The two terms of each arithmetic sequence [tex]a_{4}[/tex] = 8 [tex]a_{7}[/tex] = 20 are d = 4 and a = -4.
What is sequence?[tex]a_{4}[/tex] = 8
8 = a +3d.............1
[tex]a_{7}[/tex] = 20
20 = a + 6d...........2
equating equation 1 and 2
8 = a +3d
20 = a + 6d
d = 12/3
d = 4...............3
from equation 3
8 = a + 12
a = -4
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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The fish population in a certain lake rises and falls according to the formula F= 1000(30 + 17+ - 12) Here F is the number of fish at time t, where t is measured in years since January 1, 2002, when the fish population was first estimated. (a) On what date will the fish population again be the same as on January 1, 2002? (b) By what date will all the fish in the lake have died?
The fish population will be the same as on January 1, 2002 on January 1, 2017 and all the fish in the lake will have died by 2019
(a) On what date will the fish population again be the same as on January 1, 2002?The function is given as:
F(t) = 1000(30 + 15t - t^2)
Start by calculating F(0) --- population in 2002
So, we have:
F(0) = 1000(30 + 15(0) - 0^2)
F(0) = 30000
Substitute 30000 for F(t) in F(t) = 1000(30 + 15t - t^2)
1000(30 + 15t - t^2) = 30000
Divide by 1000
30 + 15t - t^2 = 30
Simplify
t^2 - 15t = 0
Divide through by t
t - 15 = 0
Solve
t = 15
This means that
Year = 2002 + 15
Year = 2017
Hence, the fish population will be the same as on January 1, 2002 on January 1, 2017
(b) By what date will all the fish in the lake have died?This means that F(t)= 0
So, we have:
1000(30 + 15t - t^2) = 0
Divide by 1000
30 + 15t - t^2 = 0
Rewrite as
t^2 - 15t - 30 = 0
Using a graphing calculator, we have
t = 17 (approximated)
This means that
Year = 2002 + 17
Year = 2019
Hence, all the fish in the lake will have died by 2019
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A basketball player has a 0.603 probability of making a free throw. if the player shoots 28 free throws, what is the probability that she makes no more than 20 of them?
The probability that she makes no more than 20 of them is 0.394
We use Binomial Distribution in solving this question.
The discrete probability distribution known as the binomial distribution only offers two outcomes for an experiment: success or failure.
Sum of independent Bernoulli trials is binomial distribution; a random Variable x is said to be following binomial distribution if it's density is given as
P(X=x) = (nCx) px (1−p)n−x where x=0,1,2…n
Let x denotes the number of throws that makes a free throw so here
x follows Binomial distribution with n=28 and p=0.603
Thus, we calculate
P(X≤20) =∑_(k=0)^1▒1= (28Ck)0.603k (1−0.603)28−k =0.3144
=0.394
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A builder makes staircases where each step is
28
cm
28cm28, start text, c, m, end text long and rises
18
cm
18cm18, start text, c, m, end text so people don't trip. Every staircase has a stringer — a diagonal support connecting all of the steps.
the length of the stringer for the staircase of 6 steps is 199.74 cm.
The sum of the squares of the two sides (a and b) equals to the square of the hypotenuse (c). In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
According to the question,
Each step is 28 cm long that is the length of one step of the staircase. And 18 cm high which is the height of the step at 90-degree angle thus forming a right-angle triangle and the stringer acts as a hypotenuse. Therefore, we can use Pythagoras theorem to find the length of the stringer of one step.
Length=a=28 inch
Breadth=b=18 inch
Applying the Pythagoras theorem, we get
28²+18²= (length of the stringer)²
28²+18²= = 1108
Now, √1108 = 33.29
to find the length of 6 steps multiply 33.29 with 6
33.29*6 = 199.74
Therefore, the length of the stringer for the staircase of 6 steps is 199.74 cm.
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Answer:
199.7 cm
Step-by-step explanation:
I really need help with how to do this . It’s a little bit confusing . Thank you
Answer:
just fix the cilcle more it have it looing for the answer
Step-by-step explanation:
that all i got i wish i can help u more
express 985 cm cube as a percentage of 1 litre
Answer:
98.5%
Step-by-step explanation:
1000 cubic centimeters = 1 litre
(3 decimal spaces to the left)
985 cubic centimeters = .985 liters (almost 1 litre)
.985 = 98.5% (2 decimal spaces to the right)
For a fundraiser, a school club is selling raffle tickets for $2 each and healthy snacks for $1.50 each. What is the cost of: 7 tickets and 5 snacks?
f(x)=2x - 2 ; Find f(1)
Answer:
0
Step-by-step explanation:
Substitute x for 1 and solve.
2(1) -2
2-2
0
Answer:
0 I belive
Step-by-step explanation:
f(x) =2x-2
f(1)= 2(1)-2
2-2
f(1)= 0
Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
10,12,23
The following set of numbers, 10, 12, and 23, cannot be the measures of the sides of a triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 10, b = 12, and c = 23
a + b > c 10 + 12 > 23 22 > 23 False
a + c > b 10 + 23 > 12 33 > 12 True
b + c > a 12 + 23 > 10 35 > 10 True
If at least one of these three statements is not true, then the set of numbers is not a valid measure of the sides of a triangle.
Hence, the set of numbers 10, 12, and 23 can not be the measure of the sides of a triangle.
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If the area of the triangle is 12, what is the value of x?
Answer: x = 3
Step-by-step explanation:
From the diagram above , the area of a triangle especially a right angled triangle
A = 1/2 X b X h where b is the base and h is the height.
Now,
h = x + 3
b = x + 1
Now , substitute for those values in the formula provided vide
A = 1/2 x (x+ 3)( x + 1 ) and equated it to 12
= (x+3)(x+1)
—————. = 12
2
Now, multiply both side a by 2 to make it a linear equation or better put , cross multiply
= (x+3)(x+1) = 2 x 12
= (x+3)(x+1) = 24
Then open the bracket by multiplication
= x2 + x + 3x + 3 = 24
= x2 + 4x + 3 = 24
= x2 + 4x + 3 - 24 = 0
By solving this quadratically,
= x2 + 7x - 3x - 21 = 0 ,
( x2 + 7x) - ( 3x - 21 ) = 0
x( x + 7 ) - 3( x + 7 ) = 0
Therefore
( x+ 7 )( x - 3 ) = 0
Solving this gives
x = -7 or x = 3
Therefore x = 3 since x can’t be negative, x can’t be = -7
9 is 10% of what number
Answer:
90
Step-by-step explanation:
You can find the answer by dividing 9 by .10
9 / .10 = 90
To check your answer, you can multiply 90 by .10
90 x .10 = 9
Convert -5/8 into a decimal
Answer:
-0.625
Step-by-step explanation:
A fraction is the numerator (top) divided by the denominator (bottom). In this case it is -5 divided by 8. Put that into a calculator and you will get -0.625.
Which of the following is a like radical to 3 √6x²?
Answer:
Answer: Option 3
Step-by-step explanation:
like radicals are radicals that have the same root number and the same 'radicand' (number or expression under the square root)
Max is building a set of shelves. he buys a board that is 4 yards long. he wants to cut as many pieces of board that are 3/4 yard long as he can. how many pieces can he cut? will he have any board left over? if so how much?
If Max is building a set of shelves and he buys a board that is 4 yards long and he wants to cut as many pieces of board that are 3/4 yards long as he can, then the no of pieces he can cut is 5 and he will have 0.25 yards of board left over.
3/4 is a fraction which can be represented as,
3/4 = 0.75
The number of pieces of board that Max can cut that is 4 yards long can be determined by the division of the length of the board by the length of the cut pieces. Therefore,
number of pieces cut = length of the board ÷ length of a cut piece
number of pieces cut = 4 ÷ 0.75
number of pieces cut = 5.33, that is round off to 5
Thus he can cut 5 pieces of 3/4 yards.
As 5 × 3/4 = 3.75 yards
The remaining yards of the board can be calculated by subtraction.
Board leftover = 4 - 3.75 = 0.25 yards
Hence, Max can cut 5 pieces of 3/4 yards and will have 0.25 yards of the board left over.
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Please help me with this!!!!
In the formula V= (1/3)πr²h , which expression is equal to h ? (A) V/3πr²(B) V - - -(1/3)πr² (C) 3V/πr² (D) 3Vπ/r²
In the formula V = (1/3)πr²h , (A)V/3πr² is the expression equal to h.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily
Here given that,
V= (1/3)πr²h
V/3πr² = (1/3)πr²h/3πr² (divided both sided with 3πr²)
V/3πr² = h or h = V/3πr²
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Help me out please!!
Answer:
£41.20
Step-by-step explanation:
Pack of 10 x 8 = 80
(I got the 8 from 84)
80 divided by 2 = 40
then all you need are 4 pencils = 1.20
40 + 1.20 = 41.20
Hope this makes sense aha, if it doesn't just contact me :) xx
i need help solving this
Answer:
Step-by-step explanat
36=10x-4
40=10x
10x=40
x=40/10
x=4
Choose an equivalent expression for two thirds to the fourth power times two thirds raised to the third power comma all raised to the second power.
four ninths raised to the fourteenth power
four ninths raised to the twenty fourth power
two thirds raised to the fourteenth power
two thirds raised to the twenty fourth power
The equivalent expression for the given expression is [tex](\frac{2}{3} )^{14}[/tex]. Therefore, option C is the correct answer.
The given expression is [tex]((\frac{2}{3} )^{4}\times(\frac{2}{3} )^{3})^{2}[/tex].
We need to find the equivalent expression for the given expression.
What is an equivalent expression?Equivalent expressions are expressions that work the same even when they seem different. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
Now, [tex]((\frac{2}{3} )^{4}\times(\frac{2}{3} )^{3})^{2}[/tex] using [tex]a^{m} \times a^{n}=a^{m+n}[/tex].
We get, [tex]((\frac{2}{3} )^{4+3})^{2}=((\frac{2}{3} )^{7})^{2}[/tex]
Using the exponents rule [tex](a^{m} )^{n}=a^{m\times n}[/tex]
=[tex]=(\frac{2}{3} )^{7\times 2}=(\frac{2}{3} )^{14}[/tex]
The equivalent expression for the given expression is [tex](\frac{2}{3} )^{14}[/tex]. Therefore, option C is the correct answer.
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He made that poor piano moan with melody.
O Blues!
Swaying to and fro on his rickety stool
He played that sad raggy tune like a musical fool.
Sweet Blues!
Coming from a black man's soul.
O Blues!
In a deep song voice with a melancholy tone
I heard that Negro sing, that old piano moan—
"Ain't got nobody in all this world,
Ain't got nobody but ma self.
I’s gwine to quit ma frownin'
And put ma troubles on the shelf."
What is the effect of repeating the phrase “piano moan” in the poem?
It sets a sad, mournful tone.
It adds a cheerful, melodic chord.
It adds an open, musical sound.
It sets an angry, discordant tone.
Mark this and return
The effect of repeating the phrase “piano moan” in the poem is A. It sets a sad, mournful tone.
What is tone?It should be noted that in literature, the feeling and emotions of the author is illustrated in the tone.
In this case, the repetition of the words were I
important to show the emotions of the author.
Therefore, the effect of repeating the phrase “piano moan” in the poem is that it sets a sad, mournful tone.
In conclusion, the correct option is A.
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Each sequence has eight terms. Evaluate each related series. 1/2, 3/2, 5/2, . . . . . . , 15/2
The result of the evaluation of the series described by 1/2, 3/2, 5/2, . . . . . . . , 15/2 is:
∑ = 28
What is a series?A series is the summation of a set of numbers or sequences.
What is sigma notation?The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
1/2, 3/2, 5/2, . . . . . . , 15/2
a1 =1/2an = 15/2n = 7∑ = 7(1/2 + 15/2)/2
∑ = 7(8)/2
∑ = 28
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Write an equation of each line in standard form with integer coefficients.
a line with slope of 2/3 and y -intercept (0,5)
The equation of the line in standard form with slope equal to 2/3 and y -intercept (0 , 5) is 2x - 3y = -15.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the slope-intercept form, plug in the values of the slope and the point to set up the equation.
y = mx + b
where m = 2/3 and y-intercept, b = 5
y = 2/3 x + 5
To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
y = 2/3 x + 5
2/3 x - y = -5
Multiply both sides by 3 to have integer coefficients.
3(2/3 x - y) = -5(3)
2x - 3y = -15
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A) x^8 • x^6 = x^p, where is p=
B) (x^8)^6 = x^r, where is r
Answer: p=14, r=48
Step-by-step explanation:
x^8 • x^6 = x^p
x^(8+6) = x^p
8+6=p
p=14
(x^8)^6 = x^r
x^(8*6)=x^r
8*6=r
r=48
express the ratio 2:6 in 1:n
Answer:
n=3
Step-by-step explanation:
2:6=1:3
divide by 2 on both the 2 and the six and 2/2=1 and 6/2=3 so n=3
Answer:
1:3
Step-by-step explanation:
So, what you need to do is figure out the common factor of 2 and 6
which then the answer comes out to 3, so your answer would be 1:3 ratio.
Brainliest thx
I need this answered please
How can translating written words into a numerical expression be helpful?
4th term 19 and 7th term is 7 of A5
Find d a1 an a11
Answer: a₁=31 a₁₁=-9
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{a_4=19} \atop {a_7=7}} \right. \\\\a_n=a_1+(n-1)d\\\\\left \{ {{a_1+(4-1)d=19} \atop {a_1+(7-1)d=7}} \right. \\\\\left \{ {{a_1+3d=19\ \ \ \ (1)} \atop {a_1+6d=7\ \ \ \ \ (2)}} \right.[/tex]
Subtract equation (2) from equation (1):
[tex]3d=-12[/tex]
Divide both parts of the equation by 3:
[tex]d=-4[/tex]
Thus,
[tex]a_1+(3)(-4)=19\\a_1-12=19\\a_1-12+12=19+12\\a_1=31\\a_{11}=a_1+(11-1)d\\a_{11}=31+(10)(-4)\\a_{11}=31-40\\a_{11}=-9[/tex]
Answer:
a = 43
d = -6
[tex]\sf a_{11} = -17[/tex]
Step-by-step explanation:
Arithmetic sequence:
Use the formula to find the nth term:
[tex]\sf \boxed{\bf a_n= a+(n-1)d}[/tex]
Here, a is the first term, n is the number of terms and d is the common difference.
[tex]\sf a_4 = 19\\\\a+(4-1)*d = 19\\\\a + 3d = 19 -------------------(i)[/tex]
[tex]\sf a_7 = 7\\\\a + 6d = 7 ------------------(ii)\\[/tex]
Subtract equation (i) from (ii) and thus 'a' will be eliminated and we can find the value of 'd'.
(ii) a + 6d = 7
(i) a + 4d = 19
- - = -
2d = -12
d = -12/2
[tex]\sf \boxed{\bf d = -6}[/tex]
Now, plugin d = -6 in any of the two equations. We are substituting the 'd' value in equation (i)
a + 4*(-6) = 19
a - 24 = 19
a = 19 + 24
[tex]\sf \boxed{\bf a = 43}[/tex]
[tex]\sf a_{11} = a + 10d[/tex]
= 43 + 10*(-6)
= 43 - 60
[tex]\sf \boxed{\bf a_{11} = -17 }[/tex]
Corey wrote an equation in factored form , quadratic function . Kimberly wrote the equation y = (x + 8)(x - 2); y=x^ 2 +6x-16, to represent a and Joshua wrote the equation y = (x + 3) ^ 2 - 25 A. Reason Do all three equations represent the same function ? If not, whose is different ? Explain algebraically .
All the three equations represent the same function as they equal x² + 6x - 16.
How to illustrate the equation?It should be noted that the function that Corey wrote is:
y = (x + 8)(x - 2)
y = x² - 2x + 8x - 16
y = x² + 6x - 16
Kimberly wrote y = x² + 6x - 16
Joshua wrote (x + 3)² - 25
= (x + 3)(x + 3) - 25
= x² + 3x + 3x + 9 - 25
= x² + 6x - 16
In conclusion, the three equations represent the same function as they equal x² + 6x - 16.
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translate triangle P using the vector (2 -7)
The transformation rule for the triangle P by translating the vector (2, -7) is ( x , y ) <=> ( x + 2 , y - 7 )
Transformation rule says that, if a translation occurs then each point of the shape will be shifted in the same direction with the same distance.
The original figure and the translated figure will have the same shape and size.Also they both faces in same direction.This is called a direct geometry.According to the rule , the translation for the triangle P using the vector (2,-7) is ( x + 2 , y - 7 ).
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MATH HELPERS !!! word problems involving average rate of change Please answer correctly, I have this and one more afterwards, but can only post if this is correct
(a) 2.1°C per minute
(b) 1.9°C per minute
Step-by-step explanation:(a)
O min = 222.6°C [Given]10 min = 205.6°C [Given]Difference of time = 10 minDifference of Celcius = (222.6 - 205.6)°C = 21.0°C[tex] \bf \frac{celcius}{time} = \frac{21.0}{10} = 2.1°C\: per\: minute [/tex]_____________________(b)
30 min = 157.6°C [Given]50 min = 119.6°C [Given]Difference of time = 20 minDifference of Celcius = (157.6 - 119.6)°C = 38.0°C[tex] \bf \frac{celcius}{time} = \frac{38.0}{20} = 1.9°C \:per \:minute [/tex]If 10 pounds of ice starts at ten degrees and is changed to steam at 400 degrees in twenty minutes, how many btuh are required? what size hvac unit would be needed?
As per latent heat, size of 11.61 BTUH is required to complete the whole action.
Let's assume the ice was at 32° F. So, 144 BTU/lb is required as latent heat. To melt ice and make it 32°F water required BTU is:
10 × 144 = 1440 BTU ( m× l = H where m is the mass and l is the latent heat )
To, convert 10°F ice to 32°F ice required heat is,
10×0.5035× ( 32° - 10°) = 110.77 BTU ( H = msΔt, m= mass, s = specific heat of ice, and Δ t = difference in temperature which is, 32° - 10° = 22°)
Now, to convert 32°F water to 212°F water required heat is:
10×1×180 = 1800 BTU ( SPECIFIC HEAT OF WATER IS 1 and Δt = 212-32 = 180°F )
To covert 212°F water to 212°F steam the required heat is,
10 × 970 = 9700
Now, to convert 212°F steam to 400°F steam, the required heat is ;
10 × .47 × 188 = 883.6 BTU ( The specific heat if steam is .47, Δt = 188°F )
Now total heat is, 883.6 BTU +9700 BTU + 1800 BTU + 110.77 BTU + 1440 BTU = 13934 BTU
Required power to convert it within 20 min. or 1200 sec is,
13934/1200 = 11.61 BTUH.
We can now say that, if 10 pounds of ice starts at ten degrees and is changed to steam at 400 degrees in twenty minutes, 11.61 BTUH is required.
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