Answer:
[tex]y = -\frac{3}{4}x + 5[/tex]
Step-by-step explanation:
Given equation y = -3/4x - 5
Step 1 : Find slope.
Since the lines are parallel to each other, the slopes are same.
[tex]therefore, m = \frac{-3}{4}[/tex]
Step 2 : Find the equation of the line.
[tex]( y - y_1) = m ( x - x_ 1) \ \ \ where \ x_ 1 = 4 \ and \ y_ 1 = 2[/tex]
[tex]( y - 2 ) = -\frac{3}{4}( x - 4)\\\\y - 2 = -\frac{3}{4}x + 3\\\\y = -\frac{3}{4}x + 3 + 2\\\\y = -\frac{3}{4}x + 5[/tex]
Let a=⟨1,−4,2⟩ and b=⟨−5,−5,−2⟩. Compute:
a+b=⟨ ,, ⟩
a−b=⟨ ,,⟩
2a=⟨ ,,⟩
3a+4b=⟨ ,, ⟩
|a|=
Answer:
a + b = ⟨-4, -9, 0⟩
a - b = ⟨6, 1, 4⟩
2a = ⟨2, -8, 4⟩
3a + 4b = ⟨-17, -32, -2⟩
|a| = √21
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightPre-Calculus
Vectors
OperationsScalars[Magnitude] ||v|| = √(x² + y² + z²)Step-by-step explanation:
Adding and subtracting vectors are follow the similar pattern of normal order of operations:
a + b = ⟨1 - 5, -4 - 5, 2 - 2⟩ = ⟨-4, -9, 0⟩
a - b = ⟨1 + 5, -4 + 5, 2 + 2⟩ = ⟨6, 1, 4⟩
Scalar multiplication multiplies each component:
2a = ⟨2(1), 2(-4), 2(2)⟩ = ⟨2, -8, 4⟩
Remember to multiply in the scalar before doing basic operations:
3a + 4b = ⟨3(1), 3(-4), 3(2)⟩ + ⟨4(-5), 4(-5), 4(-2)⟩ = ⟨3, -12, 6⟩ + ⟨-20, -20, -8⟩ = ⟨-17, -32, -2⟩
Absolute values surrounding a vector signifies magnitude of a vector. Follow the formula:
|a| = √[1² + (-4)² + 2²] = √21
A television and DVD player cost a total of $1230. The cost of the television is two times the cost of the DVD player. Find the cost of each item
Answer:
Television = 820
DVD Player = 410
Step-by-step explanation: Imagine the television as 2, and the DVD player as 1. If you’re were to draw it out with boxes, you’d see that the tv has two boxes and the DVD player has 1 box. All are exactly the same amount, and there are a total of three boxes. So divided 1230 by 3 and you get 410. Using the idea of the boxes, the DVD player get’s one 410, and the tv gets two 410s, or 820.
The three sides of a triangle are n, 3n+3, and 3n−1. If the perimeter of the triangle is 72m, what is the length of each side?
Answer: 10m, 33m, and 29m
Step-by-step explanation:
n + 3n+3 + 3n-1 = 72m
7n+2=72m
7n = 72-2
n = 70/7
n = 10
Solve one and two tenths plus eight and one eighteenth
47
Is this it?
1 plus 2(10) plus 8 plus 1(18)
You are playing a game by drawing a card from a standard deck and replacing it. If the card is a face card, you win $30. If it is not a face card, you pay $2. There are 12 face cards in a deck of 52 cards. What is the expected value of playing the game
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ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
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Find the area of the shaded part !
Answer:
Step-by-step explanation:
Semicircle:
Shaded area of semicircle = area of outer semicircle - area of inner semicircle
Outer semicircle:
d = 40 m r = 40/2 = 20m
Area of outer semicircle = πr²
= 3.14*20*20
= 1256 m²
Inner semicircle:
d = 30 m r = 30/2 = 15 m
Area of outer semicircle = πr²
= 3.14*15*15
= 706.5 m²
Shaded area of semicircle = 1256 - 706.5 = 549.5 m²
Shaded area of semicircle in both sides = 2 * 549.5 = 1099 m²
Rectangle on both sides:
Length = 50 m
width = 30 m
Area of shaded rectangles on both sides = 2* (length *width)
= 2* 50 * 30
= 3000 m²
Shaded area = 1099 + 3000 = 4099 m²
Consider the probability that at most 85 out of 136 DVDs will work correctly. Assume the probability that a given DVD will work correctly is 52%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
Answer:
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the necessary conditions are satisfied.
0.9945 = 99.45% probability that at most 85 out of 136 DVDs will work correctly.
Step-by-step explanation:
Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
It is needed that:
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume the probability that a given DVD will work correctly is 52%.
This means that [tex]p = 0.52[/tex]
136 DVDs
This means that [tex]n = 136[/tex]
Test the conditions:
[tex]np = 136*0.52 = 70.72 \geq 10[/tex]
[tex]n(1-p) = 136*0.48 = 65.28 \geq 10[/tex]
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the necessary conditions are satisfied.
Mean and standard deviation:
[tex]\mu = E(X) = np = 136*0.52 = 70.72[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{136*0.52*0.48} = 5.83[/tex]
Consider the probability that at most 85 out of 136 DVDs will work correctly.
Using continuity correction, this is [tex]P(X \leq 85 + 0.5) = P(X \leq 85.5)[/tex], which is the p-value of Z when X = 85.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{85.5 - 70.72}{5.83}[/tex]
[tex]Z = 2.54[/tex]
[tex]Z = 2.54[/tex] has a p-value of 0.9945.
0.9945 = 99.45% probability that at most 85 out of 136 DVDs will work correctly.
Instructions: Determine whether the following polygons are
similar. If yes, type in the similarity statement and scale factor. If
no, type 'None' in the blanks.
Answer:
None
Step-by-step explanation:
The given angles aren't equal which is needed for the polygon to be similar
No, the following polygons are not similar.
Used the concept of a similar figure that states,
In terms of Maths, when two figures have the same shape but their sizes are different, then such figures are called similar figures.
Given that,
Two polygons EFGH and JKLM are shown in the image.
Now the corresponding sides of both figures are,
EF = 27
JK = 63
And, EH = 27
JM = 63
Hence, the ratio of corresponding sides is,
EF/JK = 27/63
= 9/21
= 3/7
EH/JM = 27/63
= 3/7
So their corresponding sides are equal in ratio.
But their corresponding angles are not the same.
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4 pounds of oranges costs $ 12 . What is the unit price per pound?
Answer:
3 dollars per pound
Step-by-step explanation:
Unit Price = Cost / Pounds of oranges
Unit Price = 12 / 4
Unit Price = 3
The unit price per pound is $3
Solve the formula for the indicated variable.
1
A=-bh, for h
2
- BA
Answer:
perdón yo no hablo inglés
From a club of 18 people, in how many ways can a group of five members be selected to attend a conference?
I am struggling and I would be so happy if any of you helped me. Can someone help me with the last two red boxes please? The rest of the question is for reference to help solve the problem. Thank you for your time!
Answer:
I think you can go with:
The margin of error is equal to half the width of the entire confidence interval.
so try .74 ± = [ .724 , .756] as the confidence interval
Step-by-step explanation:
Which of the following describes a positive correlation?
As the number of hours spent on homework increases, the tests scores increase.
As the number of apples eaten per year increases, the number of times visiting the doctor every year remains the same.
As the number of times going to bed early increases, the number of times waking up late decreases.
The amount of time a team spent practicing increases, the number of games lost in a season decreases.
THIS IS A MULTIPLE CHOICE QUESTION
Answer:
First Choice: As the number of hours spent on homework increases, the tests scores increase.
Step-by-step explanation:
The definition of a positive correlation is a relationship between two given variables, in which both variables are moving in the same direction. This can mean when one variable increases and the other variable increases, too, or one variable decreases and the other decreases as well.
The first choice is a positive correlation because both variables are changing (increasing) in the same direction. As you spend more time on homework, you're likely to get a higher test score.
The second choice cannot be a positive correlation because only one variable is having some kind of change (increasing). The doctor visits amount remains the same, so we can call this a zero-correlation relationship because the number of apples eaten yearly doesn't affect the amount of doctor visits. An apple a day keeps the doctor a way is just a proverb, not to be taken literally.
The third choice cannot be a positive correlation because the two variables are going different directions. Even though the number of times going to bed early is increasing, the number of times waking up late decreases, which is not moving in the same direction as the other variable.
The fourth choice cannot be a positive correlation because, similarly to the third choice, the two variables are going different directions. One variable is increasing, which is the amount of practice time. Meanwhile, the other variable is decreasing (going in the opposite direction), which is the number of games lost in a season.
When is the Declaration of Independence?
Answer:
July 4th, 1776.
Step-by-step explanation:
By issuing the Declaration of Independence, adopted by the Continental Congress on July 4, 1776, the 13 American colonies severed their political connections to Great Britain. The Declaration summarized the colonists' motivations for seeking independence.
Find the range for the following data 14, 16, 16, 14, 22, 13, 15, 24, 12, 23, 14, 20, 17, 21, 22, 18, 18, 19, 20, 17, 16, 15, 11, 12, 21, 20, 17, 18, 19, 23
Answer:
12
Step-by-step explanation:
Range is the subtraction of the largest number and the smallest number.
The largest number is: 23
The smallest number is: 11
Now subtract:
23 - 11 = 12
Hope this helped.
Answer:
the lowest is 11 and the highest is 24 then subtract it you are going to have 13
If a, b, c are in A.P. show that
a (b + c)/bc,b(c + a) /ca, c(a-b )/bc
are in A.P.
Answer:
Step-by-step explanation:
[tex]\frac{a(b+c)}{bc} ,\frac{b(c+a)}{ca} ,\frac{c(a+b)}{ab} ~are~in~A.P.\\if~\frac{ab+ca}{bc} ,\frac{bc+ab}{ca} ,\frac{ca+bc}{ab} ~are~in~A.P.\\add~1~to~each~term\\if~\frac{ab+ca}{bc} +1,\frac{bc+ab}{ca} +1,\frac{ca+bc}{ab} +1~are~in~A.P.\\if~\frac{ab+ca+bc}{bc} ,\frac{bc+ab+ca}{ca} ,\frac{ca+bc+ab\\}{ab} ~are~in~A.P.\\\\divide~each~by~ab+bc+ca\\if~\frac{1}{bc} ,\frac{1}{ca} ,\frac{1}{ab} ~are ~in~A.P.\\if~\frac{a}{abc} ,\frac{b}{abc} ,\frac{c}{abc} ~are~in~A.P.\\if~a,b,c~are~in~A.P.\\which~is~true.[/tex]
A bag contains 35 marbles, 11 of which are red. A marble is randomly selected from the bag, and it is blue. This blue marble is NOT placed back in the bag. A second marble is randomly drawn from the bag. Find the probability that this second marble is NOT red.
Answer:
11 red + 24 blue = 35 marbles
If 1 blue is withdrawn
11 red + 23 blue = 34 marbles
P = 23 / 34 = .38 probability of drawing blue marble
The Susan B. Anthony dollar has a radius of 0.52 inches. Find the area of one side of the coin to the nearest
hundredth.
Answer:
0.85 in²
Step-by-step explanation:
really ? you need help with that ? you could not find the formula for the area of a circle on the internet and type it into your calculator ? I can't do anything else here.
a circle area is
A = pi×r²
r being the radius.
and pi being, well, pi (3.1415....)
r = 0.52 in
so,
A = pi×0.52² = pi×0.2704 = 0.849486654... in²
the area of one side of the coin is 0.85 in²
help i need help with math help if u can
According to Runzheimer International, a typical business traveler spends an average of $281 per day in Chicago. This cost includes hotel, meals, car rental, and incidentals. A survey of 50 randomly selected business travelers who have been to Chicago on business recently is taken. For the population mean of $281 per day, what is the probability of getting a sample average of more than $268 per day if the population standard deviation is $47?
Answer:
The correct answer is - 97.74%.
Step-by-step explanation:
Given:
sample mean = 281
Std Dev = 47 ==> Sample
Std Dev (s) = std dev/sqrt(n) = 6.0677
Solution:
Find : P( x > 268 )
z = ( x - u )/s = ( 268 - 281 )/6.0677
= -1.9558
then, P( x > 270) = P( Z > -1.9558)
= P( Z <1.9558)
= 0.9747
change into percentage:
= 97.471%
I NEED HELP PLEASE AND THANK YOU!!! ASAP
Answer:
71
Step-by-step explanation:
Initial angle lies in 4th quadrant
a special window in the shape of a rectangle with semicircles at each end is to be constructed so that the outside perimeter is 100 feet. find the dimensions of the rectangle tha tmaximizes the total area of the window
Answer:
The dimensions of the rectangle are length 25 feet and width 15.92 feet
Step-by-step explanation:
Let L be the length of the rectangle and w be the width.
The area of the rectangular part of the shape is Lw while the area of the two semi-circular ends which have a diameter which equals the width of the rectangle is 2 × πw²/8 = πw²/4. The area of each semi-circle is πw²/4 ÷ 2 = πw²/8
So, the area of the shape A = Lw + πw²/4.
The perimeter of the shape, P equals the length of the semi-circular sides plus twice its length. The length of a semi-circular side is πw/2. So, both sides is 2 × πw/2 = πw
P = πw + 2L
Since the perimeter, P = 100 feet, we have
πw + 2L = 100
From this L = (100 - πw)/2
Substituting L into A, we have
A = Lw + πw²/4.
A = [(100 - πw)/2]w + πw²/4.
A = 50w - πw²/2 + πw²/4.
A = 50w - πw²/2
Now differentiating A with respect to w and equating it to zero to find the value of w which maximizes A.
So
dA/dw = d[50w - πw²/2]/dw
dA/dw = 50 - πw
50 - πw = 0
πw = 50
w = 50/π = 15.92 feet
differentiating A twice to get d²A/dw² = - π indicating that w = 50/π is a value at which A is maximum since d²A/dw² < 0.
So, substituting w = 50/π into L, we have
L = (100 - πw)/2
L = 50 - π(50/π)/2
L = 50 - 50/2
L = 50 - 25
L = 25 feet
So, the dimensions of the rectangle are length 25 feet and width 15.92 feet
What is the volume of a cone with a radius of 4 inches and height of 11?
Answer:
184.22
Step-by-step explanation:
What is the probability that z equals 1.5
Answer:
0.1
Step-by-step explanation:
The probability value corresponding to z = 1.5 is 0.9332.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The standard normal curve is a special case of a normal curve with a mean of 0 and a standard deviation of 1. Since it is symmetric around the mean, 50% of the observations lie under the mean while the other 50% of the observations lie above the mean.
Thus the probability value corresponding to z = 1.5 is 0.9332.
Since the total probability value under the curve is 1, we subtract 0.9332 from 1 to calculate the area to the right.
P(Z>1.5)
=P(Z≤1.5)
=1−0.9332
=0.0668
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The mother was fed 21 fish, how many fish was the cub fed?
(d) 320 If the measurement of two angles of a triangle are 72º and 70%, find third ange in degrees. If the measurement of two angles of a triangle are 630 and 100
Please answer in detail
Answer:
y=5x-1 I think because the snd option doesn't make sense but you should try y =5x-1
Write an equation that represents the line.
Use exact numbers.
Answer: y=2/3X- 4/3
Step-by-step explanation:
Slope = (4-2)/(4-1)=2/3
Y-2=2/3(x-1)
Y-2=2/3x-2/3
Y=2/3X-2/3+2
Y=2/3X-4/3
if x¹=xcosA+ysinA and y¹=xsinA-ycosA, show that (x¹)²+(y¹)²=x²+y²
Expanding each square on the left side, you have
(x cos(A) + y sin(A))² = x² cos²(A) + 2xy cos(A) sin(A) + y² sin²(A)
(x sin(A) - y cos(A))² = x² sin²(A) - 2xy sin(A) cos(A) + y² cos²(A)
so that adding them together eliminates the identical middle terms and reduces to the sum to
x² cos²(A) + y² sin²(A) + x² sin²(A) + y² cos²(A)
Collecting terms to factorize gives us
(y² + x²) sin²(A) + (x² + y²) cos²(A)
(x² + y²) (sin²(A) + cos²(A))
and sin²(A) + cos²(A) = 1 for any A, so we end up with
x² + y²
as required.
what's the standard answer for (5×1)+(7×.2)+(2×0.4)
9514 1404 393
Answer:
7.2
Step-by-step explanation:
The order of operations tells you that quantities in parentheses are evaluated first.
(5×1)+(7×.2)+(2×0.4) = 5 + 1.4 + 0.8
Then the addition is performed, left to right.
= 6.4 +0.8
= 7.2
_____
Your calculator can work this problem for you, if necessary.
