answer: -14
Step-by-step explanation:
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.
Melissa uses 3/5 as much water as Neil to water her plants. If Melissa uses 4 and 1/3 gallons of water, how much does Neil use?
The amount of water that Neil uses is 7.22 gallons
How to calculate the fraction?From the information, Melissa uses 3/5 as much water as Neil to water her plants and Melissa uses 4 and 1/3 gallons of water.
Let Neil be illustrated as x
Therefore, 3/5 × x = 4 1/3
0.6x = 4 1/3
0.6x = 4.33
Divide
x = 4.33 / 0.6
x = 7.22 gallons
Neil used 7.22 gallons.
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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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The amount y (in dollars) of
money you have left after
playing x games at a
carnival is y=-0.75x + 10.
How much money do you
have after playing eight
games?
Answer:
You will have 4 dollars left
Step-by-step explanation:
Assuming from the question, you start with 10 dollars. You lose 75 cents for each games. If you play 8 games, you multiply 0.75 by 8 to get 6. Then you subtract 6 from 10 to get your remaining money, which is 4 dollars
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
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
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 do you estimate the product of 5 1/3 and 4 7/8
Is the absolute value of 3 less than, greater than, or equal to the absolute value of 7
Answer: 3 is less than 7, the absolute value of 3 is less than the absolute value of 7
Step-by-step explanation: Absolute value is how far a number is from 0. the best way to show absolute value is to test how far away the number is from 0 by using a number line. For example, the absolute value of -9 would be 9, or the absolute value of 5 would be 5. Absolute value is the amount of distance between the number and 0.
Hope this helps!