Answer:
1/52
Step-by-step explanation:
A deck has 52 cards and the probability of picking a specific one is 1/52, or 1.92%
If you are looking for the probability of a diamond, it is 1/4, or 25%
2. A faucet for a 30-gallon bathtub fills at a rate of 3 gallons per minute.
If the drain lets water out at 1.5 gallons per minute, how long would it
take for the tub to overflow if both the faucet and drain were open at the
same time?
Answer:
20
Step-by-step explanation:
Knowing that it is a 30-gallon bathtub.
And it fills at a rate of 3 gallons per minute.
But also drains 1.5 gallons per minute.
So this is for the first minute.
3 - 1.5 = 1.5
So there will be 1.5 gallons of water in the tub after the first minute.
Now do,
30 ÷ 1.5 = 20
It will take 20 full minutes for the bathtub to fill up.
A polynomial function has a zero at x = 1 with a multiplicity of 3 and a zero at x = -2 with a multiplicity of 1. The y – intercept for the function is (0, -8). Write an equation for this polynomial.
Answer:
f(x) = 4(x -1)^3·(x +2)
Step-by-step explanation:
Each root x=p indicates the function has a factor (x -p). The factor will be repeated according to the multiplicity of the root.
f(x) = a(x -1)^3·(x +2)
f(0) = a(-1)^3·2 = -2a = -8 ⇒ a = 4
The factored form of the equation is ...
f(x) = 4(x -1)^3·(x +2)
The function f is given by f(x)=(x^{3}+bx+6)(g(x)), where b is a constant and g is a differentiable function satisfying g(2)=3 and g′(2)=−1. For what value of b is f′(2)=0?
7
10
12
22
Answer:
[tex]\displaystyle b = -22[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = (x^3+bx+6)(g(x))[/tex]
Where b is a constant and g is a differentiable function.
And we want to determine the value of b such that f'(2) = 0.
Find f' using the product rule:
[tex]\displaystyle \begin{aligned} f'(x) & = \frac{d}{dx}\left[ (x^3+bx+6)(g(x))\right] \\ \\ & = \frac{d}{dx}\left[ x^3 + bx + 6\right] g(x) + (x^3+bx+6)\frac{d}{dx}\left[ g(x)\right] \\ \\ & = (3x^2+b)(g(x)) + (x^3 + bx + 6)(g'(x))\end{aligned}[/tex]
Substitute using known values and solve for b:
[tex]\displaystyle \begin{aligned}f'(2) = 0 & = (3(2)^2+b)(g(2)) + ((2)^3+b(2)+6)(g'(2)) \\ \\ 0 & = (12+b)(3) + (14+2b)(-1) \\ \\ 0 & = 22 +b \\ \\ b & = -22\end{aligned}[/tex]
In conclusion, the value of b is -22.
The function f is given b is a constant and g is a differentiable function the value b (-8.4),
Let's start by finding the derivative of the given function f(x) with respect to x:
f(x) = (x³ + bx + 6) × g(x)
Using the product rule for differentiation, the derivative of f(x) is:
f'(x) = (x³ + bx + 6) × g'(x) + g(x) × (3x² + b)
Now we are interested in finding the value of b for which f'(2) = 0. So, let's plug in x = 2 and use the information given about g(2) and g'(2):
f'(2) = (2³ + 2b + 6) × g'(2) + g(2) × (3 × 2² + b)
Since g(2) = 3 and g'(2) = -1,
f'(2) = (8 + 2b + 6) × (-1) + 3 × (3 × 4 + b)
= (2b + 14 - 8) + 3× (12 + b)
= 2b + 6 + 36 + 3b
= 5b + 42
Now, we want to find the value of b for which f'(2) = 0:
5b + 42 = 0
Subtracting 42 from both sides:
5b = -42
Dividing both sides by 5:
b = -8.4
To know more about function here
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Complete question:
The function f is given by f(x)=(x^{3}+bx+6)(g(x)), where b is a constant and g is a differentiable function satisfying g(2)=3 and g′(2)=−1. For what value of b is f′(2)=0?
7
10
12
22
-8.4
(01.04 MC)The elevation of city A is 80 feet below sea level; the elevation of city C is 16 feet below sea level. The elevation of city D is 1 over 2 of the elevation of city C. Part A: Write an expression to represent the elevation, in feet, of city D. (5 points) Part B: Solve the expression and explain why the answer is negative or positive. (5 points)
A) The expression to represent the elevation in feet of city D is; ¹/₂ × (-16) ft
B) The solution to the expression of the elevation of City D is; -8 fr which is negative because it falls below sea level.
First of all, sea level is at 0 ft.
Thus;
If city A has an elevation of 80 ft below sea level, then;
Elevation of city A = -80 ft
The elevation of city C is 16 feet below sea level. Thus;
Elevation of city C = -16 ft
A) The elevation of city D is ¹/₂ of the elevation of city C. Thus;
Expression for Elevation of city D = ¹/₂ × (-16)
B) Solving the expression for elevation of city D gives;
Elevation of City D = -8 ft
The reason why the answer is negative is because any distance below sea level is considered to be negative and city C which is twice the elevation of city D is negative, and so city D must also have a negative elevation.
Read more about below sea level elevations at; https://brainly.com/question/14837848
Answer:
A) The expression to represent the elevation in feet of city D is; ¹/₂ × (-16) ftB) The solution to the expression of the elevation of City D is; -8 fr which is negative because it falls below sea level.First of all, sea level is at 0 ft.Thus;If city A has an elevation of 80 ft below sea level, then;Elevation of city A = -80 ftThe elevation of city C is 16 feet below sea level. Thus;Elevation of city C = -16 ftA) The elevation of city D is ¹/₂ of the elevation of city C. Thus;Expression for Elevation of city D = ¹/₂ × (-16)B) Solving the expression for elevation of city D gives;Elevation of City D = -8 ftThe reason why the answer is negative is because any distance below sea level is considered to be negative and city C which is twice the elevation of city D is negative, and so city D must also have a negative elevation.
At noon, a tank contained 8 in. of water. After several hours, it contained 6 in. of water. What is the percent decrease of water in the tank?
Answer:
25%
Step-by-step explanation:
8-6=2
2/8=0.25
0.25×100=25%
Simplify Exponents and Roots
This question on your unit test is a fill in the blank. Be prepared to type your answer. The graph show how many minutes it takes Ziah to run a certain distance in the city. What is the meaning of the point (4, 6)?
The point (4,6) means it took Ziah 4 minutes to run 6 blocks.
This is because any point is of the form (x,y) where in this case
x = number of minutes
y = number of blocks
A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $17. For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $23. Find the cost for each pound of trail mix and each pound of jelly beans.
Answer:
Trail Mix costs $2.50 per pound, and Jelly Beans cost $1.50 per pound.
Step-by-step explanation:
Using x for trail mix and y for jelly beans, we have a system of equations being
[tex]\left \{ {{5x+3y=17} \atop {2x+12y=23}} \right.[/tex]
We can solve this system using substitution
5x+3y=17
Divide by 5 to have a coefficient of 1 before x
[tex]x+\frac{3}{5} y=\frac{17}{5}[/tex]
Subtract [tex]\frac{3}{5} y[/tex] from each side to single out one variable to one side
[tex]x=\frac{17}{5} -\frac{3}{5} y[/tex]
Now, we can plug in our value for x into the given equation
[tex]2(\frac{17}{5} -\frac{3}{5} y)+12y=23[/tex]
Open the parentheses
[tex]\frac{34}{5} -1\frac{1}{5} y+12y=23[/tex]
Merge Y values
[tex]6.8+10.8y=23[/tex]
Separate numerical values from variables
[tex]10.8y=16.2[/tex]
Divide by 10.8 in order to have a coefficient of 1
[tex]y=1.5[/tex]
Now that we have one of the values, we know that a pound of jelly beans costs $1.50. We can now plug in 1.5 for y into one of our equations to find x.
[tex]5x+3(1.5)=17[/tex]
Open parentheses
[tex]5x+4.5=17[/tex]
Single out the variable
[tex]5x=12.5[/tex]
Divide by 5 to have a coefficient of 1 before x
[tex]x=2.5[/tex]
[tex]y=1.5[/tex]
Tomatoes that regularly sell for $0.55 per pound are on sale for 20% off the regular price. What is the sale price?
Answer:
$0.44
Step-by-step explanation:
lmk if you want an explanation
Mara is playing a game. There are two marbles in a bag. Ifshe chooses the purple marble, she will win $10. If she chooses the orange marble, she will win $200. What is the expected value of Mara's winnings from the game?
Answer:
Step-by-step explanation:
Mara has a 50% chance of getting the purple marble and 50% of getting an orange marble, since there's 2 marble; 1 purple and one orange; 1/2 = 50%
So she has a 50% chance of receiving $10 and a 50% chance of receiving the $200.
Hello hello there help
Answer:
Step-by-step explanation:
A translation 1 unit left and 2 units down :)
What number must each side of the equation 3/5x= 12 be multipled by to produce the equivalent equation x = 20?
Answer:
1
Step-by-step explanation:
First, find out what the product would be if you multiply 20 with the fraction:
(3 * 20)/5 = 60/5 = 12
12 = 12 ∴ (3/5)(20) = 12
As 20 is your answer, you would need to only multiply 1 to obtain the correct balance for the equation.
Please answer it....
If [tex]a\ \textless \ b[/tex], there are three ordered pairs of positive integers [tex](a,b)[/tex] that satisfy [tex]a^{2}+b^{2}=10(123)^{2}[/tex] If two of these ordered pairs are [tex](39,387)[/tex] and [tex](201,333)[/tex]. What is the third such ordered pair?
The third ordered pair that satisfy the given equation is (123, 369).
The given parameters;
[tex]a^2 + b^2 = 10(123)^2[/tex]First pair of the equation, = (39, 387)Second pair of the equation = (201, 333).The third ordered pair of the equation can be determined by using general equation of a circle;
[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]
The radius of the circle is calculated as;
[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]
The value of a can be obtained by randomly choosing numbers less than the radius as values of b.
[tex]b < r\\\\b < 388.96[/tex]
[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]
Thus, the third ordered pair that satisfy the given equation is (123, 369).
Learn more about equation of circle here: https://brainly.com/question/1506955
What is the equation for the graph shown?
Answer: y=2/3x+4
Step-by-step explanation:
this will be written out in y=mx+b form. M stands for the slope, and b stands for the y-intercept, or where the line intersects with the y-axis.
going left to right, the line slopes upward, therefore it is a positive slope. This means that the “m” part of the equation will be a positive number. When finding the slope, we use rise over run. On your graph, if you take one point and rise 2, then run right 3, you will find another point! We have now found that the slope is 2/3x.
let’s plug this into our equation. Y=2/3x +b
lastly, we find the y-intercept. This is simply where the line intersects with the y-axis. In this case, it is positive 4. So the y-intercept is 4.
our final equation is: y=2/3x +4
i hope this is helpful.
What is 3/4+11/12= I can't figure this out
Answer:
1 2/3
Step-by-step explanation:
1 and 2/3
88, 89, 86, 90, 83, 81, 89
What is the median number
A 88
B. 89
C 90
D. 86
Please answer this I really need help
Answer:
The answer is 90.
Step-by-step explanation:
90 is in the middle
Answer:
d
Step-by-step explanation:
cause i said so
Help help help help math math math
Answer:
55º
Step-by-step explanation:
The 125º angle makes a straight angle (180º) with the one next to it. This makes the angle next to it (adjacent angle) 55º. According to the rules of a transversal, the adjacent angle said above and angle 2 are alternate interior angles, making them equal.
suppose You earn Birr 10,000.00 per month and pay 20% tax and spend 60% of it. Again the recipient of the money spent by you pays 20% tax and spends 60% of it. If this process continues without end, find the total amount that wil be paid for the tax
Answer:
Birr 5000
Step-by-step explanation:
You will pay 10,000×20% = 2000 in tax. Recipients of your spending will pay ...
0.60×10,000×20% = 1200
Recipients of the spending at the next level will pay a tax of ...
0.60×0.60×10,000×20% = 720
That is, the tax amounts have an initial value (a1) of 2000 and a common ratio (r) of 0.60. Their total is given by the formula ...
sum = a1/(1 -r)
sum = 2000/(1 -0.6) = 5000
Birr 5000 will be the total amount paid for tax in this process.
Graph the function
f(x) = 3/5x - 5
Step-by-step explanation:
okay, plot a point at (0,-5) then count 3 units up and 5 units to the right and put a point there
connect the points with a straight line
add arrows to each end of the line :)
Does (3, -50) make the equation y = -8x true?
Hey there!
y = -8x
→ -50 = -8(3)
→ -8(3) = -50
→ -8(3) = -24
→ -24 ≠ -50
Yes and no but mainly no because -24 doesn’t equal -50 (the y-intercept)
Answer: NO
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
YOU’RE GETTING A BRAINLIST IF YOU ANSWER THESE:
If you and I meet halfway between the fountain and the restrooms what are the coordinates of our meeting place?
If my cat and your dog meet halfway between the ball field and the swings what are the coordinates of their meeting place?
Now to the nearest yard how far are you and I to our pets after arriving to our meeting place?
Answer:
(0.5,-0.5)(0.5,0.5)2 yardsCircle A was dilated with the origin as the center of dilation to creat circle b
Answer: The answer is B.)
Have a great Day/Night!
E varies directly with G. When G is 6, E is 10. Find the value of G when E is 18
Answer: multiply 6 by 3 and 10 by 3
Step-by-step explanation:
G = 10.8
creds to sqdancefan
Find all perfect squares between 100 and 300.
Answer: The answer in the first image.
Explanation: The explanation is in the second image.
Which of the sets of ordered pairs represents a function? (4 points)
A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}
a
Only A
b
Only B
c
Both A and B
d
Neither A nor B
Answer: D, neither A nor B
Step-by-step explanation: In a function, the x (the input) cannot repeat in the given set of ordered pairs. In Set A, 2 repeats in the third and fourth ordered pairs. In Set B, 9 repeats in the third and fourth ordered pairs as well.
Answer: B
Step-by-step explanation:
Functions and Relations
A relation is just a set of ordered pairs (x,y) . In formal mathematical language, a function is a relation for which: if (x1,y) and (x2,y) are both in the relation, then x1=x2 . This just says that in a function, you can't have two ordered pairs with the same x -value but different y -values.
PLEASSEEE HELPP!!!!!
Answer:
m
Step-by-step explanation:
Question
Round to the nearest ten: 1,078
Answer:
7 = 7 * 10 = 70
Step-by-step explanation:
Answer:
• 1080
Step-by-step explanation:
How to Calculate Rounding to the Nearest Tens Whole Number?
If the ones digit (first number after decimal point) of the number is greater than or equal to 5 we add 1 to tens of number, If the ones digit of the number is less than 5 we change ones digit to 0.
Example:
1026The ones number is 66 is greater than 5, so we add 1 to tens.Result = 1030[tex] \: [/tex]
a painter has 3 gallons of paint and each will cover 420 ft of wall space. if the total area was 1800 ft what percent of the job could the painter finish with the paint he already has?
Answer:
23.33333%
Step-by-step explanation:
Suppose there is a 1.4 drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 52.8, what will be the temperature when the plane reaches an altitude of 11,000?
Answer:
37.4
Step-by-step explanation:
1.4 times 11 and subtract that from 52.8
which of the following represents an arithmetic sequence with a common difference of -8.5?
Answer:
C
Step-by-step explanation:
to have a common difference of -8.5, the sequence has to consistently go down by 8.5.
in the first one, y would go up by 2 every time x goes up by 1, so its not that one.
in the second one, it does go down by 8.5 the first time but the next time it goes down by 4.25, so it's not consistent.
in the third one, each time it goes down by 8.5 so this is the answer.
the fourth one also isn't correct because the graph shows that it is going up, so you know for sure it's not that one.
