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
I need help with this question pls help
Answer:
y = - 4
Step-by-step explanation:
x = - 2
3x - 2y = 2
substitute x = - 2 into 3x - 2y = 2
3(- 2) - 2y = 2 ← step 1
- 6 - 2y = 2 ( add 6 to both sides ) ← step 2
- 2y = 8 ( divide both sides by - 2 )
y = - 4
ANSWER NOW NEEDS TO BE DONE WITHIN 90 MIN!!!!
What percent of the students received a score below 64, if the mean grade on a test was 70 and the standard deviation was 6.
Using the normal distribution, it is found that 15.87% of the students received a score below 64.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, the mean and the standard deviation are given by, respectively: [tex]\mu = 70, \sigma = 6[/tex].
The proportion of students who received a score below 64 is the p-value of Z when X = 64, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{64 - 70}{6}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
Hence, 15.87% of the students received a score below 64.
More can be learned about the normal distribution at https://brainly.com/question/24663213
Find the value of X and show your work
Step-by-step explanation:
Ans of 8
x + 3x + 2x = 180 (sum of all angle of triangle is 180)
6x = 180
x = 60
Ans of 9
(2x-2)+(x+5)+90 = 180
3x+3+90 = 180
3x + 93 = 180
3x = 180-93
x = 87/3
x = 29
(PLS HELP WILL MARK BRAINLIEST TO CORRECT ANSWER)
John leaves his house one morning to go to the store which is 16 middles dude my north. Suzie, his wife, leaves the house and drives to work, which is directly east of the store.John needs to drop off lunch for suzie because she forgot to pack a lunch today. If suzie has a 20 mile drive to work from home, how far must John drive to store to deliver her lunch?
Answer: 12 miles
Step-by-step explanation:
The relative frequency of Event A in an experiment is 13.
If the experiment is performed 30 times, how many times should you expect Event A to occur?
Enter your answer as a number, like this: 42
!!PLEASE HELP ME IM NOT GOOD AT MATH AT ALL!!
Based on the relative frequency and the number of times the experiment is to be performed, the number of times Event A should occur is 10 times.
How many times should Event A occur?The relative frequency in this regard is 1/3.
The number of times it will occur can be found as:
= Relative frequency x Number of times event was performed
Solving gives:
= 1/ 3 x 30
= 10 times
Find out more on relative frequency at https://brainly.com/question/3857836.
Find the derivative of 9x³ + 4x² + x + 3 at x = 3.
Answer:
268
Step-by-step explanation:
Derivative Rule
dy/dx (xⁿ) = nxⁿ⁻¹On deriving,
dy/dx = 9x³ + 4x² + x + 3dy/dx = 27x² + 8x + 1Substitute x = 3
dy/dx = 27(3)² + 8(3) + 1dy/dx = 243 + 24 + 1dy/dx = 268Solution:
268
=============================
[tex]\sf \bold{ \rightarrow } \ y = 9x^3 + 4x^2 + x + 3[/tex]
[tex]\sf \bold{ \rightarrow } \ \dfrac{dy}{dx} = \dfrac{d}{dx} ( \ 9x^3 + 4x^2 + x + 3 \ )[/tex]
[tex]| | \ \mathrm{ If \ y = x^n , \ then \ \frac{dy}{dx} = nx^{n-1}} \ | |[/tex]
[tex]\sf derivative \ of \ constant \ is \ always \ 0 \ || \ \sf\dfrac{d}{dx}\left(a\right)=0 \ ||[/tex]
solving step wise
[tex]\sf \bold{ \rightarrow } \ \dfrac{d}{dx} ( 9x^3) + \dfrac{d}{dx}(4x^2) + \dfrac{d}{dx}(x )+ \dfrac{d}{dx}(3 )[/tex]
[tex]\sf \bold{ \rightarrow } \ \sf ( 3(9x^{3-1}) +2(4x^{2-1}) + (1)(x^{1-1} )+ 0[/tex]
[tex]\sf \rightarrow 27x^2+8x+1+0[/tex]
[tex]\sf \rightarrow 27x^2+8x+1[/tex]
when x = 3
[tex]\sf \hookrightarrow 27(3)^2+8(3)+1[/tex]
[tex]\sf \hookrightarrow 243+24+1[/tex]
[tex]\sf \hookrightarrow 268[/tex]
Hello people ~
factorise: : x^2 – 21x + 108
[tex]\\ \rm\rightarrowtail x^2-21x+108[/tex]
Use midterm splitation[tex]\\ \rm\rightarrowtail x^2-12x-9x+108[/tex]
[tex]\\ \rm\rightarrowtail x(x-12)-9(x-12)[/tex]
[tex]\\ \rm\rightarrowtail (x-9)(x-12)[/tex]
Done!
Please help me with this please and thank you
Answer:
b. [tex]3^{-x}[/tex]
Step-by-step explanation:
(-2, 9)
[tex]f(-2)=3^{-(-2)} =3^{2} =9[/tex]
(-1, 3)
[tex]f(-1)=3^{-(-1)} =3^{1} =3[/tex]
(0 1)
[tex]f(0)=3^{0} =1[/tex]
Hope this helps
An observer at the top of a building sees a car on the road below. the angle of depression to the car is 28 degrees. If the car is about 50m from the building when it is seen, how tall is the building?
Answer:
Step-by-step explanation:
The height of the building is: 26.585 m.
What is angle of Depression?The angle formed by the line of sight and the horizontal plane for an object below the horizontal.
Given:
angle of depression= 28 degree,
distance between car and building= 50m
using trigonometry,
tan 28= P/B
0.5317= P/50
P= 26.585 m
Hence, the height of the building is 26.585 m.
Learn more about angle of depression here:
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Solve the question in the picture and write the correct answer
Answer:
36.24 cm²
Step-by-step explanation:
The shaded region is the inscribed circle in the isosceles triangle. In order to find its area, we need to know the radius of the circle.
__
One way to find the radius of the circle is to make use of the Angle Bisector theorem. It tells us an angle bisector divides the sides of a triangle proportionately. In the attached figure, that means angle bisector CD divides segment AE in proportion to sides CA and CE.
Side LengthTo make use of this theorem, we need to know the length of side CA. That is the hypotenuse of right triangle AEC, so can be found using the Pythagorean theorem. Isosceles triangle ABC is given as having height AE=10 and base BC = 12.
CA² = CE² +AE²
CA² = 6² +10² = 136 . . . . . . . CE is half the base length: 12/2 = 6
CA = √136 = 2√34
__
RadiusNow we can write the proportion using the angle bisector theorem.
DE/CE = DA/CA
r/6 = (10 -r)/(2√34)
r√34 = 3(10 -r) . . . . . . . multiply by 6√34
r(3 +√34) = 30
r = 30/(3 +√34)
__
AreaFrom this, we can find the area of the shaded circle to be ...
A = πr² = (3.14)(30/(3 +√34))²
= 3.14·900/(43 +6√34) ≈ 36.2374 . . . cm²
The area of the shaded region is about 36.24 cm².
_____
Additional comment
Using area considerations, the formula for the radius of the inscribed circle in an isosceles triangle with base 'b' and sides 'a' can be found to be ...
[tex]r=\dfrac{b}{2}\sqrt{\dfrac{2a-b}{2a+b}}[/tex]
For a=√136 and b=12, this becomes ...
[tex]r=\dfrac{12}{2}\sqrt{\dfrac{2\sqrt{136}-12}{2\sqrt{136}+12}}=6\sqrt{\dfrac{(\sqrt{34}-3)^2}{34-9}}=1.2(\sqrt{34}-3)\approx3.39714[/tex]
This is the same value we found above.
90 pounds =. Ounces
I need help
Answer:
1440 ounces
Step-by-step explanation:
there are 16 ounces in a pound so multiply 90 by 16 and you get 1440 hope this helps!
The number of points scored by two basketball teams in each teams' latest
10
games are listed below. Compare and contrast the measures of central
tendency for the data sets.
Team one: {54, 47, 62, 59, 49, 51, 54, 60, 57, 53}
Team two: {63, 57, 49, 52, 61, 43, 51, 53, 56, 48}
Answer:
See below.
Step-by-step explanation:
Arranging the data in ascending order:
Team one: { 47, 49, 51, 53, 54, 54, 57, 59, 60, 62}
Team two: {43, 48, 49, 51, 52, 53, 56, 57, 61, 63}
The mean for team one = sum of the scores / 10 =
= 546/10 = 54.6.
The median for team 1 = 54.
The mean for team two = sum of the scores / 10 =
= 533/10 = 53.3.
The median for team 2 = 52.5.
Team 1 has a higher mean than team 2: 54.6 - 53.3 = 1.3 higher.
In both cases, the mean is greater than the median though the difference is < 1 in both cases. So in both cases the distribution of the scores is close to symmetrical, with team 1 being slightly more symmetrical.
help me pleasseeeee!!
Answer:
-35/91 is the required answer
Hope it helps
make me brainlist
14
Mr. Miller drew a rough map to show how his land is divided into sections. He grows corn,
soybeans, and wheat. He also has dairy cows.
Corn 107.625 acres
Soybeans
170.25
Dairy Cows
acres
108 acres
Wheat 107.65 acres
Part A
Type a sentence to compare the number of acres of corn and the number of acres of wheat. Use
<,>, or =
Answer:
Part B
Type a sentence to compare the number of acres of soybeans and the number of acres of wheat.
Use<, >, or =
Answer:
Part C
Compare each crop area to the land used for the dairy cows. Explain if more or less land is used
for each crop than for dairy cows.
Answer:
Answer:
answer is the butt world
Which expression is equivalent to Cosine (StartFraction pi Over 2 EndFraction r) for all values of r?.
The expression that is equivalent to [tex]Cos(\frac{\pi }{2}+r )[/tex] is [tex]-Sinr[/tex].
Given trigonometric expression is:
[tex]Cos(\frac{\pi }{2}+r )[/tex]
What is the value of [tex]Cos(\frac{\pi }{2}+\theta )[/tex]?The value of [tex]Cos(\frac{\pi }{2}+\theta )[/tex] is [tex]-Sin\theta[/tex] because [tex]\frac{\pi }{2} +\theta[/tex] lies in the second quadrant and the cosine function is negative in the second quadrant.
So, [tex]Cos(\frac{\pi }{2}+r )= -Sin r[/tex]
The range of sine and cosine functions is the same i.e. [-1,1].
Both the functions are periodic functions with periods 2π.
Hence, the expression that is equivalent to [tex]Cos(\frac{\pi }{2}+r )[/tex] is [tex]-Sinr[/tex].
To get more about trigonometric functions visit:
https://brainly.com/question/2193113
Select the correct answer.
mel is teaching travis how to use a compass and a straightedge to construct a square inscribed in a circle. he tells travis to begin by using a
straightedge to draw any chord of the circle and label it wx. next, his instructions are to use the tools to construct a chord that is a
perpendicular bisector of wx and label it yz. finally, he directs travis to use a straightedge to draw the four chords that make up the square: wy
yx, xz, and zw.
what is the first error, if any, mel made in his instructions to travis?
oa mel's instructions contain no errors.
ob. chord wx must be a diameter of the circle,
oc chord yz is found by constructing a segment congruent to wx.
od the four chords that make up the square are the perpendicular bisectors of wx and yz.
ое. chord wx must be congruent to the radius of the circle.
Answer:
I think the answer is B
Step-by-step explanation:
The error which is made by Mel in drawing square in the circle is that thefour chords that ob , chord wx must be a diameter
What is square?A square is a 2 dimensional figure having four sides and four angles which are equal to 90°. All sides of square are always equals to each other.
How to draw a square in a circle?First draw a circle in which we want to draw such square.
Next draw a chord in the circle.
From one end, draw a straight line connecting a point on the circle and end point of the chord in such a way that the line and chord are perpendicular to each other.
Next draw another line also from the end of line formed in second step.
Lastly draw a line from the other end of chord and join it with the line we have drawn lastly.
In this way we will get square in circle.
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The function f(x)=4x^(5)-2x^(3)+8x is:
Answer:
C. Odd
Step-by-step explanation:
If you reflect this function across the y-axis it is not symmetrical, therefore it is not an even function
But, if you rotate this function by 180 degrees, it is unchanged, therefore it is and odd function
Help!! This is iready will get brainiest!! Please answer!!
Answer:
C the number of toothbrushes :)
Step-by-step explanation:
You can show how many were given away each month on a dot plot :)
The others would not make sense with the dot plot :)
Haeva great day!
Please rate and mark brainliest!
A giraffe runs at a rate of 32 miles per hour. Which equation models the situation?
h = time spent running, in hours
d = distance run in miles
32h = d
32d = h
h = 32 + d
h = 32 – d
Answer:
32h=d
Step-by-step explanation:
yea, this is big brain time lol
also edge lol
Solve the equation for all values of x by completing the square. 5x^2-70x=-230
Solve this ASAP please
Answer:
[tex]x=7 + \sqrt{3}[/tex]
[tex]x=7 - \sqrt{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]5x^2-70x=-230[/tex]
Divide both sides by 5:
[tex]x^2-14x=-46[/tex]
Square half of the coefficient of [tex]x[/tex]: [tex](-14 \div 2)^2=49[/tex]
and add this to both sides:
[tex]x^2-14x+49=-46+49[/tex]
Factor the left side and simplify the right side:
[tex](x-7)^2=3[/tex]
Square root both sides:
[tex]x-7=\pm\sqrt{3}[/tex]
Add 7 to both sides:
[tex]x=7 \pm \sqrt{3}[/tex]
[tex]\sf x=\pm \sqrt{3}+7[/tex]
solving step wise:
[tex]\sf 5x^2-70x=-230[/tex]
divide the following by 5
[tex]\sf x^2-14x=-46[/tex]
completing square
[tex]\sf (x-\dfrac{14}{2})^2-(\dfrac{14}{2})^2 =-46[/tex]
should look like this
[tex]\sf (x-7)^2-49=-46[/tex]
simplify by changing sides
[tex]\sf x-7=\pm \sqrt{3}[/tex]
final answer:
[tex]\sf x=\pm \sqrt{3}+7[/tex]
Find the volume of a pyramid with a square base, where the side length of the base is 16.6m and the height of the pyramid is 9.1 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
Formula for volume of square pyramid:-
V = 1/3 x a^2 x h
Where 'a' is the length of one side of the base, and 'h' is the height.
Plug in our values, given that:
16.6m = side length of base.
9.1m = height of pyramid.
V = 1/3 x a^2 x h
V = 1/3 x 16.6^2 x 9.1
V = 1/3 x 275.56 x 9.1
V = 1/3 x 2507.596
V = 2507.596/3
V = 835.865, which rounds to 835.9 cubic meters.
Last year 950 people attended a town’s annual parade. This year 1,520 people attended. What was the percent increase in attendance from last year to this year?
Answer: 60% increase
Step-by-step explanation:
First, find how many more people attended this year: 1,520 - 950 = 570.
Now, find what percent of 950 570 is: 950 * x = 570 → x = .6 * 100 = 60% :)
please help I am confused
Answer: -5
Step-by-step explanation:
Opposite sides of a parallelogram are parallel, and thus have equivalent slopes.
please help :DDDD 50 pointssss and brainliest
Sasha solved an equation, as shown below:
Step 1: 8x = 56
Step 2: x = 56 – 8
Step 3: x = 48
Part A: Is Sasha's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. (6 points)
Part B: How many solutions does this equation have? (4 points)
Answer:
Her solution is incorrect. The correct solution for the equation is x=7
Step-by-step explanation:
Sasha solved the equation incorrectly.
The correct way to solve this equation would be:
8x = 56
Divide both sides by 8.
[tex]\frac{8x}{8}= \frac{56}{8}[/tex]
You would get x=7.
This equation has 1 solution.
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!
Stay Brainy!
−Kallmekrish
NEED ANSWERS QUICKLY! CORRECT ANSWER GETS BRAINLIEST
When dividing fractions that are represented in the same terms, their quotient is simply the quotient of their numerators. Write an equation that demonstrates this.
Answer/Step-by-step explanation:
Quotient is simply the ratio of the first numerator to the second numerator:
Let's [tex]\frac{x_1}{y}\;and\;\frac{x_2}{y}[/tex] are two fractions in same terms.
Thus, [tex]\frac{x_1}{y}\div\frac{x_2}{y}[/tex] {Divided by a fraction is equal to multiplied by its reciprocal}
=[tex]\frac{x_1}{y}\times\frac{y}{x_2}[/tex]
Quotient is simply the quotient of their numerators.
Example could be:
[tex]\frac{2}{7}\div\frac{3}{7}[/tex]
[tex]\frac{2}{7}\times\frac{7}3}[/tex]
[tex]\frac{2}{3}[/tex]
2 is first numerator and 3 is the second numerator.
~lenvy~
Friction creates heat and lowers the _______
Answer:
energy
Step-by-step explanation:
Answer:
energy
Step-by-step explanation:
Find the volume of a cone with a base radius of 4 ft and a height of 8 ft.
Write the exact volume in terms of , and be sure to include the correct unit in your answer.
Answer:
42.67π ft³
Step-by-step explanation:
Given
base radius = 4 feetheight = 8 feetFormula
Volume of a cone = 1/3πr²hSolving
V = 1/3 x π x (4)² x 8V = 128/3 x πV = 42.67π ft³The circumference of a circle is 27 cm. Find its radius,
in centimeters.
Answer:
4.295cm
Step-by-step explanation:
Here,
Circumference = 27cm
We know,
C=2πr
or, 27 = 2×22×r
7
or, 44×r = 27
7
27
or, r = 44
7
or, r = 27×7
44
Therefore, r = 4.295cm
A package of chocolates contains 3 caramel-
filled pieces, 3 raspberry-filled pieces and 4
fudge-filled pieces. What is the probability that
someone will reach in and select a caramel-filled
piece, keep it, and then select a raspberry-filled
piece?
Answer: 3 out of 19
Step-by-step explanation:
Answer:
P(caramel) = 3/10
P(raspberry) = 1/3
Step-by-step explanation:
Given:
Caramel chocolates = 3Raspberry chocolates = 3Fudge chocolates = 4⇒ Total chocolates = 3 + 3 + 4 = 10
[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]
[tex]\sf \implies P(picking \ caramel \ chocolate) = \dfrac{3}{10}[/tex]
If the picked caramel chocolate is NOT replaced then:
Caramel chocolates = 3 - 1 = 2Raspberry chocolates = 3Fudge chocolates = 4Total chocolates = 10 - 1 = 9[tex]\sf \implies P(picking \ raspberry \ chocolate) = \dfrac39=\dfrac13[/tex]
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}