You spin the spinner two times. If you get blue both times, you win $15.
If you don't, you lose $2. How much money do you expect to win or lose if you play this
game 1000 times?
The amount of money which is expected to lose if the game of spinner is played 1000 times is $111.
What is probability of an event?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
You spin the spinner two times.
If you get blue both times, you win $15. If you don't, you lose $2.Let suppose there are total 12 outcomes on a spinner which has 12 blocks. In this block, 4 is blue. The probability of getting blue twice in this spinner and earning $15 is,
[tex]P=\dfrac{4}{12}\times\dfrac{4}{12}\\P=\dfrac{1}{9}[/tex]
The probability of not getting two blue in two spun and losing $2 is,
[tex]P^{-1}=1-\dfrac{1}{9}\\P^{-1}=\dfrac{8}{9}[/tex]
The money to expect to win or lose if you play this is,
[tex]E(X)=15\times\dfrac{1}{9}-2\times\dfrac{8}{9}\\E(X)=-0.111[/tex]
For 1000 games,
[tex]E(X)=-0.111\times1000\\E(X)=-111[/tex]
Thus, the amount of money which is expected to lose if the game of spinner is played 1000 times is $111.
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8. In AQRS, if m/Q = 30°, what must be the
length of QR?
Answer:
=> 7√3
Step-by-step explanation:
Given :
∠ Q = 30°
RS/QR = tan 30°
7/QR = 1/√3
QR = 7√3
Find each measure. Assume that segments that appear to be tangent are tangent.
Answer: 97 degrees
Step-by-step explanation:
A manager drew this box-and-whisker plot to represent the weights, in pounds, of the 440 crates the company is shipping. box-and-whisker plot ranging from 80 to 180 with ticks at increments of 2.5. plot defined by points at 84, 99.5, 113, 143, 170. how many crates weigh more than 99.5 pounds? select from the drop-down menu to correctly complete the statement. about choose... crates weigh more than 99.5 pounds.
Deducing from the considered box plot, the number of crates that weigh more than 99.5 pounds is 330 approx.
How does a boxplot shows the data points?A box plot has 5 data description.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.What are quartiles?When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
Lower quartile, also called first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.Similarly, second quartile (also called median) is approximately in mid of the data.Third quartile (also called upper quartile) has approx 75% in its left partition, and on its right lies approx 25% of the data.Left to right is said in assumption that data was arranged increasingly from left to right
We're specified here that:
Total 440 crates is being shipped by company.
The box plot is defined by the points 84, 99.5, 113, 143, 170
The point 99.5 is the first quartile.
There are 75% observations on its right, so 75% of 440 is the number of crates which weigh greater than 99.5 pounds.
We get this value as:
[tex]\dfrac{440}{100} \times 75=330[/tex]
Thus, deducing from the considered box plot, the number of crates that weigh more than 99.5 pounds is 330 approx.
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From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon
The probability that at least one of the sides of the triangle is also a side of the octagon is 5/7
How to determine the probability?A regular octagon has 8 sides, and a triangle has 3 sides
Assume that there is a point on the triangle.
Then we select (3 - 1) points from the (8 - 1) sides.
8 - 1 = 7
3 - 1 = 2
So, the total number of selection is:
Selection = 7C2
Evaluate the combination expression
Selection = 21
Adjacent triangles have 5 lines (one line in common).
So, we have:'
n = 5 - 1
n = 4
The number of ways this points can be selected is:
Selection = 4C2
Evaluate
Selection = 6
The probability that the triangle and the octagon do noth have the same side is:
P= 6/21
The probability that at least one of the sides of the triangle is also a side of the octagon is calculated using the following complement rule
P = 1 - 6/21
Evaluate the difference
P = (21 -6)/21
P = 15/21
Reduce fraction
P = 5/7
Hence, the probability that at least one of the sides of the triangle is also a side of the octagon is 5/7
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Write the equation of the line that is perpendicular to the line which has a slope of 3 / 4 and passes through the point ( 0, - 4 ).
Answer:
y=-4/3x-4
Step-by-step explanation:
The equation of the line that is perpendicular to the line which has a slope of 3 / 4 and passes through the point ( 0, - 4 ) is equals to [tex]y= \frac{-4}{3} x-4[/tex]
What is equation of line?" Equation of line is defined as the equation which represents the set of points using slope."
Formula used
[tex]y=mx+c[/tex]
m = slope of the line
c = y-intercept
Product of the Slopes of perpendicular lines = -1
According to the question,
Slope of the given line = [tex]\frac{3}{4}[/tex]
Using condition for slope of perpendicular lines we have,
Slope of the line perpendicular to the given line 'm' = [tex]\frac{-4}{3}[/tex]
From given point (0, -4)
Y- intercept 'c' = -4
Substitute the value in the formula to get equation of required line,
[tex]y= \frac{-4}{3} x-4[/tex]
Hence, equation of the line that is perpendicular to the line which has a slope of 3 / 4 and passes through the point ( 0, - 4 ) is equals to [tex]y= \frac{-4}{3} x-4[/tex].
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Which equation would you use to find the distance between the two points? A. |2 - 4| B. |2 - (-4)| C. |-5 - 5| D. |2 + (-4)|
Answer:
Step-by-step explanation:
Could you show two points need to be calculated? A and D are the same in this case
Which is a stretch of an exponential decay function?
Answer:
C.
Step-by-step explanation:
when you put it in a graphing calculator it would show the standard graph of an exponential decay function.
pls help me with this maths question, I forgot how to do it :))
Step-by-step explanation:
thats the answer i think
20 points if you help me with this 1 thing
Answer:
0.7
Step-by-step explanation:
1+3+3+2+3+3 = 15/6 = 2.5
2+4+4+2+4 = 16/5 = 3.2
3.2-2.5 = 0.7
Please help me on this question about circle chords, find x.
A. 26.3
B. 21.1
C. 11.8
Answer: B
Step-by-step explanation:
If we add two equations in the original system, we have 6x+7y=32. Explain why the same (x,y) pair is also a solution to the equation
Answer:
simultaneous equations are used to solve for 2 variable
After adding the numbers the result obtained is called the total or the sum
Answer:
After adding the numbers the result obtained is called the sum.
Cos(B) = ?
13/5
5/13
12/13
12/5
[tex]~~~~~~\cos B = \dfrac{\text{Base}}{\text{hypotenuse}}\\\\\\\implies \cos B = \dfrac{BC}{AB}\\\\\\\implies \cos B = \dfrac{12}{13}[/tex]
need help asap will give brainlist
Answer:
D. [tex]\frac{12x+20}{5y^3}[/tex]
Step-by-step explanation:
When multiplying 2 fractions, you multiply the numerators and denominators, so we have:
[tex](\frac{3x+5}{y^6})(\frac{4y^3}{5}) = \frac{(3x+5)\cdot 4y^3}{y^6\cdot 5} = \frac{(3x+5)\cdot 4}{y^3 \cdot 5} = \frac{12x + 20}{5y^3}[/tex]
Answer:
4th option
Step-by-step explanation:
[tex]\frac{3x+5}{y^6}[/tex] × [tex]\frac{4y^3}{5}[/tex] ( cancel y³ and [tex]y^{6}[/tex] on numerator/denominator by y³ )
= [tex]\frac{3x+5}{y^3}[/tex] × [tex]\frac{4}{5}[/tex]
= [tex]\frac{4(3x + 5)}{5y^3}[/tex]
= [tex]\frac{12x+20}{5y^3}[/tex]
Mrs. Jones has eight equal-sized poster boards. She divides them evenly among three students. Between which two whole numbers does the number of poster boards each student gets lie?
The principal at Miller Street School
has 12 packs of new pencils. She
will give 3 packs to each third-grade
class. How many third-grade classes
are there?
Answer:
There are 4 third grade classes
Step-by-step explanation:
12 packs of pencils
3 packs to each class so you are making groups of 3.
12 ÷ 3 = 4
There are 4 third grade classes
3 packs × 4 classes = 12 packs of pencils
Find the integral of √(x² +4) W.R.T x
Answer:
[tex]\frac{x}{2} *\sqrt{x^{2} +4}[/tex] +[tex]\frac{1}{2}[/tex]*LN(|[tex]\frac{x+\sqrt{x^{2} +4} }{2}[/tex]|) +C
Step-by-step explanation:
we will have to do a trig sub for this
use x=a*tanθ for sqrt(x^2 +a^2) where a=2
x=2tanθ, dx= 2 sec^2 (θ) dθ
this turns [tex]\int\limits {\sqrt{x^{2}+4 } } \, dx[/tex] into integral(sqrt( [2tanθ]^2 +4) * 2sec^2 (θ) )dθ
the sqrt( [2tanθ]^2 +4) will condense into 2sec^2 (θ) after converting tan^2(θ) into sec^2(θ) -1
then it simplifies into integral(4*sec^3 (θ)) dθ
you will need to do integration by parts to work out the integral of sec^3(θ) but it will turn into (1/2)sec(θ)tan(θ) + (1/2) LN(|sec(θ)+tan(θ)|) +C
then you will need to rework your functions of θ back into functions of x
tanθ will resolve back into [tex]\frac{x}{2}[/tex] (see substitutions) while secθ will resolve into [tex]\frac{\sqrt{x^{2} +4} }{2}[/tex]
sec(θ)=[tex]\frac{\sqrt{x^{2} +4} }{2}[/tex] is from its ratio identity of hyp/adj where the hyp. is [tex]\sqrt{x^{2} +4}[/tex] and adj is 2 (see tan(θ) ratio)
after resolving back into functions of x, substitute ratios for trig functions:
= [tex]\frac{x}{2} *\sqrt{x^{2} +4}[/tex] + [tex]\frac{1}{2}[/tex]*LN(|[tex]\frac{x+\sqrt{x^{2} +4} }{2}[/tex]|) +C
Rewrite the polynomial in the form ax² + bx+c and then identify the values of a,
b, and c.
-2x+1+2x²
Answer:
See below ~
Step-by-step explanation:
The given polynomial : -2x + 1 + 2x² needs to be written in the form :
ax² + bx+ca is the coefficient of x²b is the coefficient of xc is the constant termOn rewriting in this asked format,
2x² - 2x + 1a = 2b = -2c = 1Find the solution of the system of equations. 9x - 9y = -9 and 3x + 9y = -15
Answer:
(-2 , -1)Step-by-step explanation:
[tex]\begin{cases}9x-9y=-9&\left(1 \right) \\ 3x+9y=-15&\left( 2\right) \end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}9x-9y=-9&\left( 1\right) \\ 12x=-24&\left( 1\right) +(2)\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}x-y=-1&\left( 1\right) \\ x=-2&\left( 1\right) +(2)\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}y=x+1=-2+1=-1&\left( 1\right) \\ x=-2&\left( 1\right) +(2)\end{cases}[/tex]
A car travels 98 miles in 1. 4 hours. How far can it travel in 7 hours at the same speed
Answer:
490 miles
Step-by-step explanation:
7/1.4 = 5
98*5 = 490
7-9+(9-5)^2-4•2+4/-5-1+8-3•100
Answer:
See below ~
Step-by-step explanation:
Using PEMDAS
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionOur equation
[tex]\frac{7-9+(9-5)^{2}-4*2+4 }{-5-1+8-3*100}[/tex]1. Simplifying Parentheses
[tex]\frac{7-9+4^{2}-4*2+4 }{-5-1+8-3*100}[/tex]2. Simplifying Exponents
[tex]\frac{7-9+16-4*2+4 }{-5-1+8-3*100}[/tex]3. Multiplying
[tex]\frac{7-9+16-8+4 }{-5-1+8-300}[/tex]4. Adding (As division without simplifying isn't correct)
[tex]\frac{7+7-4 }{-5+7-300}[/tex][tex]\frac{14-4 }{2-300}[/tex]5. Subtracting
[tex]\frac{10 }{-298}[/tex]6. Dividing
[tex]-\frac{5}{149}[/tex] [Simplest fractional answer]-0.03 [Simplest decimal answer]
A whole is divided into 10 equal parts.
Answer these questions.
(a) How much of a whole is 100%?
(b) How much of a whole is 10%?
Answer:
a. All of the whole - 10/10
b. A tenthof the whole - 1/10
Step-by-step explanation:
Step-by-step explanation:
a. since the entire whole represents a 100% , the number of whole that makes up for 100% is the 10 of the ten parts divided by 10 which is equal to 10.
b. since a whole equals 100% , if divided by 10 the entire 100% becomes 10% each for 10 parts. hence a single part equivalent to 1/10 is 10%
Can anyone help me I needa explanation how to do it
Answer:
1/4
Step-by-step explanation:
There are 8 sections and skating is on 2 of the 8; the probability is 2/8 = 1/4. It does not matter how many times it has appeared on previous spins.
The equation y= x-3 describes how the variables x and y are related
Answer:
The amount y is depends on what x's value is. It is helpful to make a table or graph so we can see how the y value changes like the x value :)
Have an amazing day!!
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If you want the type of relationship between 'x' and 'y'
⇒ they are a linear relationship as in they form a straight line together
If you want to describe how the value of x correlates to y
⇒ as x increases, y increases thus it is a direct variation.
Hope that helps!
Find the surface area of the cylinder (please help)
Answer:
792 cm²
Step-by-step explanation:
Surface Area (Cylinder)
⇒ 2πrh + 2πr²
⇒ 2πr (h + r)
Here, r = 9 cm and h = 5 cm.
⇒ 2π × 9 (5 + 9)
⇒ 18π × 14
⇒ 252 x 22/7
⇒ 36 x 22
⇒ 792 cm²
 Order these numbers least to greatest
Answer:
-24/16, -√2, 21/51, 0.42
Step-by-step explanation:
Look at the signs of the numbers. Negative numbers will be on the left, while positive numbers will be on the right. That means -√2 and -24/16 will be on the left, while 0.42 and 21/51 will be on the right.
Part 1:
We can change the negative numbers to decimals to compare them.
-√2 ≈ -1.41
-24/16 = -1.5
-1.5 is smaller, which means the first number in the sequence will be -24/16 and then -√2.
Part 2:
We can also change the positive numbers to decimals to compare them.
0.42 = 0.42
21/51 ≈ 0.41
21/51 is a bit smaller, so the third number in the sequence will be 21/51 and then 0.42.
I hope this helps and please mark me as brainliest!
Solve and graph on a number line. Show your work in the box below.
7x + 10 < 11x + 2
Answer:
x > 2
Graph in picture
Step-by-step explanation:
Given:
7x + 10 < 11x + 2
To Find:
Solve and graph on a number line. Show your work in the box below.
Solve:
Subtract 10 from both sides
7x + 10 -10 < 11x + 2-10
Simplify
-4x < - 8
Multiply both sides by -1 which reverse the inequality
Simplify
4x > 8
Now, Divide both sides by 4
4x ÷ 4 > 8 ÷ 4
Simplify
x > 2
Solution: x > 2
Now graphing:
> means greater than
that means x is greater than 2
Thus, the line is going to the right.
Graph below:
Answer: x > 2
Step-by-step explanation:
Subtract 10 from both sides7x+ 10 < 11x + 2
7x+10-10 < 11x + 2 -10
Simplfysubtract the numbers
7x < 11x -8
Subtact 11 from both sides7x < 11x -8
7x - 11x < 11x -8 - 11x
Combine Like terms-4x < -8
Divide both sides by the same factor, and flip the relation because the factor is negative-4x < -8
-4x/-4 > -8/-4
Cancel terms that are in both the numerator and denominatorDivide the numbersx > 2
You are a market analyst working on game consoles. Suny’s Playcom series takes up 40% of the market share, Microsoft Box series takes up 35% of the market share and Nintendo’s Wee takes the the remaining 25% of the market share. According to industry reports, 1% of Playcom is defective, 3% of YBox is defective and 5% of Wee is defective worldwide. What is the probability of a game console buyer buying a defective Suny Playcom?
Using it's concept, it is found that there is a 0.004 = 0.4% probability of a game console buyer buying a defective Suny Playcom.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 40% of the consoles bought are of the Suny Playcom series, and of those, 1% are defective, hence the probability is given by:
p = 0.4 x 0.01 = 0.004
0.004 = 0.4% probability of a game console buyer buying a defective Suny Playcom.
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Here is a set of numbers , 10,10,10,10,11,12,13,15,17,find the mode, the median , the mean b there is a mistake in the set of numbers . The 10 should be 26, find the correct value for the mode , the median and the mean
First, find the mode, median, and mean of the given set of numbers.
Mode
The mode is the number that shows up frequently within the given set. In this case, it will be 10, as it shows up 4 times, 3 times more than any other number.
Mode: 10
~
Median
The median is the number that is in the middle of the given set. In this case, there are 9 numbers, and so the 5th given number is your median:
10 , 10 , 10 , 10 , 11 , 12 , 13 , 15 , 17
Median: 11
~
Mean
The mean is combining all numbers within the given set and dividing by the amount of numbers in that said set:
(10 + 10 + 10 + 10 + 11 + 12 + 13 + 15 + 17)/9 = 108/9 = 12
Mean: 12