Answer:
This is not a function graph as no variables are present.
If\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\]where $a$ and $b$ are integers and $b$ is as small as possible, find $a+b.$
9514 1404 393
Answer:
12
Step-by-step explanation:
Apparently, you want the sum a+b when ...
[tex]\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\][/tex]
A calculator can show you the expression on the left evaluates to √243. In simplest terms, that is 9√3, so we have a=9, b=3 and ...
a+b = 9+3 = 12
Answer:
12
Step-by-step explanation:
I need two examples of rounding to the thousandths place. SHOW ALL WORK!
Answer:
3.418
Step-by-step explanation:
3.4175
3.4178
u round if the number behind it is higher than 5
It costs $7.45 for 2.5 pounds of round steak. What is the unit rate?
A.$9.95 per pound
B.$18.63 per pound
C.$2.50 per pound
D.$2.98 per pound
Answer:
D.
Step-by-step explanation:
Since the unit rate is in dollars per pound, we divide the cost (in dollars) by the weight (in pounds.)
($7.45)/(2.5 lb) = $2.98 per pound
Answer: D.
Tìm x không âm biết √x =3
Answer:
x=9
Step-by-step explanation:
[tex]\sqrt{x}[/tex]=3
[tex]\sqrt{x}[/tex]^2=3^2
x=9
find the value of X in each figure below
Answer:
168). C
169). C
170). C
Step-by-step explanation:
For the first angle, it is a right angle, so it measures 90 degrees.
x and 50 are complementary angles, meaning they add up to 90 degrees.
So, subtract 50 from 90 to get 40, which is equal to x.
45 and x are supplementary angles, meaning they add up to 180 degrees.
Subtract 45 from 180 to get 35 degrees, which is the measure of angle x.
All angles in a triangle add up to 180 degrees.
So, 70 + 56 = 126, 180 - 126 = 54.
Since the unknown angle is x - 5, 54 + 5 = 59, which the the measure of angle x - 5.
Since lim n→ infinity (.............) = ...........
Notice that
[tex]\dfrac{4n+1}{8n+2}=\dfrac{4n+1}{2(4n+1)}=\dfrac12[/tex]
So by the root test,
[tex]\displaystyle\lim_{n\to\infty}\sqrt[n]{\left|\left(\frac12\right)^{2n}\right|} = \frac14 < 1[/tex]
and so the series converges (absolutely).
Compute how many 7-digit numbers can be made from the digits 1, 2, 3, 4, 5, 6, 7 if there is no repetition and the odd digits must appear in an unbroken sequence. (Examples: 3571264 or 2413576 or 2467531, etc., but not 7234615.)
Answer:
Number of 7-digit numbers that can be made from the digit is 576
Step-by-step explanation:
Given the data in the question;
digits ⇒ 1, 2, 3, 4, 5, 6, 7
Number of odd numbers in the given digits = 4
Number of even numbers in the given digits = 3
now, we take the odd digits as a single unit.
so, number of ways the odd digits can be arranged with the unit will be 4!.
Now, lets consider the unit of 4 odd digits with 3 even digits.
there are 4 units.
so the number of possible arrangements of these 4 units = 4!
hence, Number of 7-digit numbers that can be made from the digits will be;
⇒ Number of possible arrangements of 4 units × Number of ways in which the odd digits can be arranged within the unit.
⇒ 4! × 4!
⇒ 576
Therefore, Number of 7-digit numbers that can be made from the digit is 576
What does h(40) = 1400 mean in terms of the problem? Hours of Training 10 20 30 40 50 60 70 Monthly Pay 1100 1200 1300 1400 1500 1600 1700 A. There are 40 workers who are paid $1400 per month. B. A worker who works 40 hours is paid $1400.- C. A worker with 40 hours of training is paid $1400 per month D. A worker with 1400 hours of training is paid $40 per month
Answer:
the answer is B
Step-by-step explanation:
I just know
h(40) = 1400 means that if a worker has 40 hours of training, the corresponding monthly payment is $1400.
Option C is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The given table shows the relationship between the number of hours of training and the corresponding monthly pay for a worker.
The table implies that there is a function h that relates the number of hours of training to the monthly payments.
The notation h(40) means the value of the function h when the input, or independent variable, is 40.
Therefore,
h(40) = 1400 means that if a worker has 40 hours of training, the corresponding monthly payment is $1400.
Learn more about functions here:
https://brainly.com/question/28533782
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The Science Club arranged a trip to Smithsonian. Only 2/3 of the members were able to attend, which left one seat empty on the 25-passenger bus. How many members does the Science Club have?
Answer:
36 members
Step-by-step explanation:
Let x = the number of science club members
There are 24 people on the bus (1 seat empty on the 25 seat bus)
2/3 of the club attended and that equals 24 people on the bus
2/3x = 24
Multiply each side by 3/2
3/2 * 2/3x = 24 * 3/2
x = 36
Evaluate the following as true or false. The approximate value of a definite integral that is obtained using the trapezoidal rule will always be greater than the exact value of the same definite integral.
a. True
b. False
False. Let f(x) be an integrable function that is concave on an interval [a, b] in its domain. "Concave" here means that the secant line drawn from (a, f(a)) to (b, f(b)) lies below the graph of f(x).
Marilyn is retiring and wants to set up a 25-year annuity with 140 000 of her savings . The annuity earns 7.7 compounded monthly How much will Marilyn receive every month ?
Answer:
marilyn isrestiring and wants to set up a 25-year annuity earns 7.
I need help ASAP anyone
9514 1404 393
Answer:
C
Step-by-step explanation:
The vertical asymptote tells you the denominator is zero at x=-1. The only function that has that characteristic is ...
F(x) = (x +2)/(x +1)
classmate Date 8) Solve the word problems a) If 576 balls are arranged in equal number of rows and columns, find the numbers of rows.
Answer:
24
Step-by-step explanation:
The number of rows (x) should b equal to the number of columns (x).
x²=576
x=√576 taking the square root of the product
x=24
find the lateral surface area of this cylinder. round to the nearest tenth. r=5cm 5cm LSA (in the image)
Answer:
157 cm²
Step-by-step explanation:
A cylinder is given to us and we need to find out the lateral surface area of the cylinder . We can see that the ,
Height = 5cm
Radius = 5cm
We know that we can find the lateral surface area of the cylinder as ,
[tex]\rm\implies LSA_{cylinder}= 2\pi r h [/tex]
Substitute upon the respective values ,
[tex]\rm\implies LSA = 2 \times 3.14 \times 5cm \times 5cm [/tex]
Multiply the numbers ,
[tex]\rm\implies \boxed{\blue{\rm LSA = 157 \ cm^2 }}[/tex]
Hence the Lateral surface area of the cylinder is 157 cm² .
[tex] \setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{5cm}}\put(9,17.5){\sf{5cm}}\end{picture}[/tex]
Answer:
314.2 is the Surface area
Step-by-step explanation:
Hope it Helps! If you have any questions, feel free to comment! :)
2π(5)(5)+2π(5^2)
2π(25)+2[tex]\pi[/tex](25)
50π+50π=100π
314.2 is the answer. That's what we get after rounding up! :)
A line with a slope of 4 passes through the point (2, 3) . What is its equation in slope -intercept form?
Answer:
y=4x-5
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y intercept.
Plug in what you know to solve for b.
3 = 4(2) + b
3 = 8 + b
3-8 = b
b = -5
now put b and m back into the slope- int form.
y = 4x-5
1/2 sin x sin (2x) + Cos 3 x
Answer:
1.047734151
Step-by-step explanation:
Type into calculator
1/2sin(2x)+cos(3x)
How to solve
(2.31*10^-6)+(5.87*10^-4)
Answer:
5.8931 ⋅ 10^ − 4
Step-by-step explanation:
Expanded Form:
0.00058931
What is 5% of 483759????
Step-by-step explanation:
5% of 483759 is 24187.95
Answer: The answer is 24,187.95
Step-by-step explanation:
483759 Multiplied by 0.05 = 24,187.95
I don’t know how to solve it can someone help me?
Answer:
Step-by-step explanation:
Because the arcs HI and GJ are the same, that means that the segments HI and GJ are also the same. Therefore,
c + 20 = 2c and
20 = c
If IC Rs 100 is equal to Rs 160 NC, convert IC Rs 150 into NC rupees.
Answer:
240 NC rupees.
Anarime estimates that of people booked on the fights actually show up in the e books 70 people on a fight for which the maximum number is as what is the probability at the number of people who show up will exceed the capacity of the plane
Answer:
An airline estimates that 94% of people booked on their flights actually show up. If the airline books 77 people on the flight for which the maximum number is 75, what is the probability that the number of people who show up will exceed the capacity of the plane?
-------------------------
Binomial Problem with n = 77 and p = 0.94
---
P(76 <= x <= 77) = 1-P(0 <=x <= 75) = 1 - binomcdf(77,0.94,75) = 0.0504
==================
Cheers,
Stan H.
Which best describes the relationship between the line that passes through the points (6, –1) and (11, 2) and the line that passes through the points (5, –7) and (8, –2)?
A. same line
B. neither perpendicular nor parallel
C. perpendicular
D. parallel
Answer:
Step-by-step explanation:
slope of line through (6,-1) and (11,2) = (-1 - 2)/(6 - 11) = 3/5
slope of line through (5,-7) and (8,-2) = (-7 - (-2))/(8 - 5) = -5/3
product of the slopes = -1, so the lines are perpendicular.
If my saving x$ grows 10% every year how much will I have in:
1 year
2 year
5 year
Answer:
[tex]1.1x, 1.21x, 1.61051x[/tex]
Step-by-step explanation:
If you saving grows [tex]10 \%[/tex] every year, then your saving is [tex]1.1\\[/tex] times your saving from last year. Therefore, after one year, you will have [tex]1.1x\\[/tex], then after [tex]2[/tex] years, you will have [tex](1.1)^2 \cdot x=1.21x[/tex], then after [tex]5[/tex] years, you will have [tex](1.1)^5 \cdot x = 1.61051x[/tex].
Answer:
$1.1x, $1.21x, $1.61x
Step-by-step explanation:
In the picture below, which lines are lines of symmetry for the figure?
A. 1 and 3
B. only 3
C. 2
D. 1, 2, and 3
A line of symmetry would separate a shape to make multiple shapes that are exactly the same.
The answer is C.2
Anne is building bookcases that are 3.1 feet long. How many complete shelves can be cut from a 12-foot board?
Answer: 3 shelves
Step-by-step explanation:
12 ÷ 3.1 = 3.87…
Since this is more than 3 but less than 4, we can build 3 full shelves with a leftover.
four consecutive numbers have a sum of –30. What number is x?
Answer:
- 9
Step-by-step explanation:
Let the four consecutive numbers be x, x + 1,
x + 2 and x + 3.
x + x + 1 + x + 2 + x + 3 = - 30
x + x + x + x + 1 + 2 + 3 = - 30
4x + 6 = - 30
4x = - 30 - 6
4x = - 36
x = - 36 / 4
x = - 9
Consider the initial value problem
y' + 6y = {0 if 0 < or equal to t < or equal to 2
12 if 2 < or equal to t < or equal to 6
0 if 6 < or equal to t < or equal to infinity}
a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below).
b. Solve your equation for Y(s).
c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).
y' + 6y = f(t)
where
[tex]f(t)=\begin{cases}0&\text{if }0\le t\le2\\12&\text{if }2<t\le6\\0&\text{if }6<t<\infty\end{cases}[/tex]
You can write f(t) in terms of the unit step (i.e. Heaviside theta) function u(t), which is defined as
[tex]u(t)=\begin{cases}0&\text{if }t<0\\1&\text{if }t\ge0\end{cases}[/tex]
Then the DE is written as
y' + 6y = 12 u (t - 2) - 12 u (t - 6)
(a) Take the Laplace transform of both sides:
LT[y' + 6y] = LT[12 u (t - 2) - 12 u (t - 6)]
s Y - y (0) + 6Y = 12 (exp(-2s) - exp(-6s))/s
(b) Solve for Y :
(s + 6) Y = 12 (exp(-2s) - exp(-6s))/s + y (0)
Y = 12 (exp(-2s) - exp(-6s))/(s (s + 6)) + y (0)/(s + 6)
(c) Take the inverse transform:
LT⁻¹ [Y] = LT⁻¹[12 (exp(-2s) - exp(-6s))/(s (s + 6)) + y (0)/(s + 6)]
y = 12 LT⁻¹ [(exp(-2s) - exp(-6s))/(s (s + 6))] + y (0) LT⁻¹ [1/(s + 6)]
y = 12 u (t - 2) LT⁻¹ [1/(s (s + 6))] - 12 u (t - 6) LT⁻¹ [1/(s (s + 6))] + y (0) exp(-6t )
For the remaining inverse transform, break up into partial fractions:
1/(s (s + 6)) = a/s + b/(s + 6)
1 = a (s + 6) + bs
1 = (a + b) s + 6a
==> 6a = 1, a + b = 0 ==> a = 1/6, b = -1/6
y = 2 u (t - 2) LT⁻¹ [1/s - 1/(s + 6)] - 2 u (t - 6) LT⁻¹ [1/s - 1/(s + 6)] + y (0) exp(-6t )
y = 2 u (t - 2) (1 - exp(-6t )) - 2 u (t - 6) (1 - exp(-6t )) + y (0) exp(-6t )
The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?
A) 32/3π cm^3
B) 8π cm^3
C) 64/3π cm^3
D) 16π cm^3
Answer:
32[tex]\pi[/tex]/3 cm³
Step-by-step explanation:
If the diameter is 4 cm, then the radius is 2 cm.
Use the sphere volume formula:
V = 4/3[tex]\pi[/tex]r³
Plug in the radius and solve:
V = 4/3[tex]\pi[/tex](2)³
V = 4/3[tex]\pi[/tex](8)
V = 32[tex]\pi[/tex]/3
So, the volume of the sphere is 32[tex]\pi[/tex]/3 cm³
A function is expressed by the formula y = 2x + 7. Find the value of y if x is equal to 1; -20; 43.
Answer:
when x = 1 then y = 9
when x = -20 then y = -33
when x = 43 then y = 93
Step-by-step explanation:
Just replace the given values of x ( which are 1 , -20 , 43 ) in the function
A ball is dropped from 248 feet above
the ground level and after the second
bounce it rises to the height of 62 feet.
If the height to which the ball rises
after each bounce is always the same
fraction of the height reached on its
previous bounce, what is this
fraction?
Let us say
The Height from which the ball was first dropped as H0 = 248 feet
The Height reached by the ball after second bounce is H1
The Height reached by the ball after second bounce is H2 = 62 feet
Given , Height the ball reaches after bounce is a fraction of the height the ball reached in the previous bounce
The Height reached by the ball after second bounce = H2 = X of H1
==> 62 = X * H1 ...................Equation 1
The Height reached by the ball after first bounce = H1 = X of H0
==> H1 = X * 248 ...................Equation 2
Substituting value of H1 from Equation 2 to Equation 1
62 = X * H1 = X * X * 248
X^2 = 62/248 = 31/124 = 1/4
X = 1/2
Answer is A. 1/2
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