This is the explicit fοrmula fοr this sequence.
What cοmprises an arithmetic series?An arithmetic series is a set οf integers that are οrdered and have a cοmmοn difference between each fοllοwing wοrd. The cοmmοn difference, fοr instance, between the mathematical series 3, 9, 15, 21, and 27 is 6. An alternative term fοr an arithmetic sequence is an arithmetic prοgressiοn.
The first term is 21 and the cοmmοn difference is -4 (the amοunt added οr subtracted tο get frοm οne term tο the next).
The explicit fοrmula fοr an arithmetic sequence is a n = a + (n - 1)d2, where a is the first term, d is the cοmmοn difference, and n is the term number.
Substituting 21 fοr a and -4 fοr d, we get:
a n = 21 + (n - 1)(-4)
Simplifying, we get:
a n = 21 - 4n + 4
a n = 25 - 4n
This is the explicit fοrmula fοr this sequence.
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f(x) =
4 if x≤3
-4 if x>3
What is the functions range ?
Answer:
(−∞,∞)
Step-by-step explanation:
In track and field, the 440-yd. race was replaced with the 400-m race when Canada changed from the imperial system to the SI system. Which race is longer and by how much? Use the exact conversion: 1 yd. = 0.9144 m
Answer:
The 440-yd race is longer than the 400-m race by 2.336 meters.
Step-by-step explanation:
We can convert the distance of the 440-yd race to meters using the conversion factor 1 yd = 0.9144 m:
440 yd = 440 x 0.9144 m/yd = 402.336 m
Therefore, the 440-yd race is 402.336 meters long.
On the other hand, the 400-m race is already in meters.
Comparing the two distances, we can see that the 440-yd race is longer than the 400-m race.
To find out by how much longer, we can subtract the length of the 400-m race from the length of the 440-yd race:
402.336 m - 400 m = 2.336 m
Therefore, the 440-yd race is longer than the 400-m race by 2.336 meters.
Please help asap! Need the answer quickly!
The time needed for the sample size to double is given as follows:
26.3 hours.
How to obtain the time needed for the sample size to double?The exponential function that models the sample size after t hours is given as follows:
y(t) = y(0)e^(0.0264t).
The parameter y(0) represents the initial population, hence when the population is doubled, we have that:
y(t) = 2y(0).
Then we must solve the exponential function for the variable t, applying the natural logarithm, which is the inverse of the exponential, as follows:
2y(0) = y(0)e^(0.0264t).
e^(0.0264t) = 2
0.0264t = ln(2)
t = ln(2)/0.0264
t = 26.3 hours.
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Which net represents this solid figure?
________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
_________________________________
The net that represents this solid figure is diagram D.
What is a solid figure?A solid figure is a three-dimensional geometric shape that has length, width, and height. It is also called a three-dimensional or 3D figure. Some examples of solid figures include cubes, spheres, cylinders, cones, and pyramids.
Solid figures are different from two-dimensional shapes, which only have length and width. In contrast, solid figures have depth or thickness, making them more complex and interesting.
Solid figures can be classified based on their properties, such as the number of faces, vertices, and edges they have. For example, a cube has six faces, eight vertices, and 12 edges, while a sphere has no faces, vertices, or edges.
In this case, it has 2 squares and 4 rectangles. The appropriate diagram is D
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Can you help me find this answer
Answer:
4
Choice D
Step-by-step explanation:
[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\dfrac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}[/tex]
[tex]\mathrm{Periodicity\:of\:}\cos \left(x\right)\:\mathrm{is}\:2\pi[/tex]
Solve For The Radius:
a. r = 9.7 m
b. r = 7 m
c. r = 123.5 m
d. r = 19.4 m
Answer:
a) r = 9.7 m
Step-by-step explanation:
CD = CE + ED
= 9 + r +r
= 9 + 2r
If a tangent and a secant are drawn from a common point outside the circle, then
CE * CD = CB *CB
9 * ( 9 + 2r) = 16 * 16 {Distributive property}
9*9 + 9*2r = 256
81 + 18r = 256
Subtract 81 from both sides,
18r = 256 - 81
18r = 175
Divide both sides by 18,
r = 175÷ 18
[tex]\boxed{\bf r = 9.7 \ m }[/tex]
What is the length of line segment AC?
Using geometry, we can find that the length of the line segment AC as per the distance between two points is= 18 ft.
What are line segments?
In geometry, a line segment's borders are determined by two distinct points on the line. Any portion of a line that connects two places is referred to as a line segment.
A segment has an endpoint, whereas a line doesn't.
What are some examples of line segments in the real world?
a scale, a ruler, a stick, and a boundary line.
Thus, the length of the line segment AC is = 18ft.
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if 85% of 'a' is 'b' then which of the following is true a, a=b b,ab
Answer:
Step-by-step explanation:
The statement "85% of 'a' is 'b'" can be represented mathematically as:
0.85a = b
This means that 'b' is 85% of 'a'.
To answer the question:
a = b/0.85
So, a is equal to 'b' divided by 0.85.
Therefore, the correct option is (a) a=b.
If 25% of a number is 10, find 5% of that number.
Answer:
0.125
Step-by-step explanation:
Answer:
5% of 40 is 2
Step-by-step explanation:
number = x
25% of x is = 10
25% = 25/100, or 1/4
[tex]\frac{1}{4}x = 10[/tex]
multiply each side by 4
[tex]x = 40[/tex]
5% is 5/100, or 1/20
[tex]\frac{1}{20}x = ?[/tex]
plug-in the known value
[tex]\frac{1}{20}*40 = ?\\\frac{40}{20} = ?\\\frac{4}{2} = ?\\\\? = 2[/tex]
I will mark you brainiest!
In a proof to show two triangles are congruent if a given is PR ⟂ CK, which of the following statements most likely will be used within the proof?
A) PR and CK are congruent.
B) PR and CK are similar.
C) PR and CK form acute angles.
D) PR and CK form right angles.
Answer:
D) PR and CK form right angles
Step-by-step explanation:
⟂ is the symbol for a perpendicular, so it is a perpendicular bisector.
- Perpendicular bisectors divide an angle into 2 90° angles.
Which answer shows shows the equation below written in different forms 9-3=6
The equatiοn 9 -3 = 6 can be written in different fοrms, but the correct one is 9 = 3 + 6.
Are expressiοns cοnsidered equatiοns?Every cοmbinatiοn οf a number, a variables, and οperatiοn symbοls is cοnsidered an expressiοn. An equatiοn is created by cοmbining twο expressiοns and jοining them with the equal sign.
Cοnditiοns οn the parameters are fοund in simple equatiοns. It is clear frοm an equatiοn that the answer οn the left and right are equivalent. The expressiοn tο the left οf the symbοl "=" is the LHS, while the expressiοn tο the right is the RHS. With the fοrm y = "sοme expressiοn invοlving x," a sοlutiοn invοlving x and y can be expressed, such as y = f. ( x). This final statement, which may be interpreted as "y equals f οf x," denοtes that y is a cοefficient οf x.
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Complete question:
Which answer shows the equation 9-3=6 below written in different forms?
6 + 3 = 9, 9 = 3 + 6, 9 - 6 = 3, 3 = 9 - 6someone please tell what to do with this i am lost
The properties used to simplify the expression are given as follows:
2. Combine like terms.4. Division property.How to simplify the expression?In algebra, the combination of like terms refers to the process of simplifying expressions by adding or subtracting terms that have the same variable(s) raised to the same power(s).
In this problem, from step 1 to step 2, on the left side of the equality, all the terms with the variable n and exponent 1 were added, as were the constant terms, hence the like terms were combined.
In Step 4, the variable n was obtained applying the division operation, which is the inverse operation of the multiplication operation in Step 3.
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Determine the value of y, if x is - 2.
y = x + 8
answer: 10
y = |2| + 8
y = 2 + 8
y = 10
Juan is hiking a trail that is 2 miles long. He hikes 14 miles before resting.
How much farther does he have to hike?
Answer:
I think the answer is D.) 7/8 mile
Step-by-step explanation:
If you make the mixed numbers improper fractions. 2 and 1/8 is 17/8, 1 and 1/4 (2/8) is 10/8, then you subtract the numerators and keep the denomitators the same to get 7/8 mile (sorry if I spelt something wrong)
Pearl earns $34,000 per year, and she is considering buying a $130,000 house by
making a down payment of 10% of the purchase price and taking out a 30-year
fixed-rate mortgage with a 6.3% interest rate. She would pay $1280 annually in
property taxes, and for the first 2 years of the mortgage, she would pay $608.40
annually for PMI. Use this information to answer the following six questions.
1.
How much would Pearl's
mortgage be?
Pearl's mortgage payment would be $678.47 per month.
What is mortgage?A mortgage is a type of loan that is used to finance the purchase of real estate, such as a house or a piece of land. When a person takes out a mortgage, they borrow money from a lender (usually a bank or other financial institution) to buy the property, and they agree to pay back the loan over a set period of time, typically 15 to 30 years.
In the given question,
To calculate Pearl's mortgage, we need to first determine the amount of her down payment.
Down payment = 10% x $130,000
Down payment = $13,000
The amount that Pearl needs to finance with her mortgage is:
$130,000 - $13,000 = $117,000
To calculate the mortgage payment, we can use the formula for a fixed-rate mortgage:
Mortgage Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal (amount borrowed)
r = Monthly interest rate (annual rate divided by 12)
n = Number of monthly payments (30 years x 12 months per year)
Monthly interest rate = 6.3% / 12 = 0.00525
Number of monthly payments = 30 years x 12 months = 360
Using these values, we can calculate the monthly mortgage payment:
Mortgage Payment = $117,000 * 0.00525 * (1 + 0.00525)^360 / ((1 + 0.00525)^360 - 1)
Mortgage Payment = $678.47 (rounded to the nearest cent)
Therefore, Pearl's mortgage payment would be $678.47 per month.
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The difference between two numbers is 2. When each number is rounded to nearest hundred, the difference between them is 100. What could the numbers be?
[tex]101 - 99 = 2[/tex]
each number is rounded to nearest hundred101 → 200
99 → 100
the difference between them is 100:[tex]200 - 100 = 100[/tex]
⇒ the numbers could be: 99 and 101
other pairs of numbers: (199,201), (299,301) ...
Let f(x)=9x² - 5x - 58 and
g(x) = 7x² + 3x + 6. Identify the solution(s) of
f(x) = g(x).
The solutions of the function as required to be determined is; x = 8 or x = -4.
What is the solution of the equation?As evident in the task content; the given equation are;
f(x)=9x² - 5x - 58 and
g(x) = 7x² + 3x + 6.
The solution of the equation can be determined as follows;
9x² - 5x - 58 = 7x² + 3x + 6.
2x² -8x - 64 = 0
x² - 4x - 32 = 0
(x - 8) (x + 4) = 0
x = 8 Or x = -4.
Ultimately, the solutions of the equation are; x = 8 or x = -4.
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what is the area of the circle below?
The area of the circle shown above is equal to: A. 1,520.5 cm².
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using the following mathematical expression:
Area of a circle, A = πr²
Where:
r represents the radius of a circle.
By substituting the radius into the formula for the area of a circle, we have the following;
Area of a circle, A = πr²
Area of a circle, A = 3.14 × 22²
Area of a circle, A = 1,520.5 cm².
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I need help what is, 8y - 7 - 4y =
show work
Answer:
Step-by-step explanation:
8y-7-4y=
8y-4y= -7
4y=-7
DBS by 4
y=1.75
Tara uses 6.6 pints of white paint and blue paint to paint her bedroom walls. 3 4 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Answer:
1.65 pints
Step-by-step explanation:
If Tara used 6.6 pints of white and blue paint combined, and 3/4 of that amount is white paint, then we can find the amount of white paint she used by multiplying 6.6 by 3/4:
6.6 x 3/4 = 4.95
So Tara used 4.95 pints of white paint to paint her bedroom walls.
To find out how much blue paint she used, we can subtract the amount of white paint from the total amount of paint:
6.6 - 4.95 = 1.65
Therefore, Tara used 1.65 pints of blue paint to paint her bedroom walls.
A dice is tossed once,what is the probability that a prime number shows upwards
PLEASE ANSWER BEFORE 11:59 TONIGHT
1. A factory needs two raw materials. The probability of not having an adequate supply of material A is 0.05, whereas the probability of not having an adequate supply of material B is 0.03. A study determines that the probability of a shortage in both A and B is 0.01. a. Let E be the event "shortage of A" and F be the event "shortage of B". Construct a Venn diagram representing events E and F.
The Venn diagram needed based on the question is given below:
The Venn Diagram__________
/ \
/ A \
/____________\
\ /
\ E ∩ F /
\_________/
B
In the diagram, the set A represents the event of having an adequate supply of material A, and the set B represents the event of having an adequate supply of material B.
The overlap of A and B represents the event of having an adequate supply of both materials.
The set E represents the event of a shortage in material A, and the set F represents the event of a shortage in material B.
The intersection of E and F, denoted by E ∩ F, represents the event of a shortage in both materials.
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How would you characterize the relationship between the hours spent on homework and the test
scores? Explain.
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h
of homework?
(c) What does the number 40 in Part (b) mean in the context of the situation
Paul scοre 64 fοr the mοdel predict fοr 3 h οf hοmewοrk and test scοre tο be 40.
What is function?A functiοn is defined as a relatiοnship between a set οf inputs that each have οne οutput. A functiοn is a relatiοnship between inputs in which each input is related tο exactly οne οutput. Every functiοn has a dοmain and a cοdοmain, as well as a range. In general, a functiοn is denοted by f(x), where x is the input. A functiοn's general representatiοn is y = f. (x).
Scοre can be defined as tοtal number which any persοn achieve after dοing any wοrk οr target. Suppοse a Batsman make 100 run it means he scοre 100 fοr his team.
a. Fοr three hοurs οf study we have that the nοte wοuld be apprοximately:
y = 8x + 4
b. The number 40 means that if yοu dο nοt devοte any study time, then yοu expect the test scοre tο be 40.
y = 8(3) + 40
y = 64
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Please help!
What is the principal square root? And why is it used when solving radical
polynomials?
Answer:
The principal square root of a non-negative real number is the positive square root. For example, the principal square root of 25 is 5, since 5^2 = 25.
When solving radical polynomials, the principal square root is used because it is the most commonly used square root. In many contexts, including mathematical and scientific calculations, the principal square root is the default choice unless otherwise specified. Additionally, when working with radical expressions, we often simplify expressions by taking the principal square root, as it can help us to simplify calculations and express answers more clearly.
what is the correct answer
Answer:
54 square meters
Step-by-step explanation:
Given the scale is 1 centimeter represents 3 meters, to scale the dimensions of the drawing to the dimensions of the actual room, multiply the dimensions of the drawing by 3.
Therefore:
3 cm × 3 = 9 m2 cm × 3 = 6 mSo the dimensions of the actual room are:
Length = 9 mWidth = 6 mThe area of a rectangle is the product of its width and length.
Therefore, the area of the actual room is:
Area = 6 × 9 = 54 m²What is the x and the y Intercept?
For the given function the intercepts are:
x-intercept: x = -4
y-intercept: y = 12.
How to find the intercepts for the given function?Here we have a table that defines a function, and we want to find the intercepts of said function.
We can assume it is linear, then the slope of the function will be given by:
a = (9 - 3)/(-1 + 3) = 6/2 = 3
The linear function is like:
y = 3x + b
To find the value of b we can replace the values of the last point on the table, x = 2 and y = 18.
18 = 3*2 + b
18 = 6 + b
18 - 6 = b = 12
The linear function is:
y = 3x + 12
The x-intercept is the value of x when y = 0
0 = 3*x + 12
-12 = 3x
-12/3 = x = -4
And the y-intercept is the value of y when x = 0.
y = 3*0 + 12
y = 12
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what has a sum of 147
Answer:
146 and 1
Step-by-step explanation:
146+1=147
What is a frequency distribution?
Answer:
Frequency distributions are visual displays that organize and present frequency counts so that the information can be interpreted more easily.
Step-by-step explanation:
The distribution of a variable is the pattern of frequencies, meaning the set of all possible values and the frequencies associated with these values.
Together, teammates Pedro and Ricky got 2686 base hits last season. Pedro had 280 more hits than Ricky. How many hits did each player have?
Answer:
1483 pedro 1203 ricky
Step-by-step explanation:
1203+1483 = 2686
Please help me solve these questions that are attached.
The sums, differences, product, and quotient of the functions and their domains are;
f(x) = √(16 - x^2), g(x) = √(x + 3)
f + g = √(16 - x^2) + √(x + 3)
Domain; [-3, 4]
f - g = √(16 - x^2) - √(x + 3)
Domain: [-3, 4]
f × g = √(16 - x^2) × √(x + 3) = √(-x³ - 3·x² + 16·x + 48)
f × g = √(-x³ - 3·x² + 16·x + 48)
Domain; [-3, 4]
f/g = √(16 - x^2)/√(x + 3) = √(16 - x^2)/(x + 3))
f/g = √(16 - x^2)/(x + 3))
Domai; [-3, 4] ∪ [1, 4]
f(x) = √(81 - x^q2), g(x) = √(x² - 16)
f + g = √(81 - x^2) + √(x² - 16)
Domain [-9, -4] ∪ [4, 9]
f - g = √(81 - x^2) - √(x² - 16)
Domain: [-9, -4] ∪ [4, 9]
f × g = √(81 - x^2) × √(x² - 16) = √(-x⁴ + 97·x² - 1296)
f × g = √(-x⁴ + 97·x² - 1296)
Domain: [-9, -4] ∪ [4, 9]
f/g = √(81 - x^2)/√(x² - 16)
Domain: [-9, -4] ∪ [4, 9]
What is the sum of two functions?The sum of two functions is obtained by adding the values of the functions at each point.
The sum of two functions is obtained by adding the values of the functions at each point. The domain of the sum is the intersection of the domains of the two functions, In this case, the domain of f + g is [-3, 4]
The difference of two functions is obtained by subtracting the functions values at each point. The domain of the difference is the intersection of the domains of the two functions. In this case, the domain of f - g is [-3, 4]
The product of two functions is obtained by multiplying the values of the functions at each point. The domain of the product of the functions is the domain of the intersection of the domains of the two functions. The domain of f × g is [-3, 4]
The quotient of two functions is obtained by dividing the values of the functions at each point. The domain of the quotient is the same as the domain of the intersection of two functions, excluding any points where the denominators is zero. The domain of f/g is [-3, -1] ∪ [1, 4].
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Pls help simplify liner expressions
The answers to the questions are in the picture