Hey there! I'm happy to help!
If the number of red marbles is 6 more than double the number of black marbles, we can create this equation, with r representing the red marbles and b representing the black marbles.
r=2b+6
We also know that r+b=33, and if we know that r is equal to 2b+6, we can just replace r with that and then solve for b.
2b+6+b=33
We combine like terms.
3b+6=33
We subtract six from both sides.
3b=27
We divide both sides by 3.
b=9
Now we just subtract 9 from 33 to see how many red ones there are.
33-9=24
So, there are 24 red marbles and 9 black marbles.
Now, let's see which of these options are correct.
The equation r+b=33 represents the total number of marbles.
This is true because r plus b is equal to the total, which is 33.
The equation r=2b+6 can be used to find the number of red marbles.
This is true because it we used this r-value to find how many black marbles there were.
The equation r=2b+6 represents the total number of marbles.
This is false because it does not have the total number, which is 33.
The equation r=b=33 can be used to find the number of red marbles.
This is true because we plugged in the r-value to solve for b with this equation.
There are 9 red marbles in the bag.
This is false. There are 24 red marbles.
There are 9 black marbles in the bag.
This is true.
There are 24 black marbles in the bag.
This is false. There are 9 black marbles.
There are 24 red marbles in the bag.
This is true.
Have a wonderful day! :D
Answer:
1,2,4,6,8
Step-by-step explanation:
Suppose an object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is given by the f(x) = 96x -16x^2, find the following.
A) The instantaneous velocity function v = f (x).
B) The velocity when x = 0 and x = 4 seconds.
C) The time(s) when v = 0
Answer:
A) v = f(x) = 96 -32x
B)the velocity when x = 0
V = 96 ft/s
The velocity when x =4
V = -32 ft/s
C). Time when v= 0
3 seconds = x
Step-by-step explanation:
f(x) = 96x -16x^2
The above equation represents the position of the object at x time along the x axis.
The velocity will be determined by differentiating the equation with respect with x
f(x) = 96x -16x^2,
D f(x)/Dx= 96 -2(16x)
D f(x)/Dx= 96 -32x
v = f(x) = 96 -32x
The velocity when x = 0
v = f(x) = 96 -32x
V = f(0) = 96-32(0)
V = 96 ft/s
The velocity when x = 4
v = f(x) = 96 -32x
V = f(4) = 96-32(4)
V = 96 - 128
V = -32 ft/s
Time when v= 0
v = f(x) = 96 -32x
0= 96 -32x
-96= -32x
-96/-32=x
3 seconds = x
Choose the correct equation for the parabola based on the given information. Given: Focus:(4,-3) Vertex: (-2,-3) a. 24(y+3) = (x+2)^2 b. 24(x+2)=(y+3)^2 c. 6(x-4)= (y+3)^2 d. 6(y+3)=(x-4)^2
Answer: b. 24(x + 2) = (y + 3)²
Step-by-step explanation:
Vertex: (-2, -3)
Focus: (4, -3)
↓
same y-value so equation will be y²
Equation: a(x - h) = (y - k)²
a = 4p where p is the distance from Vertex to Focush is the x-coordinate of the Vertexk is the y-coordinate of the VertexGiven: h = -2, k = -3, a = 4[4 - (-2)] --> a = 24
Input those values into the equation: 24(x + 2) = (y + 3)²
A small company that manufactures snowboards uses the relation below to model its profit. In the model,
represents the number of snowboards in thousands, and P represents the profit in ten thousands of dollars.
What is the maximum profit the company can earn? How many snowboards must it produce to earn this
maximum profit?
a. Factor P =
4x2 + 32x + 336 to find the roots.
b. Find the axis of symmetry then use it to find the vertex.
c. Therefore, we need to see snowboards to make a maximum profit of
Answer:
a) x₁ = 14
x₂ = - 6
b) x = 4
c) P(max ) = 4000000 $
Step-by-step explanation:
To find the axis of symmetry we solve the equation
a) -4x² + 32x + 336 = 0
4x² - 32x - 336 = 0 or x² - 8x - 84 = 0
x₁,₂ = [ -b ± √b² -4ac ]/2a
x₁,₂ = [ 8 ±√(64) + 336 ]/2
x₁,₂ = [ 8 ± √400 ]/2
x₁,₂ =( 8 ± 20 )/2
x₁ = 14
x₂ = -6
a) Axis of symmetry must go through the middle point between the roots
x = 4 is the axis of symmetry
c) P = -4x² + 32x + 336
Taking derivatives on both sides of the equation we get
P´(x) = - 8x + 32 ⇒ P´(x) = 0 - 8x + 32
x = 32/8
x = 4 Company has to sell 4 ( 4000 snowboard)
to get a profit :
P = - 4*(4)² + 32*(4) + 336
P(max) = -64 + 128 + 336
P(max) = 400 or 400* 10000 = 4000000
The charge to rent a trailer is $2525 for up to 2 hours plus $99 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.82.8 hours, 33 hours, and 8.78.7 hours. Then graph all ordered pairs, (hours, cost), for the function.
The question is not written properly! Complete question along with answer and step by step explanation is provided below.
Question:
The charge to rent a trailer is $25 for up to 2 hours plus $9 per additional hour or portion of an hour.
Find the cost to rent a trailer for 2.8 hours, 3 hours, and 8.7 hours.
Then graph all ordered pairs, (hours, cost), for the function.
Answer:
ordered pair = (2.8, 34)
ordered pair = (3, 34)
ordered pair = (8.7, 88)
Step-by-step explanation:
Charge for 2.8 hours:
$25 for 2 hours
$9 for 0.8 hour
Total = $25 + $9
Total = $34
ordered pair = (2.8, 34)
Charge for 3 hours:
$25 for 2 hours
$9 for 1 hour
Total = $25 + $9
Total = $34
ordered pair = (3, 34)
Charge for 8.7 hours:
$25 for 2 hours
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 0.7 hour
Total = $25 + $9 + $9 + $9 + $9 + $9 + $9 + $9
Total = $88
ordered pair = (8.7, 88)
The obtained ordered pairs are graphed, please refer to the attached graph.
Planes A and B intersect.
Which describes the intersection of line m and line n?
P
point W
point X
m
2
n
2
point y
X
w
Y
point Z
V
Answer:
Point W
Step-by-step explanation:
Planes A and B intersect at an angle. Intersection of lines is when two lines meets at a particular point and cuts each other at the same point. Its a measure of perpendicularity for right angles and greater or lesser for others.
At any point W, line m and line n cuts each other at point W to form an angle as shown from the diagram.
Find the volume of the cone.
Answer:
628 units³Step-by-step explanation:
Given,
Radius ( r ) = 10
Height ( h ) = 6
pi ( π ) = 3.14
now, let's find the volume of given cone:
[tex]\pi {r}^{2} \frac{h}{3} [/tex]
Plug the values
[tex] = 3.14 \times {10}^{2} \times \frac{6}{3} [/tex]
Evaluate the power
[tex] = 3.14 \times 100 \times \frac{6}{3} [/tex]
Calculate
[tex] = 628 \: {units}^{3} [/tex]
Hope this helps..
Best regards!!
Answer:
The answer is 200π units³ .
Step-by-step explanation:
Given that the formula of volume of cone is V = 1/3×π×r²×h where r represents radius and h is height. Then, you have to substitute the value of radius and height into the formula :
[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]
[tex]let \: r = 10 \: , \: h = 6[/tex]
[tex]v = \frac{1}{3} \times \pi \times {10}^{2} \times 6[/tex]
[tex]v = \frac{1}{3} \times \pi \times 600[/tex]
[tex]v = 200\pi \: {units}^{3} [/tex]
A spinner has 4 equal sectors with tour options Dubai, Seoul, Switzerland, and Paris. What is the probability of landing on Seoul or Paris after spinning spinner
The probability of landing on Seoul or Paris after spinning spinner is 1/2 .
What is Probability ?Probability is the measure of likeliness of an event to happen.
It is given that
Total Outcomes = 4 ( Dubai, Seoul, Switzerland, and Paris)
the probability of landing on Seoul or Paris after spinning spinner = ?
The probability of Landing on Seoul P(S) is 1 /4
The probability of Landing on Paris P(P) is 1 /4
The probability of landing on Seoul or Paris after spinning spinner is
P( S∪P) = P(S) + P(P)
= (1/4) + (1/4)
= 1/2
Therefore , The probability of landing on Seoul or Paris after spinning spinner is 1/2 .
To know more about Probability
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Which equations represent the asymptotes of the hyperbola?
Answer:
see below
Step-by-step explanation:
The equation of the hyperbola can be written as ...
((x -h)/a)² -((y -k)/b)² = 1
This has asymptotes ...
(x -h)/a ± (y -k)/b = 0
Solving for y, we have ...
y = ±(b/a)(x -h) +k
Filling in the given values a=6, b=8, h=1, k=2, we have ...
y = ±8/6(x -1) +2
[tex]y=\dfrac{\pm4x\mp4+6}{3}\\\\\boxed{y=\dfrac{4x+2}{3}\ \text{and }y=\dfrac{10-4x}{3}}[/tex]
Answer:
A. y = 4x+2/3 and y = 10-4x/3
Step-by-step explanation:
this is the correct answer for the question on edmentum and Plato
which graph represents a function?
I can determine a function by drawing a vertical line. If this line pass trought the graph only one time, it's a function.
The only function there is the last one. (Right bottom)
What is the length of AB? (Nearest TENTH) A.34 B.105.3 C.11.8 D.24.7
Answer:
The answer is option A.
Step-by-step explanation:
To find the length of AB we use sine
sin∅ = opposite / hypotenuse
From the question
AB is the hypotenuse
AC is the opposite
sin 36 = AC / AB
sin 36 = 20/ AB
AB = 20 / sin 36
AB = 34.026
AB is 34 to the nearest tenthHope this helps you
Solve the equation for X. 2(2x-4)=3(x+4) A -4 B 4 C 20 D 6
Answer:
X=20
Step-by-step explanation:
The answer is C
In a sequence, the 40th term is 70, the 41st term is 72 and the 42nd term is 74.
a) State the term-to-term rule
b) Work out the first term
c) Work out the 80th term
Answer:
term to term rule is +2
The first term is -8
80th term is 150
Step-by-step explanation:
70 to 72 is adding 2
72 to 74 is adding 2
term to term rule is +2
The equation for a sequence like this is
xn = a + d(n−1)
where n is the term number a is the first term and d is the term to term rule
Using the 40th term is 70
70 = a + 2( 40-1)
70 = a + 2( 39)
70 = a + 78
Subtract 78 from each side
-8 = a
The first term is -8
80th term
xn = a + d(n−1)
x80 = -8 +2 (80-1)
= -8+2(79)
= -8+158
= 150
Evaluate the expression 23^0-15^1+18^0+(43-12)
Answer:
18
Step-by-step explanation:
23^0 - 15^1 + 18^0 + (43 - 12) =
= 1 - 15 + 1 + 31
= -14 + 1 + 31
= -13 + 31
= 18
Find the first four terms of the sequence given a1=31 and an+1=an−3
Step-by-step explanation:
Given the formula
a(n+1)=an−3
The first term a(1) = 31
For the second term
a(2)
We have
a( 1 + 1) = a(1) - 3
a(2) = 31 - 3
a(2) = 28
For the third term
a(3)
We have
a(2+1) = a(2) - 3
a(3) = 28 - 3
a(3) = 25
For the fourth term
a(4)
That's
a(3+1) = a(3) - 3
a(4) = 25 - 3
a(4) = 22
Hope this helps you
PLEASE ANSWER FAST PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Answer:
sin = -√2 / 2
cos = √2 / 2
tan = -1
Step-by-step explanation:
Θ is in quad IV
sin = -√2 / 2
cos = √2 / 2
tan = -1
a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages.
Answer:
John is 9, Brian is 6.
Step-by-step explanation:
I)
Let [tex]J[/tex] represent John's age and [tex]B[/tex] represent Brian's age.
John is three years older than Brian. In other words:
[tex]J=B+3[/tex]
The product of their ages is 54. Or:
[tex]JB=54[/tex]
II)
Write this as a quadratic by substituting:
[tex]JB=54\\(B+3)B=54\\B^2+3B-54=0[/tex]
III)
Solve the quadratic:
[tex]B^2+3B-54=0\\B^2-6B+9B-54=0\\B(B-6)+9(B-6)=0\\(B+9)(B-6)=0\\B=-9, 6[/tex]
Since age cannot be negative, Brian must be 6 years old right now.
John is three year older, so John is 9.
What is the average rate of change of f(x)=-2/x^2 when the interval is 1 to 2
Answer:
1.5
Step-by-step explanation:
average rate of change = (f(x2) - f(x1))/(x2 - x1)
f(x) = -2/x^2
f(x2) = f(2) = -2/(-2)^2 = -2/4 = -0.5
f(x1) = f(1) = -2/1^2 = -2
average rate of change = (-0.5 - (-2))/(2 - 1)
average rate of change = (-0.5 + 2)/1
average rate of change = 1.5
Write the equation of the function of a parabola with vertex at (–1,–2) and a point (1,–6) that lies on the curve.
Answer:
f(x) = -(x + 1)² - 2
Step-by-step explanation:
f(x) = a(x - h)² + k
-6 = a(1 - -1)² + -2
-6 = a(4) -2
-4 = 4a
a = -1
f(x) = -(x + 1)² - 2
This function to calculate the area of a rectangle is not very readable. Can you refactor it, and then call the function to calculate the area with base of 5 and height of 6? Tip: a function that calculates the area of a rectangle should probably be called rectangle_area, and if it's receiving base and height, that's what the parameters should be called.
Answer:
Here is the refactored function:
def rectangle_area(base, height):
area = base * height
return area
print("The area is ", rectangle_area(5,6))
Step-by-step explanation:
The above program has a function rectangle_area that takes two variables base and height as parameters. The function then computes the area of rectangle by multiplying the values of base and height. The result of the multiplication is assigned to the variable area. Then the function returns the resultant area.
print("The area is ", rectangle_area(5,6)) statement calls rectangle_area() method by passing values of base and height i.e. 5 and 6 to compute the area. The output of this program is:
The area is 30
Note that the use of rectangle_area function name describes what the function does i.e. it computes the area of rectangle. By naming the parameters as base and height that clearly depicts that in order to compute rectangle are we need the base and height of rectangle. So this makes the code readable.
(a) The only even prime number is ....
Answer:
2 is the only even prime number
Answer:
2
Step-by-step explanation:
2 is the only even prime number. There is no even prime number other than 2. Prime numbers are the numbers which can only be divided by 1 and the number itself.
heLpPppPPpppPPpppppPPpppPPpppPPpppPPPpppPPPpppPPPPppppp
Answer:
Triangle D is your answer.
Answer:
Hey there!
Triangle C is unique, as one side and two angles determine a unique triangle.
Hope this helps :)
Help please, this is annoying lol
Answer:
Cost=x25+200
Step-by-step explanation:
The amount of people is unknown but each person the cost will be $25 for refreshments per each passenger; the limo cost $200 once you figure out how many people will go to prom x will be, EXAMPLE: x=6 times $25 plus $200 which will give you the cost.
This table shows values that represent an exponential function.
What is the average rate of change for this function for the interval from x = 1
to x = 3?
Answer:
B. 3
Step-by-step Explanation:
To find the average rate of change of the exponential function represented by the table of values above can be calculated using the general formula for average rate of change of a function, which is given as [tex] m = \frac{f(b) - f(a)}{b - a} [/tex]
Where,
[tex] a = 1, f(1) = 7 [/tex]
[tex] b = 3, f(3) = 13 [/tex]
Plug in the above values in the average rate of change formula:
[tex] m = \frac{13 - 7}{3 - 1} [/tex]
[tex] m = \frac{6}{2} [/tex]
[tex] m = 3 [/tex]
Average rate of change is B. 3
Answer:
3
Step-by-step explanation:
Identify the P-VALUE used in a hypothesis test of the following claim and sample data:
Claim: "The proportion of defective tablets manufactured in this factory is less than 6%."
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective. Test the claim at the 0.05 significance level.
Answer:
The calculated value Z = 2 > 1.96 at 0.05 level of significance
Alternative Hypothesis is accepted
The proportion of defective tablets manufactured in this factory is less than 6%."
Step-by-step explanation:
Step(i):-
Given Population proportion P = 0.06
Sample size 'n' = 500
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective.
Sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{20}{500} =0.04[/tex]
Null hypothesis :H₀: P = 0.06
Alternative Hypothesis :H₁:P<0.06
Level of significance = 0.05
Z₀.₀₅ = 1.96
Step(ii):-
Test statistic
[tex]Z = \frac{p^{-} -P}{\sqrt{\frac{P Q}{n} } }[/tex]
[tex]Z = \frac{0.04 -0.06}{\sqrt{\frac{0.06 X 0.94}{500} } }[/tex]
Z = - 2
|Z|= |-2| = 2
Step(iii):-
The calculated value Z = 2 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
Alternative Hypothesis is accepted
The proportion of defective tablets manufactured in this factory is less than 6%."
Tunde and Martha are married and share their income. Tunde earns $1,500 per year less than Martha. If their annual income is $47,500, how much does each earn?
Answer:
p=2m
p+m=51
take the 2m and plug that in for p -> 2m+m=51
3m=51
m=51/3
m=17 then plu the value of m into Paula's points
p=2(17)
p=34
7987.1569 to the nearest thousandth
Answer:
7987.1569 to the nearest thousandths is 7987.157
Step-by-step explanation:
here is the picture pls answer another for my lil friend lol
Answer:
Hey there!
The perimeter can be expressed as 140+140+68[tex]\pi[/tex]
This is equal to 493.52 m
Hope this helps :)
i need help emergrncy shots fire shots fire we neeed all back ups
Answer:
a = 9h + bn
Step-by-step explanation:
total = $9 an hour + (bonus x number of items repaired)
Simply this expression (3 + 2i)^2
Answer:
5 + 12i
Step-by-step explanation:
(3 + 2i)^2 = (3 + 2i)(3 + 2i) = 9 + 6i + 6i + 4i^2 = 9 + 12i - 4 = 5 + 12i
Answer:
5 + 2i
Step-by-step explanation:
since [tex]\sqrt{-1} = i[/tex]
Use the perfect square formula ( a + b )^2
= 3^2 + 2 · 3 · 2i + (2i)^2
= 5 + 2i
or,
[tex]5+2\sqrt{-1}[/tex]
Which type of graphs allows the reader to view the raw data values?
Answer:
bar graphs
Step-by-step explanation:
as in a bar graph, we don't do any calculations to graph on a paper,
so the data values, are taken RAW while graphing.