Using it's concept, it is found that the probability that John's next three spins land on the number 2 is of [tex]\frac{1}{125}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that out of 5 numbers, one is 2, hence the probability of three consecutive spins landing on two is given by:
[tex]p = \left(\frac{1}{5}\right)^3 = \frac{1}{125}[/tex].
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IMPORTANT HELP PLEASE ANSWER IMMEDIATELY!!!!!
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Type it out please!
Solve the following equation. Show all your work.
(x/(x−2))+((x−1)/(x+1))=−1
Answer:
[tex]\displaystyle x = 0 \text{ and } x = 1[/tex]
Step-by-step explanation:
We are given and asked to solve the equation:
[tex]\displaystyle \frac{x}{x-2} + \frac{x-1}{x+1} = -1[/tex]
We can first remove the rational expressions by multiplying both sides of the equation by its LCM (in this case, by (x - 2)(x + 1)):
[tex]\displaystyle (x-2)(x+1) \left( \displaystyle \frac{x}{x-2} + \frac{x-1}{x+1}\right) = -1(x-2)(x+1)[/tex]
Simplify:
[tex]\displaystyle x(x+1)+(x-1)(x-2) = -(x-2)(x+1)[/tex]
Expand and isolate:
[tex]\displaystyle \begin{aligned} (x^2 + x) + (x^2 - 3x + 2) & = -(x^2 -x -2) \\ \\ 2x^2 - 2x + 2& = -x^2 + x + 2 \\ \\ 3x^2 - 3x & = 0 \end{aligned}[/tex]
Hence solve for x:
[tex]\displaystyle \begin{aligned} 3x(x - 1) & = 0 \\ \\ x & = 0\text{ or } x = 1\end{aligned}[/tex]
In conclusion, the solutions of the equation are x = 0 and x = 1.
Calculate volume of hemisphere with radius 3.2 cm
The volume, V, of a sphere with radius r is V = [4/3 pi r^3]
Answer:
V ≈ 68.63 cm³
Step-by-step explanation:
the volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex]πr³
the volume of a hemisphere is half the volume of a sphere, so
V = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] πr³ = [tex]\frac{2}{3}[/tex] πr³ , then
V = [tex]\frac{2}{3}[/tex] π × 3.2³
= [tex]\frac{2}{3}[/tex] π × 32.768
≈ 68.63 cm³ ( to 2 dec. places )
For the quadratic equation 3x^2-18x-21=0, x1 and x2 are the roots. Find:
x1^2+x2^2
|x1-x2|
(x_1+x_2)=-b/a=18/3=6
x_1x_2=c/a=-21/3=-7
So
(x_1+x_2)²-2x_1x_2=x_1^2+x2²x1²+x2²=(6)²-2(-7)=36+14=50(x_1-x_2)²
x1²+x2²-2x_1x250+1464x_1-x_2=8
Answer:
[tex]x{_1}^2+x{_2}^2=50[/tex]
[tex]|x_1-x_2|=8[/tex]
Step-by-step explanation:
Given equation:
[tex]3x^2-18x-21=0[/tex]
Factor to find the roots:
[tex]\implies 3(x^2-6x-7)=0[/tex]
[tex]\implies x^2-6x-7=0[/tex]
[tex]\implies x^2+x-7x-7=0[/tex]
[tex]\implies x(x+1)-7(x+1)=0[/tex]
[tex]\implies (x-7)(x+1)=0[/tex]
Therefore:
[tex]\implies (x-7)=0 \implies x=7[/tex]
[tex]\implies (x+1)=0 \implies x=-1[/tex]
Therefore, the roots of the quadratic equation are:
[tex]x = 7,\quad x = -1[/tex]
Let [tex]x_1 = 7[/tex]
Let [tex]x_2 = -1[/tex]
[tex]\implies x{_1}^2+x{_2}^2=7^2+(-1)^2=50[/tex]
[tex]\implies |x_1-x_2|=|7-(-1)|=8[/tex]
Use the figure to find the measure of each arc for #1-4.
1.) mFE
2.)mBC
3.)mCE
4.)mCFE
5.)m
Answer:
Step-by-step explanation:
You can use the surface area formula for a right cone to find the surface area
of an oblique cone.
A. True
B. False
Answer:
False
Step-by-step explanation:
False. Both surface area cannot be find using the same formula.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Right cone is a cone where the axis of the cone is perpendicular to the base .
Whereas, oblique cone has the axis of cone not perpendicular to the base.
Base area would be same for both right and oblique cones.
But the lateral surface area will be different.
Hence the surface area will be different.
Hence the surface area formula for a right cone is not same to find the surface area of an oblique cone.
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PLEASE HELP!!!!! I WILL MARK BRAINLIEST AND RATE 5 STARS!!
Answer:
37°
Step-by-step explanation:
sum of exterior angles of a polygon is 360°
so, 41+(x+13)+(2x-14)+(3x-22)+(x-3)+38+(x+11)=360
8x+64=360, subtract 64 from both sides
8x=296
x=37°
100 Points for this Question. PLEASE HELP ASAP.
[tex]\\ \rm\Rrightarrow \dfrac{AB}{AD}=\dfrac{BC}{CD}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{18}{x}=\dfrac{19}{11}[/tex]
[tex]\\ \rm\Rrightarrow 19x=198[/tex]
[tex]\\ \rm\Rrightarrow x=10.4[/tex]
Answer:
x = 10.4 (nearest tenth)
Step-by-step explanation:
Angle Bisector Theorem
The angle bisector of any angle in a triangle will divide the side opposite the bisected angle in the ratio of the sides containing the angle.
Therefore:
AD : DC = BA : BC
Given:
AD = xDC = 11BA = 18BC = 19Substituting the given values into the ratio and solving for x:
[tex]\implies \sf x : 11 = 18 : 19[/tex]
[tex]\implies \sf \dfrac{x}{11}=\dfrac{18}{19}[/tex]
[tex]\implies \sf 19x=18 \cdot 11[/tex]
[tex]\implies \sf 19x=198[/tex]
[tex]\implies \sf x=\dfrac{198}{19}[/tex]
[tex]\implies \sf x=10.4 \: (nearest\:tenth)[/tex]
Which statements about the octagon are true? select two options. the length of segment yz is 15.3 cm. the measure of the angle formed by the radius and the apothem is 30°. the length of segment xy can be found by solving for a in 202 – 7.652 = a2. the length of segment wz is 20 cm. the measure of the central angle, ∠zxw, is 45°.
The statements about the octagon that are true are:
The length of segment xy can be found by solving for a in 202 – 7.652 = a2. The measure of the central angle, ∠zxw, is 45°.What is Octagon?This is known to be a kind of 2D shape object that is said to be made up of eight-sided polygon.
Note that when one measure the central angle, ∠zxw, as 45° it will therefore holds true for an octagon true shape and as such the two options above are correct.
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Answer:
its C and E my friend
Step-by-step explanation:
i took the test
yw :)
hope i helped/ made life easier
Use the properties of limits and the facts given below to find each of the limits given
Answer:
where are the limit questions?
A store buys 17 sweaters for $68 and sells them for $561. How much profit does the store make per sweater?
He makes a profit in total of $8381
The store makes a profit of $29 per sweater.
Here, we have to calculate the profit per sweater, we need to find the difference between the selling price and the cost price (purchase price) of each sweater.
Given:
Number of sweaters bought = 17
Cost of buying 17 sweaters = $68
Selling price of 17 sweaters = $561
Profit per sweater = Selling price per sweater - Cost price per sweater
First, calculate the cost price per sweater:
Cost price per sweater = Total cost / Number of sweaters
Cost price per sweater = $68 / 17
Cost price per sweater = $4.
Now, calculate the profit per sweater:
Profit per sweater = Selling price per sweater - Cost price per sweater
Profit per sweater = $561 / 17 - $4
Profit per sweater = $33 - $4
Profit per sweater = $29.
The store makes a profit of $29 per sweater.
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calculate the length of ed and be
Answer:
ED = 6.5 cm
BE = 14.4 cm
Step-by-step explanation
AB/BC = AE/ED is less than or eqauls ED = BC×AE/AB
so
ED = 5×26/20 = 130/20 = 6.5 cm
and
AB/AC = BE/CD => BE = AB×CD/AC
so
BE = 20×18/25 = 360/25 = 14.4 cm
Match the real-world situation with the appropriate algebraic expression. Mary is 2 years younger than her sister Claire. x/2 Monday is half-price movie day. 3x Each topping costs an additional $3. x-2 ←
Answer:
Step-by-step explanation:
A is 3 You have to minus Clares age by two to get Mary's age
B is 1 You have to divide the price in half
C is 2 the only one left
Write in scientific notation:
0,007 832
Answer:
The scientific notation for this will be
[tex]7.832 \times {10}^{ - 3} [/tex]
As there are three zero in expression
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEHello, please answer the question
Determine the equation of the perpendicular bisector of AB and state the coordinates of the point where the perpendicular bisector meets or intersects with the y-axis.
Gradient: -1
Midpoint : [5,1]
Coordinates for A: [3,5] , B: [7,1]
Answer:
the equation will be in the form of:
y = -x + b
To find be take any point on the line. Hence we have (5,1) which is the midpoint where the line meets.
Therefore, substitute (5,1) in the above equation:
1 = -5 + b
b = 6
So the question of the line will be:
y = -x + 6
find the area of each shaded sector. round to the nearest tenth.
Answer:
a.
Step-by-step explanation:
the area of a whole circle (360°) is
pi×r²
in our case
pi×10² = 100pi
but here we don't need the full circle. we only need a fraction of the whole circle : 128/360
so, the area of the sector is
100pi × 128/360 = 100pi × 16/45 = 20pi × 16/9 =
= 111.7010721... cm² ≈ 111.7 cm²
Detemine which equation has the same solutions as the equation below.
4X² + 32X - 28 = 0
A. (X+4)²=23
B. 4(X+4)²=36
C. (X+8)²=57
D. 4(X+8)²=28
The answer is B i hopes this helps
Brian brought $36.50 to the art supply store. He bought a brush, a sketchbook, and a paint set. The brush was 1/3 as much as the sketchbook, and the sketchbook cost 1/2 the cost of the paint set. Brian had $4.00 left over after buying these item.What was the cost of each item?
So I got it wrong in my homework how do i translate it?
To translate something:
⇒ is to write out the equations
Let's examine what information this problem gives us:
Mrs. Albert has $400 ⇒ Total money = 400Mrs. Albert bought two adult tickets at $62.50 each⇒ with '2' being the number of adults tickets
⇒total charge from purchasing adult tickets = 2 * 62.5 = 125
Each child ticket costs $42.5⇒ with 'x' being the number of child tickets bought
⇒total charge from purchasing child tickets = 42.5x
Since the sum of total charge from purchasing adult tickets and total charge from purchasing child tickets is equal to 400:
⇒ 42.5x + 125 = 400 <== translated form
Let's solve:
[tex]42.5x+125=400\\42.5x=275\\x=6.47[/tex]
Since we can only buy whole tickets:
Mrs. Albert could have bought at most 6 child tickets
Answer: Mrs. Albert can bring 6 kids
Hope that helps!
x^2=6x+1
1) rewrite the equation by completing the square
2) what are the solutions to the equation?
Answer:
x=+-√10+3
Step-by-step explanation:
x^2=6x+1
x^2-6x=1
To create a trinomial square on the left side of the equation, find a value that is
equal to the square of half of b
a is the number next to x^2
b is the number next to x
c is the last number
b is -6
half of b is -3
square of half of b is 9
put 9 on both sides of the = sign
x^2-6x+9=1+9
x^2-6x+9=10
(x-3)^2=10
take the square root of both sides of the = sign
√(x-3)^2=√10
x-3=√10
x=+-√10+3
Ms. Crane has a jar with 6 white marblos, 4 red marbles, and 5 blue marbles. If
she closes her eyes and picks one marble out of the jar, what is the probability
that it is not red?
A. 4/15
B. 2/5
C.11/15
D. 2/3
Answer:
11/15
Step-by-step explanation:
To find probability, you divide whatever you're looking for over your total. In this case, you have 11 marbles that are not red, and 15 marbles total, so your answer would be 11/15.
A line includes the points (7, 4) and (5, 0). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = 2x – 10
Step-by-step explanation:
ΔY divided by ΔX
= 5-7/0-4
= 2/1 = 2 (simplified)
plug in 2 into; 0=2(5)+b
= -10=b
so we have: y=2x-10
The area of a rectangular field is 6942m2. If the length of the field is 89m, what is its width?
Answer:
78m
Step-by-step explanation:
6942 ÷ 89 = 78, here you go!
which postulate or theorem proves that these two triangles are congruent?
a. ASA Congruence Postulate
b. SAS Congruence Postulate
c. AAS Congruence Theorem
d. HL Congruence Theorem
On a recent math test, Carlos had to find the volume of the rectangular prism below. He gave the answer of 60 in3, which was marked incorrect. Help Carlos understand how to correctly find the volume of the prism.
A cube that is eight inches in length, ten inches in width, and six inches in height.
Answer:
480 in
Step-by-step explanation:
Rectangular Prism Formula :
V=whl
Which,
W = Width
H = Height
L = Length
Solve:
Given that:
Length = 8 in
Width = 10 in
Height = 6 in
Since the formula is:
V = whl
Then,
V = 8 × 10 × 6
V = 80 × 6
V = 480 in
Kavinsky
Find mQTS⌢, m∠RQS and mQS⌢.
If the measure of the angle ∠RQT is 125°. Then the measure of the angles ∠RQS and ∠SQT will be 44° and 81°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
If the measure of the angle ∠RQT is 125°. Then the measure of the angles ∠RQS and ∠SQT will be
Then we have
∠RQS + ∠SQT = 125°
(3x - 10)° + (4x + 9)° = 125°
7x - 1 = 125°
7x = 126°
x = 18°
Then the measure of the angle ∠RQS will be
∠RQS = 3 × 18 - 10
∠RQS = 44°
Then the measure of the angle ∠SQT will be
∠SQT = 4 × 18 + 9
∠SQT = 81°
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I. Collect data from several fast food chains on the number of fat calories and grams of saturated fat in menu items. Record at least 12 ordered pairs of (fat calories, grams of saturated fat). Organize your data in a table. II. Make a scatter plot of the data on graph paper. Be sure to label the axes and use an appropriate title for the graph. You may wish to use a graphing calculator, spread sheet, or other technology resource (such as the graphing utility link below) to aid you in graphing. Create a Graph III. Draw a trend line for the scatter plot. Use the following scatter plot of the ordered pairs (fat grams, total calories) as an example. IV. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.) Note: Graphing calculators and spread sheets have features with which to draw trend lines and determine the equation. You may choose to use one of these options. If you use technology, indicate what steps were taken to arrive at your equation. V. Using the slope and y-intercept, write the equation of the trend line ( y = mx + b). VI. Choose a "calories from fat" value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step V to predict the number of fat grams in an item having that number of fat calories. Be sure to show your work. VII. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.
The regression line is y = 10x + 125, and the value of calories is 135, and when x = 12 the value of y = 245 from the regression line, butbut the actual value is 225.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dot's relationship.
Here the scatter plot is not given, but we can draw the scatter plot using the data which is given with two variables such as (x, y) and the line which is best fit of the given data.
From the data given, we can write the line of best fit in slope and y-intercept form:
y = mx + b
Plug m = 10 and b = 125
y = 10x + 125
The number of fat grams in an item having that number of fat calories.
As we have the regression line:
y = 10x + 125
Put x = 1 in the regression line:
y = 10(1) + 125
y = 135 calories
For x = 12
y = 10(12)+125 = 245
But the actual value from the graph is 225.
Thus, the regression line is y = 10x + 125, and the value of calories is 135, and when x = 12 the value of y = 245 from the regression line, but but the actual value is 225.
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math hw 2
The Binomial Distribution
pls help me with my homework!!
thanks,
Using the binomial distribution, we have that:
a) The distribution is given by:
P(X = 0) = 0.0625.P(X = 1) = 0.25.P(X = 2) = 0.375.P(X = 3) = 0.25.P(X = 4) = 0.0625.b) 0.3125 = 31.25%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we have that:
There are 4 children, hence n = 4.Each children has a 50% chance of being female, hence p = 0.5.The distribution is given by the probability of each outcome, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.5)^{0}.(0.5)^{4} = 0.0625[/tex]
[tex]P(X = 1) = C_{4,1}.(0.5)^{1}.(0.5)^{3} = 0.25[/tex]
[tex]P(X = 2) = C_{4,2}.(0.5)^{2}.(0.5)^{2} = 0.375[/tex]
[tex]P(X = 3) = C_{4,3}.(0.5)^{3}.(0.5)^{1} = 0.25[/tex]
[tex]P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.0625[/tex]
The probability of at least 3 daughters is given by:
[tex]P(X \geq 3) = P(X = 3) + P(X = 4) = 0.25 + 0.0625 = 0.3125[/tex].
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pls my test is tomorrow and its 11:30pm lol:(. so the question, a person at the top of a 25 yard tall hill looks down at a tree that is 100 yards diagonally away from the person. what is the angle of depression from the person to the tree
Answer:
76°
Step-by-step explanation:
Taking the cosine ratio of the angle of depression :
cos θ = height of hill / distance from person diagonallycos θ = 25/100cos θ = 1/4θ = cos⁻¹ (0.25)θ = 76° (nearest whole degree)Karim is painting a design on a cylindrical
barrel. the height of the barrel is 1.2 m.
the radius of its base is 0.3 m. what area
will the paint have to cover? (remember to
include the bottom and lid of the barrel.)
Composite Figures
Find the volume of the composite figure.
First, find the volume of the cylinder.
Use 3.14 for TT.
Cylinder
8 cm
Volume = [?] cm³
5 cm
4 cm
Rectangular prism
Volume = [] cm³
8 cm
1,005.44
Pir^2h
3.142*8*8*5
1,005.44