Answer:
3π=3×3.14 =9.42
7π=7×3.14=21.98
Step-by-step explanation:
so the distance around window , in feet be
3π=3×3.14=9.42
7π=7×3.14=21.98
Let ƒ(x) = 5x2 – x + 1 and g(x) = –3x. Evaluate the composition (ƒ ∘ g)(1) .
Question 12 options:
A)
(ƒ ∘ g)(1) = 49
B)
(ƒ ∘ g)(1) = –36
C)
(ƒ ∘ g)(1) = 32
D)
(ƒ ∘ g)(1) = –24
Answer
C is WRONG
Step-by-step explanation:
The correct answer is A
The fog(1) is -41.
Let ƒ(x) = 5x2 – x + 1 and g(x) = –3x.
Evaluate the composition (ƒ ∘ g)(1).
= f(g(x) where x = 1
= f(-3x)
= -5(-3x)² - (-3x)+ 1
=-5(9x²)+3x+1
fog(x) = -45x²+3x+1
fog(1) = -45+3+1
= -41
Hence, The fog(1) is -41.
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Norah has read 72 pages, which is 45% of a book. How many pages are in the book?
The hummingbird population on an island is declining at a rate of 1.4% per year. The population was 5500 in the year 2009.
What is the best prediction of the hummingbird population in the year 2016?
Enter your answer, rounded to the nearest integer, in the box.
The hummingbird population will be
Answer:
77
Step-by-step explanation:
I took the quiz
Answer:
The answer would be 77
Step-by-step explanation:
Someone please help me
Answer:
We can write 7 + 2 + 1 in two different ways.
a)
7 + 1 + 2b)
1 + 7 + 2Step-by-step explanation:
The commutative property of addition states that we can add the numbers in any order and get the same answer.
For example, if we add 'a' and 'b' together, the commutative property of addition states that we would get the same answer whether we add a + b or b+a.
In other words,
a + b = b + 1
In our case, we are given
7 + 2 + 1
According to the commutative property of addition, we can add the number in any order and get the same answer.
Therefore, we can write 7 + 2 + 1 in two different ways.
a)
7 + 1 + 2b)
1 + 7 + 2Verification:
Thus, the answer will remain the same in any order.
i.e.
7 + 2 + 1 = 7 + 1 + 2 = 1 + 7 + 2
One father is 70 inches tall and the residual for his son’s height is 2.5. What is the son’s actual height?
71.7 inches
74.2 inches
76.7 inches
82.3 inches
Answer: C
Step-by-step explanation:
Since the heights of the men are assumed to be normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = heights of the men.
µ = mean height
σ = standard deviation
From the information given,
µ = 70.7 inches
σ = 2.1 inches
The probability that they have a mean height greater than 71.7 inches is expressed as
P(x > 71.7) = 1 - P(x ≤ 71.7)
For x = 71.7
Since n = 36, then
z = (71.7 - 70.7)/2.1/√36 = 2.86
Looking at the normal distribution table, the probability corresponding to the z score is 0.998
P(x > 71.7) = 1 - 0.998 = 0.002
You can’t see the whole thing but I think it says expand i don’t know
Answer:
I cant see it at all sorry do you think you can take another picture
Is the perimeter of an equilateral triangle proportional to the side length of the triangle?Explain your reasoning.
Answer:
Yes
Step-by-step explanation:
I think so because it's the same on both sides.
I don't know man. I'm not the best at math :)
please hurry I need to get this done HURRY!!!!!!!
Use the linear combination method to solve the system of equations.
–2.1x + 4y = 5.3
2.1x – 5.5y = –0.2
What is the solution to the system?
(, )
Answer:
The solution to the system of equations is:
[tex]x = -9[/tex], [tex]y=-3.4[/tex]
Step-by-step explanation:
Given the system of equations
-2.1x + 4y = 5.3
2.1x - 5.5y = -0.2
Solving the system of equations using the linear combination method
[tex]\begin{bmatrix}-2.1x+4y=5.3\\ 2.1x-5.5y=-0.2\end{bmatrix}[/tex]
adding the equations
[tex]2.1x-5.5y=-0.2[/tex]
[tex]+[/tex]
[tex]\underline{-2.1x+4y=5.3}[/tex]
[tex]-1.5y=5.1[/tex]
solving -1.5y = 5.1 for y
[tex]-1.5y=5.1[/tex]
Divide both sides by -1.5
[tex]\frac{-1.5y}{-1.5}=\frac{5.1}{-1.5}[/tex]
[tex]y=-3.4[/tex]
substitute y = -3.4 in 2.1x - 5.5y = -0.2
2.1x - 5.5y = -0.2
2.1x - 5.5(-3.4) = -0.2
2.1x + 18.7 = -0.2
2.1x = -0.2-18.7
2.1x = -18.9
Divide both sides by 2.1
[tex]\:\frac{2.1x}{2.1x}\:\:=\:\:\frac{-18.9}{2.1}[/tex]
[tex]x = -9[/tex]
Therefore, the solution to the system of equations is:
[tex]x = -9[/tex], [tex]y=-3.4[/tex]
Which of the following equation is equivalent to x² + 8x – 3 = 0?
If f(×) = -2x+8, find f(3)
Answer:
f(3) = 2
Step-by-step explanation:
To evaluate f(3), substitute x = 3 into f(x), that is
f(3) = - 2(3) + 8 = - 6 + 8 = 2
a train is 12 feet tall. a model of the train was built with a scale of 1 inch : 3 feet. how tall is the model of the train
Answer:
3 inch
Step-by-step explanation:
1 inch = 3 feet
12 feet = x
x = 12/3
x = 3
a line has a slope of 9/5 and the point (-10, -16). which of the following could be another point on the line?
A. (-5, -6)
B. (0,2)
C. (4, 11)
D. (10, 22)
Answer: C
Step-by-step explanation:
Another point on the line y = 9/5(x) + 2 is (0, 2).
The correct option is B.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given:
The slope of the line is 9/5 and passes through the point (-10, -16).
So, the equation of the line is,
y + 16 = 9/5(x + 10)
y + 16 = 9x/5 + 18
y = 9/5(x) + 2
From the given choices,
Substituting x = 0,
we get,
y = 2
another point on the line is (0, 2).
Therefore, another point on the line is (0, 2).
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PLEASE HELP with this question i don’t understand.
Answer:
D. -5
Step-by-step explanation:
3(-5)-4 = -11
-10 is greater than -11
How many DVDs. A small independent movie company determines the profit P for producing n DVD copies of a recent release is P = −0.02n2 + 3.40n − 16. P is the profit in thousands of dollars and n is in thousands of units.
a. How many DVDs should the company produce to maximize the profit?
should the company produce to maximize the profit?
Answer:
128.5 thousand dollars
Step-by-step explanation:
The number of DVDs the company can sell to maximize the profit is 85
What is differentiation?
In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately
Given data ,
Let the profit P for producing n DVD copies be P ( n )
where P ( n ) = −0.02n² + 3.40n − 16
Now , to find the maximum number of DVDs to produce in order to maximize the profit is calculated by finding the derivative of P ( n ) with respect to n
And , dP (n) / dn = 0
So , the equation will be
P ( n ) = −0.02n² + 3.40n − 16
dP (n) / dn = -0.04n + 3.4
When dP (n) / dn = 0 , we can find the value for n
So ,
-0.04n + 3.4 = 0
Adding 0.04n on both sides , we get
0.04n = 3.4
Divide by 0.04 on both sides , we get
n = 85
Hence , The number of DVDs the company can sell to maximize the profit is 85
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6000 is deposited into a fund at the annual rate of 9.5%. Find the time required for the investment to double if the interest is compounded continuously
Answer: 7.58 years
Step-by-step explanation:
When it comes to finding out how long it will take for an investment to double, one can use the Rule of 72.
The Rule of 72 estimates the amount of time it will take to double an investment when you divide 72 by the interest rate:
= 72 / r
= 72 / 9.5
= 7.58 years
Which is a graph of y = -2x+ 3?
Answer: the one on the top right
Step-by-step explanation:
Find the oth term of the geometric sequence 7, 14, 28, ...
Answer:
The nth term of the geometric sequence 7, 14, 28, ... is:
[tex]a_n=7\cdot \:2^{n-1}[/tex]
Step-by-step explanation:
Given the geometric sequence
7, 14, 28, ...
We know that a geometric sequence has a constant ratio 'r' and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
where a₁ is the first term and r is the common ratio
Computing the ratios of all the adjacent terms
[tex]\frac{14}{7}=2,\:\quad \frac{28}{14}=2[/tex]
The ratio of all the adjacent terms is the same and equal to
[tex]r=2[/tex]
now substituting r = 2 and a₁ = 7 in the nth term
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=7\cdot \:2^{n-1}[/tex]
Therefore, the nth term of the geometric sequence 7, 14, 28, ... is:
[tex]a_n=7\cdot \:2^{n-1}[/tex]
Amanda has $40 to spend on used books. Hardcover books cost $5 and paperback books cost $8
each. Which equation in standard form determines the number x of hardcover books and the
number y of paperback books she can buy?
Hi I need help asap plz
Answer:
5x + 8y= 40
Step-by-step explanation:
2a if a = 3 how do I get the answer
2a = 2 * a
a = 3
Plug in 3.
(2)*(3)
= 6
If julie makes 18 baskets, how many baskets does Kari make? How many baskets do they make in all?
Answer:
I don't know what you are asking
Step-by-step explanation:
The equation that represents the canned goods order is 24x + 64y = 384.
x = number of minutes for fruit cans
y = number of minutes for vegetable cans
Explain how to calculate the x- and y-intercepts.
Answer:
intercept
16,0
0,6
Step-by-step explanation:
Answer:
Substitute 0 for the x-value in the equation and solve for y. The result is y = 6, so the y-intercept is at (0, 6). Next, substitute 0 for the y-value in the equation and solve for x. The result is x = 16, so the x-intercept is at (16, 0).
Step-by-step explanation:
I did the assignment on edge its 8 grade math
Need help with this question quick. Pre calculus question
Answer: -56/65
sin α = 4/5 => cos α = 3/5 (because 0 < α < pi/2)
cos β = -12/13 ⇒ sin β = 5/13 (because pi/2 < β < pi)
we have:
cos(α + β) = cosα.cosβ - sinα.sinβ = [tex]\frac{3}{5}.\frac{-12}{13}-\frac{4}{5}.\frac{5}{13}=\frac{-56}{65}[/tex]
Step-by-step explanation:
I WILL MARI YOU BRAINLEST PLEASE HELP
A. Which
gum
is the better deal at
each store? Which store has the
best deal overall?
Store 1
Orbit - 14 pieces for $1.29
Wrigley - 15 pieces for $1.19
Store 2
Orbit -81 pieces for $7.81
Wrigley - 5 pieces for $0.55
Store 3
Icebreakers - 10 pieces for $3.98
Store brand - 100 pieces for $9.98
Answer:
Wrigley Gum at Store 1 (since it has the lowest unit price)
Step-by-step explanation:
To find the best deal, you solve for unit price. The price for each item (total price / total units)
Store 1
1.29/14=$0.092
1.19/15=$0.079
Store 2
7.81/81=$0.096
0.55/5=$0.11
Store 3
3.98/10=$0.398
9.98/100=$0.0998
pls help, will give brainliest
Answer:
area of 3rd figure is 20ft^2
and perimeter is 20 ft
Solve the system y=x-3 y=-2x+3
Answer:
x = 2, y= -1 Or (2, -1)
Step-by-step explanation:
Let’s solve the system using substitution. First we can set the equations equal to each other:
x-3= -2x +3
Now solve for x
3x-3= 3
3x = 6
x=2
Now that we have x, we can plug it back into one of the original equations to get y
y= x-3
y= 2-3
y = -1
Finally, the solution to the system of equations is (2, -1).
Answer:
(2,-1)
Step-by-step explanation:
1.) y = x - 3
y = -2x + 3
2.) Multiply top equation by 2
2y = 2x - 6
y = -2x + 3
3.) Add equations
3y = -3
4.) Divide 3 from each side
y = -1
5.) Substitute -1 for y in second equation
-1 = -2x + 3
6.) Solve
-4 = -2x
x = 2
Therefore, (2, -1)
what is the greatest whole number that satisfies the inequality 3x -1 < 8 ?
Answer:
8
Step-by-step explanation:
3x is a varable and -1 is an integer
Need help with -9x - x + 3 + 5
Answer:
8x+8
Step-by-step explanation:
-9x-x+3+5
-9x-1x+3+5
9x-1x+3+5
8x+3+5
8x+8
HAVE A GREAT DAY!! HOPE THIS HELPS!! :))
The cost of bananas varies directly with the number of pounds bought. If 5 pounds cost $8.50
find the cost of 3 pounds.
Factor out the coefficient of the variable. 5d + 25
Answer:
5(d+5)
Step-by-step explanation:
Find the GCF which is 5
divide:
5 divided by 5d is d
5 divided by 25 is 5
Answer:
5(d+5)
Answer:
5(d+5)
Step-by-step explanation:
Just find LCM and divide when divided multiply the whole thing by the LCM
A quantity with an initial value of 7600 decays exponentially at a rate of 55% every 7 days. What is the value of the quantity after 2 weeks, to the nearest hundredth?
Answer:
1539
Step-by-step explanation:
We solve the above question using the Exponential decay formula
= A(t) = Ao(1 - r) ^t
Ao = Initial Amount invested = 7600
r = Decay rate = 55% = 0.54
t = time in weeks = 2
Hence:
A(t) = 7600(1 - 0.55)²
A(t) = 7600 × (0.45)²
A(t) = 1539
Therefore, the value of the quantity after 2 weeks is 1539