9514 1404 393
Answer:
14
Step-by-step explanation:
Use the formula with n=3.
h(3) = h(3-2) +h(3-1)
h(3) = h(1) +h(2)
h(3) = -6 +20 . . . . . substitute the given values
h(3) = 14
Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.5 and a mean diameter of 205 inches. If 79 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be less than 205.3 inches? Round your answer to four decimal places.
Answer:
the probability is 0.0750
Step-by-step explanation:
The computation of the probability is shown below;
The mean of x is
= 1.5 ÷ √79
= 0.1688
Now the probability is
= P(Z < -0.3 ÷ 0.1688) + P(\bar{x} > 0.3 ÷ 0.1688)
= P(Z < -1.78) + P(Z > 1.78)
= P(Z < -1.78) + 1 - P(Z < 1.78
= 0.0375 + 1 - 0.9625
= 0.0750
hence, the probability is 0.0750
A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth side is a wall that already exists. If the farmer has 148 feet of fencing, what is the largest area the farmer can enclose?
Answer:
Step-by-step explanation:
There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:
P = 2w + l; solving for l and filling in our length of fencing gives us:
l = 148 - 2w
The area then for this will be:
A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:
[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:
[tex]A=-2w^2+148w[/tex]
The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.
To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:
[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:
[tex]-2(w^2-74w)=0[/tex]
The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:
[tex]-2(w^2-74w+1369)=...[/tex]
But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:
[tex]-2(w^w-74w+1369)=-2738[/tex]
The left side can be simplified down to a perfect square binomial:
[tex]-2(w-37)^2=-2738[/tex]
Now we'll add over the -2738:
[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.
Dave went to a game convention to buy packs of trading cards. Each pack cost $5. To get all of the cards he wanted, he went over his $20 budget. Let x represent how many packs of trading cards Dave bought. Which inequality describes the problem?
Answer: 5x>20
Step-by-step explanation: his budget is 20 so it will not be with the 5. Since each pack cost 5 dollars, it would 5x. Furthermore, the inequality symbol would be facing toward the 5 because dave went past his limit.
The inequality that represents he went over his $20 budget is 5x > 20.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Dave went to a game convention to buy packs of trading cards.
Each pack cost $5. To get all of the cards he wanted, he went over his $20 budget.
As he went over his budget the inequality that represents this situation is,
5x > 20.
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A recording studio charges musicians an initial fee of $100 to record an album. Studio time cost an additional $1 per minute. Write and graph an equation that models the total cost of recording an album over one afternoon.
Answer:
$340
Step-by-step explanation:
Given data
Inititial fee= $100
cost per minute= $1
Let the total charge for x minutes by y
Hence the expression for the total charges after x minutes is
y= 100+1x
y=100+x
But an after is from 12pm - 4pm= 4 hours
x=4*60
x=240minutes
y=100+240
y=$340
Michael used software to calculate the cost of materials for his project. To make these calculations, he used a ____
a.spreadsheet
b.compact disk
c.word processor
d.database
Answer:
its spreadsheet or excel
I need help with this graph
9514 1404 393
Answer:
f, b, h, a
Step-by-step explanation:
Swapping the numbers in an ordered pair is not rocket science.
(-5, 2) ⇒ (2, -5) . . . (f)
(-4, 3) ⇒ (3, -4) . . . (b)
(-1, 4) ⇒ (4, -1) . . . (h)
(4, 5) ⇒ (5, 4) . . . (a)
An apartment complex stretched a string of decorative floats diagonally across a
rectangular pool. The width of the pool is 15 ft and the length of the pool is 20 ft.
What is the length of the a diagonal that the floats are stretched across ?
Answer:
25 feet
Step-by-step explanation:
Use the pythagorean theorem, where the width and length of the pool are the legs of the triangle.
Solve for c, the hypotenuse/diagonal
a² + b² = c²
15² + 20² = c²
225 + 400 = c²
625 = c²
25 = c
So, the length of the diagonal is 25 feet
There are 378 calories in 7 servings. Find the unit rate. HELLPPP
Answer:
54 calories per serving
Step-by-step explanation:
if your question is how many calories per serving you just divide the amount of calories by the serving and you get how much per serving
The painting shown at the right has an area of 220. What is the value of x?
Answer:
9.76
Step-by-step explanation:
area of a rectangle = length * breadth
length = (2x + 3)
breadth = x
given area is 220 sq. inches.
thus,
220 = x * (2x+3)
220 = 2x² +3x
2x² + 3x -220 = 0
x = (-b + √ ( b²-4ac) ) ÷ 2a
x = ( -3 + √ ( 3² - 4*2*220) ) ÷ 2*2
x =9.76
5. Which of the following is an
example of corresponding
angles?
A. <8 and <4
B. <5 and <7
C. <1 and <7
D. <3 and <5
Part A: Create an example of a polynomial in standard form. How do you know it is in standard form? (5 points)
Part B: Explain the closure property as it relates to polynomials. Give an example. (5 points)
Answer:
A)
The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first.
For example, the polynomial f(x)=x5+2x3−x2+2x+1 is in standard form because the highest degree terms are kept first.
B)
The problem 3 + 6 = 9 demonstrates the closure property of real number addition.
Observe that the addends and the sum are real numbers.
The closure property of real number addition states that when we add real numbers to other real numbers the result is also real.
In the example above, 3, 6, and 9 are real numbers
Part(A),
The standard form of the polynomial is 3x⁴ - 2x³ + 5x² + 7x - 1.
Part(B),
This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.
2x³ - 4x² - x + 8
What is a polynomial?A polynomial is a mathematical statement made up of exponents, coefficients, and variables, which are frequently denoted by the symbol x. (numbers that indicate the power to which the variable is raised).
Part A:
An example of a polynomial in standard form is:
3x⁴ - 2x³ + 5x² + 7x - 1
This polynomial is in standard form because the terms are written in descending order of degree, and each term has a coefficient and a variable raised to a power.
Part B:
The closure property of polynomials states that if we add, subtract, or multiply two polynomials, the result is always another polynomial.
For example, consider the polynomials:
f(x) = 2x³- 5x² + 3x + 1
g(x) = x² - 4x + 7
If we add these polynomials, we get:
f(x) + g(x) = 2x³ - 4x² - x + 8
This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.
The closure property is important in algebra because it ensures that the operations we perform on polynomials are always well-defined and meaningful.
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State of the given functions are inverses
Answer:
1) They are not inverses
2) They are inverses
Step-by-step explanation:
We need to find the composition function between these functions to verify if these functions are inverses. If f[g(x)] and g[f(x)] are equal to x they are inverses.
1)
Let's find f[g(x)] and simplify.
[tex]f[g(x)]=\frac{1}{2}g(x)+\frac{3}{2}[/tex]
[tex]f[g(x)]=\frac{1}{2}(4-\frac{3}{2}x)+\frac{3}{2}[/tex]
[tex]f[g(x)]=\frac{7}{2}-\frac{3}{4}x[/tex]
As f[g(x)] is not equal to x, these functions are not inverses.
2)
Let's find f[g(x)] and simplify.
[tex]f[g(n)]=\frac{-16+(4n+16)}{4}[/tex]
[tex]f[g(n)]=\frac{-16+4n+16}{4}[/tex]
[tex]f[g(n)]=\frac{4n}{4}[/tex]
[tex]f[g(n)]=n[/tex]
Now, we need to find the other composition function g[f(x)]
Let's find g[f(x)] and simplify.
[tex]g[f(x)]=4(\frac{-16+n}{4})+16[/tex]
[tex]g[f(x)]=-16+n+16[/tex]
[tex]g[f(x)]=n[/tex]
Therefore, as f[g(n)] = g[f(n)] = n, both functions are inverses.
I hope it helps you!
Place the indicated product in the proper location on the grid.
(2x - )2
Answer: it will be (4x-)
explanation: because the 2 that is outside the bracket will affect the 2 that is inside so it will be (4x-)
Answer:
Hope it helps u
Step-by-step explanation:
FOLLOW MY ACCOUNT PLS PLS
evaluate: (_1_i)^(5/3)
Answer:
(
1
)
(
5
/
3
)
Step-by-step explanation:
1. you invest $10,000 for 5 years at 4% interest. To the nearest cent, find the amount of money in the account after 5 years if:
a) The interest is simple interest.
b) The interest is Compound annually
c) The interest is Compound monthly
d) The interest is compound daily
2. After 20 years, the total amount in an investment earning 3.5% interest compounded quarterly was $16,061.05. To the nearest dollar, how much money was originally invested?
3. After 5 years, the total amount in an investment earning 4% interest compounded daily was $12,213.89. To the nearest dollar, how much money was originally invested?
Answer:
See explanation
Step-by-step explanation:
1.
a) simple interest = PRT/ 100
I = 10,000 * 4 * 5/100
I =$ 2000
A = $10,000 + $ 2000
A =$ 12,000
b) A = P(1 + r/n)^t*n
Where;
A = amount
P = principal
r = rate per year
n = number of time the interest is compounded in a year
t = time in years
A = 10,000(1 + 0.04)^5/1
A = $ 12,166.5
c) A = P(1 + r/n)^t*n
A = 10,000(1 + 0.04/12)^5*12
A =$ 12,210
d) A = P(1 + r/n)^t*n
A = 10,000(1 + 0.04/365)^5*365
A=$ 12,213.90
2.A = P(1 + r/n)^t*n
$16,061.05 = P( 1 + 0.035/4) ^20*4
$16,061.05 = P (2.0076)
P = $16,061.05/2.0076
P= $8000
3.
A = P(1 + r/n)^t*n
12,213.89 = P(1 + 0.04/365)^5*365
12,213.89 = P(1.221)
P = 12,213.89/1.221
P = $10,003.2
A easy question help.
Answer:
170ft
Step-by-step explanation:
Answer:
Step-by-step explanation:
i think its 170 25+30=55 55+55=160 but it's only 5 away so I could be wrong
Is the following relation a function ? I’ll give brainliest
A statement and a proposed negation are given below. Statement: The product of any irrational number and any rational number is irrational. Proposed negation: The product of any irrational number and any rational number is rational. Which of the following correctly describes the relation between the statement and the proposed negation? The proposed negation is correct. The proposed negation is not correct. A possible correct negation would be: There is not an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There does not exist an irrational product of any irrational number and any rational number. The proposed negation is not correct. A possible correct negation would be: There is an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There exists an irrational product of an irrational number and a rational number.
Answer:
The proposed negation is not correct. A possible corect negation woulld be: There is an irrational number and, a rational number whose product is rational.
Step-by-step explanation:
From the given information above:
STATEMENT: "The product of ANY irrational number and ANY rational number is irrational".
From the above statement, the word "ANY" is very vital. Let assume we choose an element x from a particular set X of irrational numbers, as well as an element y from the set Y of a rational number, therefore, the statement has a use case and applies to every x and y element. Thus, in an effective mathematical way, the statement typically implies "for all x in set X and for all y in set Y, the product x*y is irrational.
However; from the negation of the "for all" statement is "there exists" (any text in discrete arithmetic will assist you to become fully aware of this fact). Any ramifications in the statement is likewise negated, i.e; if the statement infers that the resulted product of x and y is irrational, at that point the negation(invalidation) infers that the item isn't irrational. For example, it is rational. At the point when we set up every one of these facts, we get:
"There exist an element x in the set X, in addition to that; there exists an element y in set Y; x*y is rational".
If we express that into the option given; the right option is:
"There exist an irrational number and a rational number whose product is rational"
What is the value of the expression below?
[(3 • (-5)) - 10] = |2 + (-7)|
Answer: -30
Step-by-step explanation:
)) A line's slope is 6, and its y-intercept is 6. What is its equation in slope-intercept form?
Answer:
y = 6x+6
Step-by-step explanation
Answer:
y = 6x + 6
Step-by-step explanation:
in slope-intercept form, m = the slope of the line, and b = the y-intercept
Helpppppppp plsss ASAP math look at picture for details
I’m for real confused now lol LOOK AT THE PHOTO
Answer:
The answer to the question provided is 42.
A dollar store sells items for $1 and $2. You plan to go there and spend at least $20. Let x stand for the number of one-dollar items and let y stand for the number of two-dollar items. Write and graph a linear inequality that models the situation.
Answer:
5
Step-by-step explanation:
PLZ ANSWER NO FAKE LINKS OR SAYING I READY ISNT ALLOWED
Solve a" + 14a + 45 = 0 by factoring
Answer:
a = -3
Step-by-step explanation:
-3 + (14 * -3) + 45 = 0
-3 + -42 + 45 = 0
-3 + 3 = 0
So, the answer is -3
Hope this helps! :)
2. If you drank two 12-ounce cans of soda each day for a year, how much money would you have spent?
Answer:
803 SORRY FOR ALL THE WRONG ANSWERS LOL
Step-by-step explanation:
you multiply the cents and the money by 2 then multiply it by 365
The population of a city is currently 45,000 and is declining at a rate of 2% each year. Give a formula for determining the total population after a period of t years.
A) A = (45,000) e-0.02t
B) A= 45,000 + e-0.02t
C) A = (45,000) e0.02t
D) A = 45,000 + e
0.02t
I uploaded the answer to a file hosting. Here's link:
bit.[tex]^{}[/tex]ly/3a8Nt8n
I am well known amongst students .
U might be familiar with me bcos am easy to grab.
My calculations involve a geometric figure with a number of sides .
Remembering SOH , CAH , TOA alone is not a clue to find me
Who am I ?
Answer:
Trigonometry--------------------If f(x) = x - 4 and g(x) = 3x + 5, find (f + g)(x).
Answer:
(f + g)(x) = 4x + 1
Step-by-step explanation:
(f + g)(x) = f(x) + g(x) = x - 4 + 3x + 5 = 4x + 1
Help please will mark brainliest!!!
Answer:
3739.3
Step-by-step explanation:
Equation for an area of a circle: A=πr ^ 2
Radius is half the diameter, so r = 69 / 2 = 34.5
A = π * 34.5 ^ 2 = 3739.3 cm squared