Find y. right triangles
Answer:
√2
Step-by-step explanation:
Angle ( θ ) = 45
Hypotenuse side = 2
Opposite side = x
Formula : -
sin θ = Opposite side / Hypotenuse side
Note :
The value of sin 45 = 1/√2
sin 45 = x/2
1/√2 = x/2
Cross multiply,
x*√2 = 2*1
x√2 = 2
2 can be simplified as √2 * √2
x√2 = √2*√2
Divide √2 on both sides,
x = √2
Order from least to greatest. 10/8, 1.2, 0.556, 0.8%
The order from least to greatest is 0.8%, 0.556, 1.2 and 10/8
Ordering of numbersIn order to order the given numbers, we will first have to write them as a percentage as shown.
Given the number below
10/8, 1.2, 0.556, 0.8%
Convert to percentage
10/8 = 125%
1.2 = 120%
0.556 = 55.6%
0.8%
Hence the order from least to greatest is 0.8%, 0.556, 1.2 and 10/8
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Consider a deck with 2626 black and 2626 red cards. You draw one card at a time and you can choose either guess on whether it is red beforehand or simply observe the result. If the card is red you get \$1$1 and the game ends whenever you decide to guess. What is your strategy to play this game and the expected earnings
The maximum earning is v(r,b)
Let v(r,b) be the expected value of the game for the player, assuming optimal play, if the remaining deck has r red cards and b black cards.
Then v(r,b) satisfies the recursion
and
The stopping rule is simple: Stop when v(r,b)=0.
To explain the recursion . . .
If r,b>0, and the player elects to play a card, then:
The revealed card is red with probability [tex]\frac{r}{r+b}[/tex], and in that case, the player gets a score of +1, and the new value is V(r-1,b)The revealed card is black with probability [tex]\frac{b}{r+b}[/tex], and in that case, the player gets a score of −1, and the new value is V(r,b-1)Thus, if r,b>0, electing to play a card yields the value f(r,b).
But the player always has the option to quit, hence, if r,b>0, we get v(r,b)=max(0,f(r,b)).
Implementing the recursion in Maple, the value of the game is
v(26,26)=41984711742427/15997372030584
v(26,26) ≈2.624475549
and the optimal stopping strategy is as follows . . .
If 24≤b≤26, play while r≥b−5.If 17≤b≤23, play while r≥b−4.If 11≤b≤16, play while r≥b−3.If 6≤b≤10, play while r≥b−2.If 3≤b≤5, play while r≥b−1.If 1≤b≤2, play while r≥b.If b=0, play while r>0.So, The maximum earning is v(r,b)
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Write the product in its simplest form:
-4y²• 8y4
1. On the number line above, the ratio of AE to
AG is equal to the ratio of DF to which of the
following?
Answer:
(C) BE
Step-by-step explanation:
AE = 4
AG = 6
-> AE/AG = 2/3
DF = 2
We need a segment that is 3/2 the length of DF, which is 2.
The only option that works is (C) BE
If 7846, 7896 and 8802 are rounded to the nearest hundred and then added, the answer will be
Answer:
the answer is 24500
Step-by-step explanation:
7800+7900+8800
=24500
Determine the equation of the altitude from A.
Answer:
y = - 3x + 11
Step-by-step explanation:
the altitude is a line from the vertex A drawn perpendicular to the opposite side BC
calculate the slope of BC using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = B (- 7, 3 ) and (x₂, y₂ ) = C (- 1, 5 )
[tex]m_{BC}[/tex] = [tex]\frac{5-3}{-1-(-7)}[/tex] = [tex]\frac{2}{-1+7}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept ) , then
y = - 3x + c ← is the partial equation
to find c substitute A (4, - 1 ) into the partial equation
- 1 = - 12 + c ⇒ c = - 1 + 12 = 11
y = - 3x + 11 ← equation of altitude from A
Annalise makes rectangular patchwork quilts out of leftover fabric scraps. The first scrap she is using to make a quilt has a width of 2x feet and a length of 5x feet. When finished, the entire quilt will be 5 feet wider and 3 feet longer than the first fabric scrap used. Which of the following functions will give the area, f(x), of the quilt in square feet?
The function that will give the area, f(x), of the quilt in square feet is
Area = f(x) = 10x²+31 + 15
Which of the following functions will give the area, f(x), of the quilt in square feet?Generally, the equation for Area of Rectangle is mathematically given as
A = Length *Width
Therefore
A= (5x+3)(2x+5) square feet.
inconclusion, Area
f(x)= (5x+3)(2x+5)
f(x)=10x+25+ 6+15
(fx) 10x^2 +31x+15
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Answer:
f(x)=10x^2 + 31x + 15
Step-by-step explanation:
Did it and got it right
the other people put so much things for no reason lol
If a gallon of gas costs 368 9/10 cents, how much does 1/2 gallon cost?
Answer:
[tex]737\frac{4}{5}[/tex]cents
Step-by-step explanation:
1 Gallon of Gas = 368.9 cents (Note: 9/10 = 0.9)
1/2 Gallon of gas = [tex]\frac{368.9}{\frac{1}{2} }cents\\ =368.9 * 2\\= 737.8 cents[/tex]
or [tex]737\frac{4}{5}[/tex] cents (Reduced to simplest form)
The function P(t) = 21e^0.01823t represents the population of Texas, in millions, t years after 2000. What was the population of Texas in the year 2000? Write your answer in millions (for example 4,000,000 would be expressed as 4).
The population in the year 2000 is 21
How to determine the population in 2000?The function is given as:
P(t) = 21e^0.01823t
The year 2000 is 0 years after 2000.
This means that
t = 0
So, we have:
P(0) = 21e^(0.01823 *0)
Evaluate the product
P(0) = 21e^0
Evaluate the expression
P(0) = 21
Hence, the population in the year 2000 is 21
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For a 4-units class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on students, and the distribution of total study hours per week is bell-shaped with a mean of 15 hours and a standard deviation of 3 hours. a) 95% of the students have study hours that are between_____and_____hours.
b) What percentage of the students have study hours that are above 12?
95% of the students have study hours between 10.75 and 13.25 hours and the percentage of the students have study hours that are above 12 is 92%.
Given average of 12 % studying required, population mean of 15 hours, standard deviation of 3 hours.
We have to find the confidence interval for 95% students and the percentage of the students that have studied above 12 hours.
Margin of error=z*σ[tex]\sqrt{n}[/tex]
z value for the p value 0.95 is 1.96.
Margin of error=1.96*3/[tex]\sqrt{22}[/tex]
=5.88/4.69
=1.25
Upper interval=Mean +margin of error
=12+1.25
=13.25
Lower interval=Mean- margin of error
=12-1.25
=10.75
The confidence interval (10.75,13.25).
Now we will calculate the percentage of the students that are above 12.
z value when X=12, z=12-15/15
=-3/15
=-0.2
p value of -0.2 will be =0.5+0.4207=0.9207
=0.9207*100
Percentage=92.07%
Approx=92%.
Hence the confidence interval is (10.75 , 13.25) and 92% students have studied above 12.
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Question is incomplete as it should include sample size of 22.
Professor Nwamabi is conducting an experiment in which he is examining the effects of air conditioning on sleep habits. 100 participants are randomly assigned into two groups, one of which sleeps for a week in an air conditioned setting and of which sleeps in a room without air conditioning. After a week he has various physiological markers assessed to see if the groups are different. In this research, the use of air conditioning represents a(n) ________ variable.
In the research of Professor Nwamabi the use of air conditioning represents independent variable.
Given 100 participants are randomly selected in a research in which effects of air conditioning on sleep habits is studied.
Dependent variable is the variable whose value is dependent on the other variables like increase in profit and production.
Independent variable is the variable whose value is not dependent on the other variables.
In the research of Professor Nwamabi in which he is examining the effects of air conditioning on sleep habits, use of air conditioning represents independent variable. In this study the effect is on sleep habits means the value of sleep habits will change due to use of air conditioning. It shows that the use of air conditioning is not depending on other variable in the research.
Hence the use of air conditioning represents the independent variable.
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Write equations for the vertical and horizontal lines passing through the point (5,3)
Answer:
Horizontal line - y=3
Vertical line - x=5
Step-by-step explanation:
See both graphs below
Directions: Find the product and simplify
Answer:
x^4-9x^2+26x-24
Step-by-step explanation:
Answer:
[tex] {x}^{3} - 9 {x}^{2} + 26x - 24[/tex]
Step-by-step explanation:
[tex](x - 3)( {x}^{2} - 6x + 8)[/tex]
[tex] {x}^{3} - 6 {x}^{2} + 8x - 3 {x}^{2} + 18x - 24[/tex]
[tex] {x}^{3} - 9 {x}^{2} + 26x - 24[/tex]
A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink receipts totaled $360, and 4 times as many cold beverages were sold as hot beverages.
Which system of linear equations represents the beverage sales on Saturday?
c = 4 times h
Linear equation: 1.5c + 2h = 360
Hello!
Your answer should be..
c=4h ( as there are 4 hours )
1.5c+2h=360
c is 1.50 and h is 2.00 so you must add them to reach 360
Hope this helps! :)
Choose the expression that is equivalent to 9w² +(20w² - 15w+10) +2w.
OA. 9w² - 17w +6
B. 21w² -7w+10
C. 21w²-7w+6
D. 9w² -w+10
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: 9w² - 13w + 10[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + (20 {w}^{2} - 15w + 10) + 2w[/tex]
[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + 20 {w}^{2} - 15w + 10+ 2w[/tex]
[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + 20 {w}^{2} - 15w +2w + 10[/tex]
[tex]\qquad \tt \rightarrow \: 29 {w}^{2} - 13w + 10[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
For which of the given p-values would the null hypothesis be rejected when performing a level 0. 05 test?.
Using a significance level of 0.05, the null hypothesis would be rejected for p-values less than 0.05.
What is the relation between the p-value and the conclusion of test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.If it is less, it is rejected.Hence, the null hypothesis would be rejected for p-values less than 0.05.
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PLEASE HELP I DONT UNDERSTAND I HAVE A FEW MIN TO SUBMIT
Answer:
Increasing: [tex](\infty, -1) \cup (2, \infty)[/tex]
Decreasing: [tex](-1, 2)[/tex]
Step-by-step explanation:
So when an equation has and odd degree, it will go in the opposite direction on both ends, so if y went towards infinity as x went towards infinity, then y would go towards negative infinity as x goes towards negative infinity. In this case, by looking at the graph it has an odd degree, due to opposite end behaviors, although on both ends it's increasing because even though it appears that it's going down on the left side, that's only if you start from the right and go towards the left. So it's really increasing from negative infinity to -1, and then it decreases from -1 to 2, until it once again starts increasing from 2 to infinity. This can be represented as (-infinity, -1) U (2, infinity) for increasing and (-1, 2) as decreasing
If < A and < B form a linear pair, and m< A = x - 21 degrees, and m< B = x + 15 degrees, then find x.
The value of x = 93 degree and value of angle A and B is 72 , 108 degree
What is a Linear Pair ?The pair of triangles that are supplementary and they add to form 180 degree angle are called Linear Pairs.
It is given that
∠ A = x -21
∠ B = x+15
also it is given that
angle A and B form a linear pair
∠ A + ∠ B = 180 degree
To find the value of x
x -21 + x+15 = 180
2x - 6 = 180
2x = 186
x = 93 degree
so
∠ A = x -21 = 93 -21 = 72 degree
∠ B = x+15 = 93+21 = 108 degree
Therefore the value of x = 93 degree and value of angle A and B is 72 , 108 degree.
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Wade wants to buy two shirts and a tie and must spend no more than $60.00. The tie he likes costs $12.50. If the two shirts are the same price, how much can he pay for each shirt?
Answer:
$23.75
Step-by-step explanation:
first, we know the tie he bought is $12.50, so we want to subtract that from the total ($60). Now we have 47.50 dollars left and if he wants to buy two shirts, we divide $47.50 by 2, which is $23.75. So if the two shirts are the same price, he can pay $23.75 for each shirt.
2. when a newspaper poll produces a statistic that is biased, it means that
When a newspaper poll produces a statistic that is biased, it mean that
(b) Repeated polls would give, results that are very different from each other.
What is biased in statistics?Statistical bias is anything that leads to a systematic difference between the true parameters of a population and the statistics used to estimate those parameters when people say that the newspaper poll is biased, they mean that:
(b) Responding was voluntary, and only these with access and interest would answer.
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Complete question:
When a newspaper poll produces a statistic that is biased, it means that
(a) Repeated polls would give the truth, about the population, in the same direction.
(b) Repeated polls would give results that are very different from each other.
(c) Repeated polls would give results that would not yield a normal distribution.
(d) Repeated polls would give results that are very similar to each other.
d = 6 when v = 20 Work out an equation connecting d and v work out the value of d when v =30
The value of d is 27/2 when v =30
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal
Suppose that d is directly proportional to the square of v.
So the equation is, d ∝ v² equals to d = kv², where k is a constant.
So in order to find the value of k,
d = k v²
d = 6, v = 20,
Substitue the value of d and v into the equation :
6 = k(20)²
k = 6/400
k = 3/200
Substitue the value of k and v =30 into the equation,
d = 3/200(30)²
d = 2700/200
d = 27/2
Hence, the value of d is 27/2 when v =30
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Samuel invested money in his bank account. he had a principal, p, of $100 in his account at the beginning of the period, which increased at a rate, r, of 0.15 per year. at the end of the period, he had interest, i, of $105 in his account. use the simple interest formula i = prt, to solve for the time, t, in months that it took to earn this amount. (1 point) 7 months 58 months 84 months 700 months
The correct answer is 700 months .
What is simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account. Simple interest doesn't compound, which means a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.Given,
I = 105
P = 100
r = 0.15
Now use simple interest formula,
[tex]S.I. = \frac{p * r* t}{100}[/tex]
105=100×(0.15)×(t)
Swap sides so t is on the left.
100 ×(0.15)×(t)=105
Divide both sides by 100.
0.15t=1.05
Divide both sides by 0.15
t=700
So, we see that it takes 700 months to earn this amount.
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Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set of this problem?
O xx-5
0 x>-5
O x>-1
O x<-1
Answer:
x > -5
Step-by-step explanation:
[tex] \frac{2}{5} (x - 1) < \frac{3}{5} (x + 1)[/tex]
[tex]2(x - 1) < 3(x + 1)[/tex]
[tex]2x - 2 < 3x + 3[/tex]
[tex] - 5 < x[/tex]
[tex]x > - 5[/tex]
The legths of the sides of a rectangle are in a ratio of 4:7. If the length is 31.5 in., find the width, perimeter an area of this rectangle.
Step-by-step explanation:
when given a ratio like this 4:7, it means that one item represents 4 units, and the other 7 units.
let's assume that length is larger than width, so the given 31.5 in are these 7 units.
that means 1 ratio unit is
31.5 / 7 = 4.5 in
the width is 4 units, therefore
width = 4×4.5 = 18 in
the perimeter is
2×length + 2×width = 2×31.5 + 2×18 = 63 + 36 = 99 in
the area is
length × width = 31.5×18 = 567 in²
Point o is the center of dilation. triangle x y z is dilated to create triangle x prime y prime z prime. the length of o z is 2 and the length of z z prime is 4. the length of side x prime y prime is 9 and the length of side y prime z prime is 12. triangle xyz was transformed by do,3. what is the length of side xy?
The length of xy in the triangle XYZ is 9 units if xyz is dilated to create triangle x prime, y prime and z prime.
Given triangle xyz is dilated to create x prime, y prime and z prime.The length of oz is 2, the length of Zz Prime is 4,the length of x prime y prime is 9 and the length of side y prime z prime is 12.
Dilation is basically technique of creating similar shapes. Each point is streched outwards from the center point by multiplying the scale.
After dilation the side of the shape used to reduce according to factor. It is reduced by number of times of factor.
The line xy is equal to 9 units after dilation by a factor of 3. So the length of xy is 9/3.
=3 units.
Hence the length of side xy is 3 units if xyz is dilated to create x prime, y prime and z prime.
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Answer: 3
Step-by-step explanation: just did it on edge
+
Which statement is true?
UV LAB and WXZY
ZYLWX and AB 1 WX
OUVI AB and UV || ZY
AB|| UV and AB || WX
Answer:
the answer is c
Step-by-step explan
UV ⊥ AB and UV ║ ZY is the correct statement about the given figure.
What is a parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.
As we can observe in the graph Line ZY is parallel to the UV and WX is parallel to AB.
Similarly, WX is perpendicular to ZY and UV(Parallel)
And AB is perpendicular to UV and ZY(Parallel)
Therefore, the correct statement is
UV ⊥ AB and UV ║ ZY
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What is the solution for w in the equation?
w+1/2=1/4w+2
A. 4
B. 2
C. 10/3
D. 9/3
Answer:
B. 2
w=2
Step-by-step explanation:
hope this helps!
It takes, on average, 6 minutes to do all the steps but the actual time can vary according to an exponential distribution with a standard deviation of 6 minutes. Assume students arrive on average every 6.6 minutes and their inter-arrival times are also exponentially distributed. What is the expected waiting time in this system according to the Kingman (PK) Formula
The expected waiting time is 1.2 minute
According the statement
We know that the kingman formula is
[tex]{ E(W) = \left ( \frac{p}{1-p} \right )\cdot \left ( \frac{ C_{a}^{2}+ C_{s}^{2} }{2} \right ) \cdot \mu_{s} }[/tex]
According to statement the mean value μs is 6 min.
Here the value of P is 6/36 = 1/6
And the value of ca and cs is 1
Substitute the values in formula then
[tex]{ E(W) = \left ( \frac{0.17}{1-0.17} \right )\cdot \left ( \frac{ 1^{2}+ 1^{2} }{2} \right ) \cdot \m6} }[/tex]
[tex]{ E(W) = \left ( \frac{0.17}{0.83} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]
[tex]{ E(W) = \left ( 0.20} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]
[tex]{ E(W) = 1.22[/tex]
So, the expected waiting time is 1.2 minute
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Please help I need this by tommorrow
Answer:
I think you would have to do 2 times 7
Answer:
h = 2.5cm or 5/2 cm
Step-by-step explanation:
Vol = Basearea•h
In your question, the base is the triangle shape. The rectangles go around the sides of the 3-d shape and on top is another triangle that we can't really see. In your image it is kind of laying on its side. So if we stand it up properly, the triangles are on the top and bottom. The triangle is the base.
Volume was given; it is 35. Also given is one side of the rectangles, that is 7.
So we can fill in 35 and 7 into the volume formula and calculate the Basearea.
V = B • h
35 = B • 7
35 = 7B
Divide by 7.
5 = B.
We have calculated the Basearea. This is the area of the triangle shaped bottom. The area formula for a triangle is:
A = 1/2bh
We just found that A=5 and we were given that the base of the triangle is 4.
A = 1/2bh
5 = 1/2•4•h
5 = 2h
Divide by 2.
5/2 = h
This is the height of the triangle, h in the picture. (The h in the volume formula and h in the triangle are different)
This is what the question is asking for, h = 5/2 or in decimals, h = 2.5cm