Well considering that
F (1) = 8
F (x) = f(x-1) + 13
(Meaning the previous term plus 13)
So
F (x) = 13x - 5
F (0) = -5
The 20th term of the given arithmetic sequence 8, 21, 34, 47, 60... is 255.
Explanation:In the field of mathematics, this type of problem is referred to as an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference.
In your question, the arithmetic sequence provided is 8, 21, 34, 47, 60... Here, the common difference is 13 (i.e., every term after the first is 13 more than the preceding term).
To find any term (let's say the nth term) in an arithmetic sequence, you can use the formula:
nth term = first term + (n - 1) * common difference
Applying this formula to find the 20th term:
20th term = 8 + (20 - 1) * 13 = 8 + 247 = 255
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1. In a certain company, 30 percent of the men and 20 percent of the women attend night school. If 40
percent of all employees are men, what percent of all the employees attend night school?
Answer: 24% of all employees attend night school.
Step-by-step explanation: If 40% of all employees are men and 30% of the men attend night school, we can multiply 0.40 by 0.30 to get the percentage of men who attend night school: 12% or 0.12. To find the number of women who attend night school, multiply 0.20 by 0.60(assuming percentage of men and women add up to 100%) to get 12%. Add 12% and 12% to get 24% of all employees attend night school.
Please HELP on geometry I need this answer quick. At a high school, the probability that a student is a senior is 0.20. The probability that a student plays a sport is 0.15. The probability that a student is a senior and plays a sport is 0.05. What is the probability that a randomly selected student plays a sport, given that the student is a senior. A: 0.15 B: 0.05 C: 0.25 D: 0.33
Answer:
C: 0.25
Step-by-step explanation:
We will use conditional probability formula to solve our given problem.
[tex]P(B|A)=\frac{P(\text{A and B})}{P(A)}[/tex], where,
[tex]P(B|A)[/tex]= Probability of event B, given probability of event A.
[tex]P(\text{A and B})[/tex]= Probability of event A and event B.
[tex]P(A)[/tex]= Probability of event A.
Let us substitute our given values in conditional probability formula.
[tex]P(B|A)[/tex]= Probability that a student plays a sport given that student is a senior.
[tex]P(\text{A and B})[/tex]=The probability that a student is a senior and plays a sport = 0.05.
[tex]P(A)[/tex]= Probability that a student is a senior = 0.20.
[tex]P(B|A)=\frac{0.05}{0.20}[/tex]
[tex]P(B|A)=\frac{1}{4}[/tex]
[tex]P(B|A)=0.25[/tex]
Therefore, the probability that a randomly selected student plays a sport, given that the student is a senior will be 0.25 and option C is the correct choice.
Answer:
probability that a randomly selected student plays a sport, given that the student is a senior is 0.25
Step-by-step explanation:
Let, A be an event that a student is senior.
Probability can be given as , p(A) = 0.20
B be the event where student plays a sport
Probability can be given as , p(B) = 0.15
We have given that the probability of a student is a senior and plays a sport is 0.05.
i.e p(A∩B) = 0.05
We need to find the probability that a randomly selected student plays a sport, given that the student is a senior i.e p(B/A) .
Use the formula: p(B/A) = p(A∩B) / p(A)
Plug corresponding values to get p(B/A).
p(B/A) = p(A∩B) / p(A) = 0.05 /0.20
p(B/A) = 0.25 , this is the answer
Pat listed all the multiples for 15. Write the numbers in pats list
Answer: Answer : Answer : 15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,270,285,300,315,330,345,360,375,390,405,420,435,450,465,480,495,510,525,540,555,570,585,600,615,630,645,660,675,690,705,720,735,
Step-by-step explanation:
the intial value is also known as?
Answer:
Cauchy problem
Step-by-step explanation:
If you are talking about 'initial value problem', it is when talking about differential equations, an initial value problem is called a Cauchy problem by some authors as well. This is an ordinary differential equation together with a specified value which is called the initial condition. I really hope this helps!
The initial value is also known as the y intercept
What is the initial valueThe initial value, also known as the y-intercept or constant term, is a fundamental concept in mathematics, particularly in linear equations or functions. It represents the starting point or baseline on a graph, indicating the value of x is zero.
The y-intercept is where a line intersects the y-axis and serves as a reference for the function's behavior, influencing its direction and movement on the coordinate plane.
Hence we can say that The initial value is also known as the y intercept
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-7(k-8)+2k
Please help. My mom doesnt think my answer is right :( my answer is 3k+(-1) and she thinks its -5k +56
Step-by-step explanation:
-7(k-8)+2k Use distributive property.
-7k+56+2k Combine like terms.
-5k+56
Mother knows best :)
a weekly salary of $325 plus a 6.5% commission on sales at a store. How much would she make in a work week if she sold $4800 worth of merchandise?
Answer:
Income = 637
Step-by-step explanation:
Income = weekly salary + commission
commission = 6.5% * sales
commission = .065* 4800
= 312
Income = weekly salary + commission
Income = 325+312
Income = 637
What is the measure of angles 5 and 6.
5
180°-(90°+68°)=180°-158°=22°
6
180°-22°=158°
Answer:
22° and 158°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 angles in the triangle from 180
∠5 = 180° - (90 + 68)° = 180° - 158° = 22°
∠5 and ∠ 6 form a straight angle, thus the angles are supplementary
∠6 = 180° - ∠5 = 180° - 22° = 158°
352 ft is ____ % of 2 mi; 2 mi is ____ % of 352 ft
Answer:
352 ft is 3.34% of mi ;
2 mi is 3000% of 352 ft
Step-by-step explanation:
To calculate : 352 ft is ___% of 2 mi and 2 mi is ___% of 352 ft.
We can calculate first:
352 is x% of 2 mi.
Solve for x;
Use conversion:
1 mi = 5280 ft
2 mi = 10560 ft
x% of 10560 ft means [tex]\frac{x}{100} \times 10560 = 105.60 x[/tex]
then, our equation become;
352 = 105.6 x
Divide both sides by 105.6 we get;
x = 3.333333...
or
x ≈3.34
Similarly, for
2 mi is y% of 352 ft
Solve for y;
2 mi = 10560 ft
y% of 352 = [tex]\frac{y}{100} \times 352 = 3.52y[/tex]
then;
10560 = 3.52 y
Divide both sides by 3.52 we get;
[tex]y = \frac{10560}{3.52}[/tex]
y = 3000
Therefore; 352 ft is 3.34% of mi ; 2 mi is 3000% of 352 ft
find the distance between the points (-3,-4) and (5,4)
find the distance between the points (-3,5) and (0,1 )
The distance between the points (-3,-4) and (5,4) is approximately 11.31 units, and the distance between the points (-3,5) and (0,1) is exactly 5 units.
To find the distance between two points in a plane, you can use the distance formula derived from the Pythagorean Theorem, which is
d² = (x2 - x1)² + (y2 - y1)²
Let's calculate the distances for the given pairs of points.
Distance between (-3,-4) and (5,4)
d² = (5 - (-3))² + (4 - (-4))²
d² = (8)² + (8)²
d = 64 + 64 = 128
d = √128
≈ 11.31
Distance between (-3,5) and (0,1)
d² = (0 - (-3))² + (1 - 5)²
d² = (3)² + (-4)²
d = 9 + 16 = 25
d = √25
d = 5
Maria is in the state park riding her bike on the new bike trail. She starts at the beginning of the trail and rides for 4 miles. After the first 4 miles, her friend Aiden joins her and they ride the rest of the trail. By the end of the trail, Maria has been riding for two and half hours, while Aiden has been riding for two hours. Assuming they are both riding their bikes at a constant speed the entire time, how long is the bike trail?
Answer:
10 miles
Step-by-step explanation:
Thinking process:
The distance that Maria rides: 4 miles
Total time by Maria = 2.5 hrs
The friend = 2hrs
A snail moves 9feet in 3days at this rate how long will it take for the snail to move 15feet
Find the value of y when x = 4 in the equation 3x - 7/y = 1/3 Show your work help
Answer:
y = ⅗
Step-by-step explanation:
3x – 7/y = 1/3 Substitute the value of x
3×4 – 7/y = 1/3
12 – 7/y = 1/3 Multiply each side by 3
36 – 21/y = 1 Subtract 36 from each side
-21/y = -35 Multiply each side by y
-21 = -35y Divide each side by -35
y = 21/35 Divide numerator and denominator by 7
y = ⅗
=====
Check:
3×4 – 7/(⅗) = 1/3
12 -7×5/3 = 1/3
12 – 35/3 = 1/3
(36 – 35)/3 = 1/3
1/3 = 1/3
65 are drawing for a prize what is the probability for one person to win the prize
Answer:
1 in 65 chances.
Step-by-step explanation:
What is the first step when solving the equation below for x 4x - 0.3 = 1.9
A. Add 1.9 to both sides of the equation
B. Subtract 0.3 from both sides of the equation
C. Divide each side of the equation by 4
D. Add 0.3 to both sides of the equation
Answer:
The answer my frind is D
Step-by-step explanation:
When you divide,
you must
blablabla
The first step in solving the equation 4x - 0.3 = 1.9 is to D) add 0.3 to both sides of equation, isolating the term with the variable 'x'.
Explanation:The question is asking how to begin solving the equation 4x - 0.3 = 1.9 for the variable x.
The first step in solving this equation would be to eliminate the subtraction part of the equation. In other words, we want to isolate the term with the variable, which is '4x' in this case. So our best course of action is to add 0.3 to both sides of the equation.This balances the equation and moves us closer to discovering what x is, so the correct option would be 'D. Add 0.3 to both sides of the equation'.
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Grant is planting one large tree and several smaller trees. He has a budget of $1400. A large tree coast $200. Each smaller tree is $150. How many total trees can grant purchase on his budget
He is buying one large tree, so subtract the cost of a large tree from the total:
1400 - 200 = 1200
He can spend 1200 on small trees.
Divide 1200 by the cost of a small tree to find how many small trees can be bought:
1200 / 150 = 8
He can buy 8 small trees.
Total number of trees = 8 small + 1 large = 9 total
x/ 2 = 7
A) x = 5
B) x = 7
C) x = 9
D) x = 14
Answer:
D) x = 14
Step-by-step explanation:
x/2 = 7
We want to isolate x
We can multiply by 2 on each side.
2 * x/2 = 7*2
x = 14
Answer:
14
Step-by-step explanation:
Well if you simplify or divide how ever you want to say it, it will be simplified to 7.
parentheses 3 squared - 2 cubed parentheses 66
[tex]( {3}^{2} - {2}^{3} ) ^{66} [/tex]
Answer:
1
Step-by-step explanation:
evaluate the parenthesis before raising to power 66
3² = 9 and 2³ = 8, hence
(3² - 2³)= (9 - 8) = 1
[tex](3^2-2^3)^{66}[/tex] = [tex]1^{66}[/tex] = 1
using a scale, or rate, of 1/4 inch per foot, calculate the rooms dimensions for your drawing
Answer: 81 in. (6.75 ft.) by 60 in. (5 ft.)
First, convert 27 ft. and 20 ft. to inches to make it easier to work with. This would convert like this:
27 ft. x 12 in. = 324 in.
20 ft. x 12 in. = 240 in.
This also means that the scale converts to 1/4 in. = 12 in.
Now, take your 324 in. and 240 in. and apply them to the scale.
For every 12 in. (1 ft.) in the non-scale room dimensions, there will be one 1/4 in. on the scale. That would apply like this:
324 in. (27 ft.) x
1/4 in. =81 in. [or 6.75 ft.]
240 in. (20 ft.) x
1/4 in. = 60 in. [or 5 ft.]
Step-by-step explanation: If incorrect sorry, Hope this helps!!
the eauation of the line has the points (0,-1) and (2,5) is:
Answer:
y = 3x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 5)
m = [tex]\frac{5+1}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3
the line crosses the y-axis at (0, - 1) ⇒ c = - 1
y = 3x - 1 ← equation of the line
sal is making bracalets for a fundraser he uses 6 inches of yarn per bracalet how many bracalets can sal make with 5 ft of yarn
Answer:
10 bracelets
Step-by-step explanation:
we need to convert 5 ft to inches
1 ft = 12 inches
multiply by 5
5 ft = 60 inches
60 inches of yarn, 6 inches per bracelet
60/6 = 10
10 bracelets
Tom want to buy a sweater for $30.in which city will it be the most expensive
Answer:
Long Beach, California, tax = 10.25%
HELP!! ANSWER IF YOU KNOW!!!
Solve:
7 = x + 12
A) -19
B) -5
C) 4
D) 5
Need help I’m really dumb
Answer: 83485
=====================
Explanation:
The formula we will use is
A = P*(1+r)^t
with
A = final amount = unknown (what we want to find)
P = starting amount = 24000
r = growth rate in decimal form = 0.12
t = number of years elapsed = 11 (since we go from 2014 to 2025)
Plug those values mentioned into the formula. Then use a calculator to simplify
A = P*(1+r)^t
A = 24000*(1+0.12)^11
A = 24000*(1.12)^11
A = 24000*3.47854999334551
A = 83485.199840292
A = 83485
The investment will be worth about 83485 dollars
what is the area of a square with a diagonals of the length of 6?
Answer:
Area = 18
Step-by-step explanation:
We know that a square has side lengths of s
We can use the Pythagorean theorem to find s
a^2 + b^2 = c^2
We know that the hypotenuse or c = the length of the diagonal or 6
Substituting in what we know
s^2 + s^2 = 6^2
2s^2 = 36
Divide each side by 2
2s^2/2 = 36/2
s^2 = 18
Take the square root of each side
sqrt(s^2) = sqrt(18)
We only have to take the positive square root since it is a length
s = sqrt(9) sqrt(2)
s= 3sqrt(2)
The side length of the square is 3sqrt(2)
To find the area, we multiply the side by the side or s^2
s^2 = (3sqrt(2))^2
From above
s^2 = 18
*NEED MAJOR HELP!*
Drag each equation to show if it could be a correct first step to solving the equation 2(x + 7) = 36.
A 2x + 14 = 36
B (2 • x) + (2 • 7) = 36
C 2x + 7 = 36
D 2(x + 7) = 72
E x + 14 = 36
F x + 7 = 18
Yes No Not Enough Information
Answer:
I believe a) is your answer
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2(x+7)=36
Simplify: (Show steps)
2x+14=36
A line passes through the point (8,7) and has a slope of negative 3/4 Write an equation in slope-intercept form for this line.
The slope-intercept form for the line that passes through the point (8,7) and has a slope of -3/4 is y = -3/4x + 13. We found this by substituting the given slope and point into the slope-intercept equation and solving for b, the y-intercept.
Explanation:We're working on a mathematics problem here that involves the slope-intercept form of a line, which is usually written as y = mx + b. Here, m represents the slope of the line and b is the y-intercept, the point where the line intercepts the y-axis.
To write an equation for this line, we're given that the line passes through the point (8,7) and has a slope (rise over run) of negative 3/4, a negative value indicating the line decreases as it moves to the right.
We can substitute the slope and the given point into the slope-intercept equation to solve for the y-intercept: 7=(-3/4)*8+b, this simplifies to: 7=-6+b, and finally b=7+6 which gives us 13.
Therefore, the slope-intercept equation for this line with a slope of -3/4 and passing through the point (8,7) is y = -3/4x + 13.
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Final answer:
The equation of the line passing through the point (8,7) with a slope of negative 3/4 is y = -3/4x + 13 in slope-intercept form.
Explanation:
To write an equation for a line in slope-intercept form given a point and a slope, we use the formula y = mx + b, where m is the slope and b is the y-intercept. For a line that passes through the point (8,7) with a slope of negative 3/4, we first input the slope into the equation, getting y = -3/4x + b. We then substitute the x and y values from the point (8,7) into the equation and solve for b: 7 = -3/4(8) + b. This simplifies to 7 = -6 + b, and adding 6 to both sides gives us b = 13. Thus, the equation of the line in slope-intercept form is y = -3/4x + 13.
How many complex zeros does the polynomial function have?
F(x)=2x^4 +5x^3 - x^2 +6x-1
Answer:
Two complex roots.
Step-by-step explanation:
F(x)=2x^4 +5x^3 - x^2 +6x-1
is a polynomial in x of degree 4.
Hence F(x) has 4 roots. There can be 0 or 2 or 4 complex roots to this polynomial since complex roots occur in conjugate pairs.
Use remainder theorem to find the roots of the polynomial.
F(0) = -1 and F(1) = 2+5-1+6-1 = 11>0
There is a change of sign in F from 0 to 1
Thus there is a real root between 0 and 1.
Similarly by trial and error let us find other real root.
F(-3) = -1 and F(-4) = 94
SInce there is a change of sign, from -4 to -3 there exists a real root between -3 and -4.
Other two roots are complex roots since no other place F changes its sign
Final answer:
The polynomial function has 4 complex zeros.
Explanation:
A polynomial function is a function of the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_1, a_0 are constants and n is a non-negative integer. The number of complex zeros of a polynomial function is equal to its degree.
The given polynomial function is f(x) = 2x^4 + 5x^3 - x^2 + 6x - 1. The highest power of x in the function is 4, so the degree of the function is 4. Therefore, the function has 4 complex zeros.
What is the solution of this linear system? 2x + y = -4 y = -3x + 2
A house on the market was valued at 34,000 . After several years, the value decreased by 16%. By how much did the house's value decrease in dollars? What is the current value of the house?
plug in the number of years for where x is
34,000(.84)ˣ
and then do
.84ˣ
and then when you get that answer, multiply by 34,000
Evaluate the following.
Click on "Not a real number" if applicable.
Answer:
1) [tex]\sqrt{-64}[/tex] is not a real number.
2) [tex]-\sqrt{25} =-5[/tex]
Step-by-step explanation:
1) The square root of a number is defined for real numbers if and only if the number under the square root sign is greater than or equal to zero.
This implies that [tex]\sqrt{-64}[/tex] is not a real number because [tex]-64\:<\:0[/tex]
2) [tex]-\sqrt{25} =-\sqrt{5^2} =-5[/tex].
The number under the square root sign is [tex]25[/tex], which is greater than zero. Note that the negative sign is not inside the square root sign, it is outside it.
The value √-64 is not a real number, and -√25 is a real number.
√-64 and -√25 involve taking the square root of negative numbers, which results in complex numbers because real numbers do not have square roots of negative values.
Let's evaluate both:
√-64:
The square root of -64 is denoted as √(-64). In the realm of complex numbers, it's represented as 8i, where 'i' stands for the imaginary unit. So, √-64 = 8i.
-√25:
The square root of 25 is 5, and when you add a negative sign in front of it, you get -5. So, -√25 = -5.
In summary, √-64 is not a real number, and it is equal to 8i in the realm of complex numbers, while -√25 is a real number and equal to -5.
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