Using the combination formula, it is found that your family could choose the desserts in 495 ways.
The order in which the desserts are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 desserts are chosen from a set of 12, hence:
[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]
Your family could choose the desserts in 495 ways.
More can be learned about the combination formula at https://brainly.com/question/25821700
A parabola can be represented by the equation y2 = –x. What are the coordinates of the focus and the equation of the directrix? focus: (negative one-fourth, 0); directrix: x = One-fourth focus: (one-fourth, 0); directrix: x = Negative one-fourth focus: (–4,0); directrix: x = 4 focus: (4,0); directrix: x = –4.
The focus and directrix of the parabola are (–0.25, 0) and x = 0.25. Then the correct option is A.
What is the parabola?It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
A parabola can be represented by the equation y² = – x.
The coordinates of the focus and the equation of the directrix will be given as
We know that the standard equation of the parabola y² = – 4ax.
On comparing, we have
a = 1/4 = 0.25
The focus of the parabola is at (–a, 0) that is (–0.25, 0).
The directrix of the parabola will be given as
y = a
x = 0.25
More about the parabola link is given below.
https://brainly.com/question/8495504
Answer:
A. focus: (negative one-fourth, 0); directrix: x = One-fourth
Step-by-step explanation:
i did it
The following double line graph represents the enrollment of students at Jefferson Middle School for 2006 through 2009. If enrollment continues in the same trend, which of the following is a good prediction for eighth grade enrollment in 2010?
130
200
165
75
Considering the double line graph, it is found that a good prediction for eighth grade enrollment in 2010 is of 165.
What does the graph state?It states that:
The number of students enrolled in the 7th grade is falling by about 20 students per year.The number of students enrolled in the 8th grade is increasing by about 20 students per year.In 2009, there were 150 students enrolled in the 8th grade, hence an estimate for 2010 should be of about 165 or 170 students.
More can be learned about graphs at https://brainly.com/question/24808124
Answer:
165
Step-by-step explanation:
A ladder leans against a 40ft building. The foot of the ladder is 16 feet from the building. About how
long is the ladder? Round to the nearest hundredth
Answer:
60 feet
Step-by-step explanation:
find inverse equation for y=(x-3)^2
Answer:Rewrite the cartesian equation as a polar equation.
Rewrite the cartesian equation as a polar equation.r
Rewrite the cartesian equation as a polar equation.r2
Rewrite the cartesian equation as a polar equation.r2cos
Rewrite the cartesian equation as a polar equation.r2cos2
Rewrite the cartesian equation as a polar equation.r2cos2(
Rewrite the cartesian equation as a polar equation.r2cos2(θ
Rewrite the cartesian equation as a polar equation.r2cos2(θ)
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6r
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−r
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−rsin
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−rsin(
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−rsin(θ
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−rsin(θ)
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−rsin(θ)=
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−rsin(θ)=−
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−rsin(θ)=−9
Rewrite the cartesian equation as a polar equation.r2cos2(θ)−6rcos(θ)−rsin(θ)=−9Tap to view steps...
The quadratic function which is represented by the graph of a Parabola fails the Horizontal Line Test thus is not a one to one function. Therefore the inverse is not a function unless with restricted domain.
Edit: Adding the solution below to address update in the comments:
y
=
(
x
+
3
)
2
x
=
(
y
+
3
)
2
±
√
x
=
y
+
3
y
=
−
3
±
√
x
=> inverse relation
Restricting the domain: Recall that the domain and the range of the inverse function are the range and the domain of the original function respectively. The range of the original function in this case is
y
≥
0
, that should be the domain of the inverse function so for the inverse function we take the positive square root as follow:
f
−
1
(
x
)
=
−
3
+
√
x
=> this is the inverse function the domain and the range are:
domain:
x
≥
0
range:
y
≥
−
3
This means we need to restrict the domain of the original function to:
x
≥
−
3
in order for it to have an inverse function.
PLS HELP WILL GIVE BRAINLIEST :)
Step-by-step explanation:
the slope intercept form is
y = ax + b
"a" being the slope, "b" being the y- intercept (which is the y-value when x = 0).
the slope here :
in the table x is always increasing by 2.
and y is always investing by 1.
so, the slope is 1/2
the y-intercept :
we need to find the y-value for x = 0.
but we don't have a data point with x = 0 in the table.
so, we have to extend the structure of the table to the left.
x decreases by 2 (making it 0), and y decreases by 1 (making it -1).
therefore, the y- intercept (b) is -1.
and the line equation is
y = (1/2)x - 1
not sure about "the other method".
there is the point-slope form of the equation :
y - y1 = a(x - x1)
again with "a" begin the slope, and (x1, y1) being a point on the line.
if we get the y-intercept in the table, then this point is (0, y1).
and the equation would be
y - y1 = ax
in our case
y + 1 = (1/2)x
and another method ?
sometimes people write
nx + my = c
in our case starting with the original equation
y = (1/2)x - 1
2y = x - 2
-x + 2y = -2
x - 2y = 2
Which measurement is more precise? 45 fluid ounces or 79 cups
Answer:
45 fluid ounces
Step-by-step explanation:
Weight will be more accurate and consistent
To think of it simply, you may not always fill a measuring cup completely to the top and never spill out of it, weight is a given, cup measurements turn into a very close measurement that isn't 100% exact
Determine the value of k so that the relation {(2, 5), (k, 0), (–9, 2), (0, –9)} can be a function
Step-by-step explanation:
in a function every valid values of x has exactly one assigned y value.
in an ordered pair the first number is x, the second number is y.
the y in (k, 0) is therefore 0.
and this y is different to all other y values in the relation.
therefore, k must be different to all other defined x values (otherwise it would give an x value a second y value, which would make this a not-function).
so, k must be an integer not out of {-9, 0, 2}
A student has gotten the following grades on his tests. What is the minimum grade he must get on the last test in order to have an average of 787
83, 81, 70, 74
The minimum grade he must get on the last test in order to have an average of 78 is
Answer:
82
Step-by-step explanation:
The sum of his previous grades were 308. In order to get an average grade of 78, he needs to have a score of 78*5 or 390. His necessary grade minus his current grade is 390 - 308, which is 82. The minimum score the student needs to get on his test in order to have an average of 78 is 82
Answer:
82.
Step-by-step explanation:
The sum of the 5 tests must be 5*78 = 390 for the average to be 78.
So in the last test is grade must be 390 - (83+81+70+74)
= 390 - 308 = 82.
Sam had some money in his pocket, and he found another $6.50 in his dresser drawer. he then had a total of $19.75. let p represent the amount of money sam had in his pocket. which equation can you use to find the amount of money sam had in his pocket? how much money did sam have in his pocket?
Answer:
13.25$
Step-by-step explanation:
p+6.50=19.75
substract 6.50 on both side : p=13.25$
The total amount of money sam had in his pocket is $13.25.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0.
Sam had some money in his pocket, and he found another $6.50 in his dresser drawer. The total amount sam had was $19.75.
Here, let p represent the amount of money sam had in his pocket.
The equation formed
p + $6.50 = $19.75
p = $19.75 - $6.50
p = $13.25
Therefore, the total amount of money sam had in his pocket is $13.25.
Learn more about linear equations here:
https://brainly.com/question/11897796
If ∠QSR≅∠QST and QT=65, what is QR?
Answer:
it would also be 65 degrees because the angles match up and because the statement says that both angles are congruent.
Answer:
QR would equal 65
Step-by-step explanation:
It is 65 because if you look at QSR = QST, this tells you that QT and QR are equal to eachother. :)
Hope this helps!!
Have a wonderful day!!
Please rate and mark brainliest!!
A line segment has endpoints at (2, 10) and (18, -18). What is the approximate length of the segment?
Answer:
32.2 units
Step-by-step explanation:
The length of a line segment can be found from its endpoint coordinates using the distance formula.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((18 -2)² +(-18 -10)²) = √(16² +(-28)²) = √1040
d ≈ 32.2
The line segment is about 32.2 units long.
The approximate length of the segment is 32.25 units if the line segment has endpoints at (2, 10) and (18, -18).
What is a distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
We have two points (2, 10) and (18, -18)
From the distance formula:
[tex]\rm d= \sqrt{(x_2-x_2)^2+(y_2-y_1)^2}[/tex]
[tex]\rm d= \sqrt{(18-2)^2+(-18-10)^2}[/tex]
[tex]\rm d= \sqrt{(16)^2+(-28)^2} \\\\\rm d= \sqrt{(256+784)\\[/tex]
[tex]\rm d =\sqrt{1040} \\\\d = 32.249[/tex] units or
d = 32.25 units
Thus, the approximate length of the segment is 32.25 units if the line segment has endpoints at (2, 10) and (18, -18).
Learn more about the distance formula here:
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#SPJ4
What is the radius of a circle given by the equation x2 y2 – 2x 8y – 47= 0?
Answer:
the answer is 8 units
Step-by-step explanation:
The radius of a circle given by the equation [tex]\rm x^2+y^2-2x+8y-47=0[/tex] is 8 units.
It is given that the circle equation is given by [tex]\rm x^2+y^2-2x+8y-47=0[/tex]
It is required to find the radius of the circle.
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We circle the equation:
[tex]\rm x^2+y^2-2x+8y-47=0[/tex]
Converting this equation into the standard form of the circle:
[tex]\rm (x-a)^2+(y-b)^2=r^2[/tex]
[tex]\rm x^2+y^2-2x+8y-47=0[/tex]
[tex]\rm x^2+y^2-2x+8y-47+1-1+16-16=0[/tex] (by adding and subtracting by
1 and 16)
[tex]\rm x^2-2x+1+y^2+8y+16-1-16-47=0\\\\\rm (x-1)^2+(y-(-4))^2-64=0\\\\\rm (x-1)^2+(y-(-4))^2=64\\\\\rm (x-2)^2+(y-(-4))^2=8^2 \\\\[/tex]
By comparing with the standard circle equation, we get:
r = 8
Thus, the radius of a circle given by the equation [tex]\rm x^2+y^2-2x+8y-47=0[/tex] is 8 units
Learn more about circle here:
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L1S2
Area - Compound Shapes
Find the area of the shaded region in each figure. Round your answer to 2 decimal
places if required. (Use = 3.14)
PLEASE HELP I WILL MARK BRAINLIEST!
Answer:
just trust yourself
Step-by-step explanation:
passes through (-2, 1) and (2, -5)
I need to find the y=mx+b
Answer:
[tex]y = (-3/2)\, x + (-2)[/tex].
Step-by-step explanation:
If [tex](x_{0},\, y_{0})[/tex] is on the equation of the line [tex]y = m\, x + b[/tex], then substituting [tex]x = x_{0}[/tex] and [tex]y = y_{0}[/tex] into the equation would still give an equality: [tex]y_{0} = m\, x_{0} + b[/tex].
In this question, since [tex](-2,\, 1)[/tex] is a point on the line [tex]y = m\, x + b[/tex], equality shall still hold after substituting in [tex]x = (-2)[/tex] and [tex]y = 1[/tex]:
[tex]1 = m\times (-2) + b[/tex].
Similarly, since [tex](2,\, -5)[/tex] is a point on this line, equality shall still hold after substituting in [tex]x = 2[/tex] and [tex]y = (-5)[/tex]:
[tex](-5) = m\times 2 + b[/tex].
The unknowns of both equations are [tex]m[/tex] and [tex]b[/tex].
Solve this system of two equations and two unknowns:
[tex]\left\lbrace\begin{aligned}& (-2)\, m + b = 1\\ & 2\, m + b = (-5)\end{aligned}\right.[/tex].
[tex]\left\lbrace\begin{aligned}& m = -\frac{3}{2} \\ & b = -2\end{aligned}\right.[/tex].
Therefore, the equation of this line would be:
[tex]y = (-3/2)\, x + (-2)[/tex].
Sue is touring San Francisco with her family. They want to visit the Golden Gate Bridge, Alcatraz, and Chinatown before their dinner reservations at 7:30 P.M. They want to spend 45 minutes at the Golden Gate Bridge, 2 hours and 30 minutes on the tour of Alcatraz, and 1 hour and 15 minutes in Chinatown. What is the latest time Sue's family can start their tour of San Francisco and still make it to dinner on time?
please help n explain ily
Answer:
3pm
Step-by-step explanation:
so for this you want to work backwards, starting at 7:30pm because that's when they have dinner.
how i would solve this is I would add up all the amount of time they want to tour around San francisco
so 45 + 1hr15mins = 2hrs
2hrs +2hrs30mins= 4hrs30mins
so starting at 7:30 take away 4hrs 30mins
7:30 - 4hrs = 3:30pm
3:30 - 30 minutes = 3pm
They must start their tour at 3pm.
hope that helps :)
Answer:
The latest time Sue's family can start their tour but still make it home for dinner would be:
3:00 p.m
Step-by-step explanation:
Starting at 7:30pm because that's when they have dinner:
45min. + 1hr & 15mins = 2hours
2hours + 2hours & 30mins= 4hours & 30mins
Starting at 7:30 take away 4hrs 30mins:
7:30p.m - 4hrs = 3:30p.m
3:30 - 30 minutes = 3:00p.m
In conclusion, they must start their tour at 3:00 p.m to be able to reach dinner by 7:30 p.m (which is the latest time).
Have a great rest of your day
#TheWizzer
The expressions (30-2)(30+2) and 30^2-2^2 are equivalent and can help us find the product of two numbers. which two numbers are they?
Answer:
28 and 32
Step-by-step explanation:
The product indicated in your problem statement is ...
(30 -2)(30 +2)
= 28 × 32
The two numbers are 28 and 32.
__
The equivalent (30^2 -2^2) means that product is 900 -4 = 896.
In exercises, 4 and 5, find the unknown or marked angles.
Answer:
alternate angle and counter
Lukas plotted these points on the number line.
Point A: −12
3
Point B: −2
3
Point C: −11
3
Point D: −22
3
Which point did he plot incorrectly?
Point
Please mark BRAINLIEST
Answer: Point A: −12 3
explanation: I hope that helps
A pet store has 5 tanks of fish. Each tank has 30 fish. How many fish does the store have?
Answer:
30 fish
Step-by-step explanation:
Answer:
150
Step-by-step explanation:
5 tanks with 30 fish each so 5x30
5x30=150
Help me, please! It's all in the question...!
Answer:
the answer is the first one
Step-by-step explanation:
because
Answer
c hope it helps
what is the median of the data set below? 45 57 41 67 33 43 A.41 B.44 C.54 D.67
Answer:
41
Step-by-step explanation:
The middle number is the median
what is
Find p(rolling a 4)
Answer: 4/6
Step-by-step explanation: This because most dice have a 6 sides on them and others have more and if you roll a 6-sided dice you will get 4/6 of a probabilty that you will role a 4.
Hope This Helps!Given the following geometric sequence, find the 12th term: {2, -4, 8, ...}.
-4096
2048
4096
-2048
A geometric sequence has a common ratio.
The formula for the nth term is
[tex]\sf{a_n =ar^{n-1} }[/tex]
where,
an = nth term of the sequence,a = first term of the sequence and r = common ratioGiven -
A geometric sequence 2, -4, 8, ...To find -
the 12th term of the given geometric sequenceSolution -
A.T.Q, a = 2 and r = -2
[tex]\rightarrow\sf{a_{12} =2(-2)^{12-1} }[/tex]
[tex]\rightarrow\sf{a_{12 }=2(-2)^{11} }[/tex]
[tex]\rightarrow\sf{a_{12} =2×(-2048) }[/tex]
[tex]\rightarrow\bf{a_{12 }=-4096 }[/tex]
Hence, the 12th term is -4096.
Help!!!!! This is i-ready !!! Will mark brainiest please help!!!!
Answer:
I think answer C
Step-by-step explanation:
You can display how many toothbrushes were distributed each month on the dot plot :)
Have an amazing day!!
Please rate and mark brainliest!!
HELP ASAP!!! ILL GIVE LOTS OF POINTS AND BRAINLIST
PLEASE SHOW HOW YOU GOT THE ANSWER!
Answer: 27
Step-by-step explanation:
What is the trigonometric ratio for cosn? enter your answer, as a simplified fraction, in the boxes. $$ triangle l m n with right angle m. l m equals 15. l n equals 39. m n equals 36.
The trigonometric ratio will be Cos(n)=12/13
What will be the trigonometry ratio?Given is a Right triangle LMN with right angle at M i.e. angle M = 90 degrees.
Given are the sides LM = 15, MN = 36, and LN = 39.
It says to find cos(n) = ?
So opposite side would be LM, adjacent side would be MN, and LN is the hypotenuse.
We know that the cosine ratio is given by :-
[tex]Cos(n)=\dfrac{adjacent}{Hypotenuse}[/tex]
[tex]Cos(n)=\dfrac{MN}{LN}[/tex]
[tex]Cos(n)=\dfrac{36}{39}[/tex]
[tex]Cos(n)=\dfrac{12}{13}[/tex]
Hence the required ratio will be [tex]Cos(n)=\dfrac{12}{13}[/tex]
To know more about trigonometry, follow
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What is the surface area of each figure 11 m 7 m 6 m?
Answer:
hi, I'm glad to help! 185
Step-by-step explanation:
11*7=77
11*6=66
6*7=42
77+66+42=185
HELPPPP URGNT!!!!!!!
Find the area of the figure two red triangles
I need to see some picture or whatever the problem is
A. Directions/Instructions:
Given
Solution (3 points)
Final Answer (1 point)
Ex. : 5ab( 4a3 + 2ab - 3b4)
=5ab( 4a3 + 2ab - 3b4)
=20a4b+10a2b2-15ab5
=20a4b+10a2b2-15ab5
1. (6k + 5)(5k + 5)
2. (a2+6a-4)(2a-4)
3. (4x2-5x-21)÷(x-3)
Perform the operation on the following algebraic expressions and apply the laws of exponents. (3 points)
B. Directions/Instructions:
Perform the operation on the following algebraic expressions and apply the laws of exponents. (3 points)
Given
Solution (2 points)
Final Answer
Example: 8c52d42
=8c52d42
=64c104d8
=16c10d8
1. (4x5y3)2
2. 18c8(-2c)2
3. 3a2bab24ab2c3c
Answer:
Hope the pictures will help. I have done what I knew