What is the equation of the line that passes through (4, 3) and (-4, -1)?
y = 2 x + 7
y = + 1
2 x + 1
y = + 7
Answers
Answer:
Step-by-step explanation:
First find the slope of the line
(4 , 3) ; x₁ = 4 ; y₁ = 3
(-4,-1) ; x₂ = -4 ; y₂ = -1
slope \(= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\)
\(=\frac{-1-3}{-4-4}\\\\=\frac{-4}{-8}\\\\=\frac{1}{2}\)
m = 1/2 , and take any one point (4 , 3)
y -y1 = m(x - x1)
\(y - 3 = \frac{1}{2}(x - 4)\\\\y -3 = \frac{1}{2}x-4*\frac{1}{2}\\\\y - 3 =\frac{1}{2}x - 2\\\\y = \frac{1}{2}x - 2 + 3\\\\y =\frac{1}{2}x + 1\)
Related Questions
a) josie makes fruit punch by mixing fruit juice and lemonade in the ratio 3:4, she needs to make 49 litres of punch for a party. how much of each ingredient does she need (in lires)
b) During the party josie decides tio make some more. she has 15 litres of fruit juce left and plenty of lemonade. how much extra punch can she make? (answer in letres)
c) to make the second batch of punch go further josie adds 4 more lires of lemonade. what is the ratio of fruit juice and lemonade in the second batch? (answer in ratios e.g 5:9)
Answers
Answer:
1. Josie needs 21 litres of fruit juice need 28 litres of lemonade.
2. Josie can make an extra of 35 litres of punch.
3. 5:8
Step-by-step explanation:
a) The ratio of the fruit juice to lemonade = 3:4
Total litres of punch to be made = 49
Amount of fruit juice needed = \(\frac{3}{7}\) x 49
= 21 litres
Amount of lemonade needed = \(\frac{4}{7}\) x 49
= 28 litres
Thus, she would need 21 litres of fruit juice need 28 litres of lemonade.
b) She has 15 litres of fruit juice left. Let the litres of punch to be made be represented by s.
\(\frac{3}{7}\) x s = 15
s = 35
Josie can make an extra of 35 litres of punch.
c) For the second batch, she needs;
15 litres of fruit juice needs 20 litres of lemonade.
But adding 4 more litres to the lemonade makes the total litres of lemonade to be 24.
Thus the ratio of the juice to lemonade = 15:24
= 5:8
1. (10pts) Let A and B be two events such that each occurs with probability greater than zero but less than one. (a) (3pts) Suppose C is a third event which occurs with probability between zero and one. If we know that P(A c
∪C c
∣B)=0.6, and P(A c
∣B)=0.4, what is P(C∣A∩B) ? (b) 1
(7pts) Suppose P(A)=0.7 and P(B)=0.4. Answer the following: i. Are the events A and B mutually exclusive? Justify your answer. ii. Suppose A and B are independent. What is the probability that at least one of the two events occurs? iii. Suppose P(A∣B)=0.8. What is the probability that at least one of the two events occurs?
Answers
(a) P(C∣A∩B) = 0.25
(b) i. No, the events A and B are not mutually exclusive.
ii. The probability that at least one of the two events occurs is 0.82.
iii. The probability that at least one of the two events occurs is 0.92.
To find P(C∣A∩B), we can use the conditional probability formula: P(C∣A∩B) = P(C∩A∩B) / P(A∩B). We are given P(A c∪C c
∣B) = 0.6, which implies that the complement of the union of A and C, given B, occurs with a probability of 0.6. Since A c
∪C c
is the complement of (A∩C), we have P(A∩C∣B) = 1 - 0.6 = 0.4. We are also given P(A c
∣B) = 0.4, which implies that the complement of A, given B, occurs with a probability of 0.4. Therefore, P(A∩C∣B) / P(A∣B) = 0.4, which gives us P(C∣A∩B) = 0.4 / 0.7 = 0.25.
Two events are mutually exclusive if they cannot occur simultaneously. Since the probability of A∩B is not zero, A and B are not mutually exclusive. If A and B are independent events, then P(A∩B) = P(A) × P(B). Given P(A) = 0.7 and P(B) = 0.4, we can calculate P(A∩B) = 0.7 × 0.4 = 0.28. The probability that at least one of the two events occurs can be found using the complement rule: P(A∪B) = 1 - P(A c∩B c
). Since A and B are not mutually exclusive, P(A c
∩B c
) = P(A c
) × P(B c
) = (1 - P(A)) × (1 - P(B)) = 0.3 × 0.6 = 0.18. Therefore, P(A∪B) = 1 - 0.18 = 0.82.
Given P(A∣B) = 0.8, we can use Bayes' theorem to find the probability that at least one of the two events occurs. P(A∣B) = P(A∩B) / P(B), which implies P(A∩B) = P(A∣B) × P(B) = 0.8 × 0.4 = 0.32. Using the complement rule, we can find P(A∪B) = 1 - P(A c∩B c
) = 1 - (1 - P(A∪B)) = P(A∪B). Therefore, the probability that at least one of the two events occurs is 0.32.
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show that the dimensions of the largest area rectangle that can be inscribed into a circle of radius 4 is a square. then, show that this is true for any radius r.
Answers
Rectangle ABCD is a square.
Relation between rectangle and square?
Squares and rectangles each have four straight sides. However, a square's and a rectangle's mathematical characteristics are very dissimilar. For instance, a common distinction is that squares have equal sides on each side, whereas only the opposite sides of a rectangle are equal.
Radius of circle R = 4cm
let sides of rectangle is a,b
let rectangle be ABCD in which AB =CD= a , AC=BD=b
ACD is right angled triangle on C.
Then,
\(AD^{2} =AC^{2} +CD^{2} \\\\8^{2} =b^{2} +a^{2} \\\\64=b^{2} +a^{2} \\\\b^{2} =\sqrt{64-a^{2} }\)------(1)
Area of rectangle = Area of ΔACD + ΔABD
= \(\frac{1}{2} \times a\times b + \frac{1}{2} \times a\times b\)
Area of rectangle = a×b
by eqn (1)
Area = \(a\times (\sqrt{64-a^{2} } )\)
For maximum area
\(\frac{dA}{da} =0\\\\a \times \frac{1}{\sqrt{64-a^{2} } } (-a)+(\sqrt{64-a^{2} } )\times(1)=0\)
\(\sqrt{64-a^2} -\frac{a^2}{\sqrt{64-a^2} } =0\\\\\frac{64-a^2-a^2}{\sqrt{64-a^2} } =0\\\\64-2a^2=0\\\\a^2=32\\\\a=\sqrt{32} \\\\In (1) eqn\\b=\sqrt{64-a^2} \\\\b=\sqrt{64-32} \\\\b=32\)
So, a=b
Means Rectangle ABCD is a square.
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Ava and her three friends went out for lunch. Their total bill was $96. If each person paid the same amount, how much would each person pay?
$______
Answers
Answer:
$24
Step-by-step explanation:
Ava + her 3 friends = 4 people total.
The bill was $96
To split this evenly among 4 people we can divide the bill by 4.
96/4 = 24
Therefore each person would pay $24.
Hope this helps! :)
HELP! offering 75 points
Answers
Answer: C
Step-by-step explanation:
hope this helped
sec(pi/2 -x) =csc x true or false
Answers
Answer:
true
Step-by-step explanation:
if you rewrite \(sec\left(\frac{\pi }{2}\:-x\right)\) with trigonometric identities:
\(sec\left(\frac{\pi }{2}\:-x\right)\) \(=\frac{1}{\sin \left(x\right)}\)
\(\frac{1}{\sin \left(x\right)}\) \(=\csc \left(x\right)\)
so, yes, \(sec\left(\frac{\pi }{2}\:-x\right)\) \(=\csc \left(x\right)\)
hope this helps!!
What is pooled mean standard error?
Answers
The pooled mean standard error is a measure of the variability associated with the difference between two group means in a statistical hypothesis test with equal variances.
The pooled mean standard error is a measure of the variability or uncertainty associated with the difference between two group means in a statistical hypothesis test, where the two groups have equal variances. Specifically, it is the standard error of the difference between the means of two independent samples, calculated by combining the standard errors of the two sample means into a single estimate.
The formula for the pooled mean standard error is:
SEp = \(\sqrt{ [ (s1^2/n1) + (s2^2/n2) ]}\)
where SEp is the pooled mean standard error, s1 and s2 are the standard deviations of the two samples, n1 and n2 are the sample sizes, and sqrt represents the square root function.
The pooled mean standard error is used in the calculation of the t-statistic in a two-sample t-test, which is used to test the hypothesis that there is a significant difference between the means of the two groups. By accounting for the variability of both groups, the pooled mean standard error provides a more accurate estimate of the standard error of the difference between the means, which in turn allows for more precise hypothesis testing.
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It is asking what is the measure of the inscribled angle JHI
Answers
Answer:
45 degrees
Step-by-step explanation:
central angle = the arc
inscribed angle = 1/2 the arc
If
x and
y vary directly and
y is 48 when
x is 6, find
y when
x is 12.
Answers
Answer:
y is 96 when x is 12
Step-by-step explanation:
If x and y vary directly, it means that they are proportional to each other. Mathematically, we can write this relationship as:
y = kx
where k is the constant of proportionality.To find the value of k, we can use the information given in the problem. We know that when x is 6, y is 48. Substituting these values in the equation above, we get:
48 = k * 6
Solving for k, we get:k = 8
Now that we know the value of k, we can use the equation to find y when x is 12:
y = kx
y = 8 * 12
y = 96
Therefore, when x is 12, y is 96.
also in my head I just said if 12 is double of 6, just double 48, which is 96. but that doesn’t always work so that’s why I provided “correct” work above
Pablo drove 715 miles in 11 hours.
At the same rate, how many miles would he drive in 9 hours?
Answers
Answer:
585 miles
Step-by-step explanation:
divide 715 by 11 so that you can see the mph (miles per hour). Then multiply that number by 9 for the amount of miles he would travel in nine hours
715/11=65
65x9=585
why might we not be able to build a regression model to predict a dependent variable? group of answer choices we might not know the independent variables. there might not be any data available for the independent variables. the regression model might not fit the data well. all of these are true.
Answers
There are several reasons why we might not be able to build a regression model to predict a dependent variable. These reasons include:
1. Unknown independent variables: If we do not know the independent variables that have a significant impact on the dependent variable, it would be challenging to build an accurate model. Identifying relevant independent variables is crucial for creating a robust regression model.
2. Lack of data for independent variables: Even if we know the relevant independent variables, we might not have enough data for them. Regression models require sufficient data to estimate the relationship between the dependent variable and independent variables accurately. Without enough data, the model may be unreliable or may not provide meaningful results.
3. Poor model fit: Sometimes, a regression model might not fit the data well due to the nature of the relationship between the dependent and independent variables. This could occur if the relationship is non-linear, or if there are other factors influencing the dependent variable that we have not considered in the model. In these cases, alternative modeling techniques may be more appropriate.
In summary, all of these reasons - unknown independent variables, lack of data for independent variables, and poor model fit - can contribute to the inability to build a suitable regression model to predict a dependent variable.
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What is the best first step to take in solving the equation
x2+11x+24/ x2+3x =0
Answers
x=root[3]{-1.500}=-1.14471
Use the theoretical method to determine the probability of the outcome or event given below. The next president of the United States was born on Sunday or Tuesday. The probability of the given event is ______? ( Type an integer of a simplified fraction)
Answers
The probability of the next president of the United States being born on Sunday or Tuesday can be determined by considering the total number of days in a week and the assumption that each day of the week is equally likely. The probability is 2/7.
In a week, there are seven days. Assuming that each day of the week is equally likely to be the day of birth for the next president, we need to determine the number of favorable outcomes (birthdays on Sunday or Tuesday) and divide it by the total number of possible outcomes (seven days).Out of the seven days of the week, Sunday and Tuesday are the two days that satisfy the condition. Therefore, the number of favorable outcomes is 2.
Hence, the probability of the next president being born on Sunday or Tuesday is given by 2/7, where 2 represents the number of favorable outcomes (birthdays on Sunday or Tuesday) and 7 represents the total number of possible outcomes (seven days of the week).
Therefore, the probability of the given event is 2/7.
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please help for both of these questions! its due soon! i'll mark brainlist
Answers
X=-9 or X=10
First you factor the left side of the question
(X+9)(X-10)=0 then u set factors equal to zero
X+9=0 or x -10=0
X=-9 or X=10
Now for question two is the second bubble of answer
help asap pls pls pls
Answers
Answer:
the answer is 13, all you had to do was substitute 5 for N, so all you had to do was 3 + 2(5) which is 13
Determine K such that 2/3, k, 5/8,K are consecutive terms of an ap
Answers
Answer:
k = 16/33
Step-by-step explanation:
Determine k so that 2/3,k and 5/8k are the three consecutive terms of an a.p
k - 2/3 = 5/8k - k
3k-2/3 = 5k-8k/8
Cross product
(3k-2)(8) = (3)(5k-8k)
24k - 16 = 15k - 24k
24k - 16 = -9k
24k + 9k = 16
33k = 16
k = 16/33
Mean Time Between Failures (MTBF), Mean Time To Replacement (MTTR), and Mean Time To Failure (MTTF) are useful metrics for evaluating the reliability and availability of a storage resource. Explore these concepts by answering the questions about devices with the following metrics. Given: MTTF = 3 years, MTTR = 1 day (a) Calculate (i) MTBF and (ii) availability. (b) What happens to availability as the MTTR approaches 0? Is this a realistic situation? (c) What happens to availability as the MTTR gets very high, i.e., a device is difficult to repair? Does this imply the device has low availability?
Answers
MTTF = 3 years * 365 days/year * 24 hours/day = 26,280 hours, MTTR = 1 day * 24 hours/day = 24 hours.As MTTR approaches 0, the availability will increase, approaching 100%. If the MTTR gets very high, it means that the device is difficult to repair, and the availability will decrease.
To calculate MTBF and availability for a storage resource with an MTTF of 3 years and an MTTR of 1 day, we will follow these steps:
Step 1: Convert MTTF and MTTR to the same unit of measurement. In this case, we will convert both to hours.
MTTF = 3 years * 365 days/year * 24 hours/day = 26,280 hours
MTTR = 1 day * 24 hours/day = 24 hours
Step 2: Calculate MTBF using the formula: MTBF = MTTF + MTTR
MTBF = 26,280 hours + 24 hours = 26,304 hours
Step 3: Calculate availability using the formula: Availability = MTTF / (MTTF + MTTR)
Availability = 26,280 hours / (26,280 hours + 24 hours) = 26,280 / 26,304 ≈ 0.9991, or approximately 99.91%.
As MTTR approaches 0, the availability will increase, approaching 100%. However, this is not a realistic situation, as repair and replacement times can never truly be zero in the real world. There will always be some amount of time required to repair or replace a device.
If the MTTR gets very high, it means that the device is difficult to repair, and the availability will decrease. This implies that the device has low availability, as the time to repair or replace the device is a significant factor in determining its overall reliability and availability. A device with a high MTTR is less desirable because it will be unavailable for extended periods when it does fail, negatively impacting the system it is a part of.
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Instructions: given the following coordinates complete the reflection transformation.
a(-5,2)
b(-1,5)
c(0,3)
transformation: complete the double reflection over the lines x = 1 followed by x = 3.
a"
b"
c"
Answers
To complete the double reflection transformation over the lines x = 1 and x = 3, we need to reflect each point twice.
For point a(-5,2), the first reflection over x = 1 will give us a'(-9,2).
The second reflection over x = 3 will give us a"(-7,2).
For point b(-1,5), the first reflection over x = 1 will give us b'(-3,5).
The second reflection over x = 3 will give us b"(-5,5).
For point c(0,3), the first reflection over x = 1 will give us c'(2,3).
The second reflection over x = 3 will give us c"(4,3).
So, the coordinates after the double reflection transformation are:
a"(-7,2), b"(-5,5), and c"(4,3).
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What is the value of x?
Answers
Answer:
62 is the answer to your question
one quick way to know the answer is to know that the two opposite interior angles has to add up to the outer external angle, so x + 38 = 100
Answer:
B. 62°
Step-by-step explanation:
First, solve the unknown interior angle. Interior angles and exterior angles add up to 180°.
? + 100 = 180
? = 80
The sum of the angles of a triangle is 180°. Form and solve the following equation.
x + 80 + 38 = 180
x + 118 = 180
x = 62
Triangle MNP is congruent to triangle SQR. If measure S = (3x+5), measure N = (4x-6), measure R = (2x+1), and measure Q = (94-x), find the value of x.
Answers
For the given question value of x will be 20
Congruent triangle:
If two triangle are congruent then all the corresponding sides and corresponding angles ill be equal. Symbol for congruent is ≅.Congruent triangles are also known as identical triangle.
For example,
if ΔMNP and ΔSQR are congruent,
that is,
if ΔMNP ≅ ΔSQR
then,
∠M = ∠S
∠N = ∠Q
∠P = ∠R
and ,
MN = SQ , NP = QR , MP = SR
According to question,
∠S = (3x+5)°
∠N = (4x-6)°
∠R = (2x+1)°
∠Q = (94-x)°
As,
ΔMNP ≅ ΔSQR
so,
∠N = ∠Q
(4x-6)° = (94-x)°
4x + x = 94 + 6
5x = 100
x = 100/5
x = 20
Hence, for the given congruent triangle ΔMNP and ΔSQR value of x will be 20.
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2
614
eft
3.
9m
Please help
Answers
2.
\( area=\frac{1}{2} \times 6 \times 8 \\ = 24 \)
3.
\(area = \pi \times 9m \\ = 3.14 \times 9 \\ = 28.26 {m}^{2} \)
Fine the slope of the line in simplest form.
A. m= -2/1
B. m= 1/2
C. m= 4/2
D. m= 2/1
Answers
BRIDGES The lower arch of the Sydney Harbor Bridge can be modeled by g(x) = - 0.0018 * (x - 251.5) ^ 2 + 118 where in the distance from one base of the arch and g(x) is the height of the arch. Select all of the transformations that occur in g(x) as it relates to the graph of f(x) = x ^ 2
Answers
The transformations to the graph of the quadratic function are given as follows:
The graph stretches vertically because of the multiplication by 3.The graph is translated left because x -> x + 7.The graph is translated down because y -> y - 6.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.Additionally, when the function is multiplied by |a| > 1, it is said that the function is vertically stretched by a factor of a.
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Help help help help help please please please
Answers
Answer:
49°
Step-by-step explanation:
Line ED is 180°, so you can subtract 180 - 67 to find the value of ∠ACB, which is 113°. Since the angles of a triangle will always add up to 180°, you just need to subtract 180 - 18 - 113. This will get you 49°.
The porosity of soil is 0.32. Given that Gs=2.60. Calculate the following, when the soil has a unit weight of 19.00kN/m 3
, Water Content (Round your answer to two decimal places)
Answers
The water content of the soil is approximately 0.23 is the answer.
To calculate the water content of the soil, we need to use the formula:
Water Content (WC) = (Gs × Porosity) / (1 + Gs)
Given:
Porosity = 0.32
Gs = 2.60
Unit weight of soil (γ) = 19.00 kN/m³
Substituting the values into the formula:
Water Content (WC) = (2.60 × 0.32) / (1 + 2.60)
Water Content (WC) = 0.832 / 3.60
Water Content (WC) ≈ 0.2311
Rounding the water content to two decimal places, we get:
Water Content (WC) ≈ 0.23
Therefore, the water content of the soil is approximately 0.23
Porosity is a measure of the void or empty spaces within a material, specifically in the context of soil or rock. It shows the ratio of the volume of voids (pores) to the total volume of the material. Porosity can expressed as a percentage or a decimal fraction between 0 and 1.
In the case of soil, porosity refers to the amount of space between the solid particles that can be occupied by air or water. It is an essential property that influences the soil's ability to hold and transmit fluids, such as water and air. Soils with high porosity generally have more pore spaces, allowing for greater water infiltration, storage, and drainage.
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What does the symbol "⊄" represent?
A) is not a member of
B) null set
C) is not a subset of
D) infinite set
Answers
(2x³y + 5)(2x³y - 5)
Answers
Answer: 4x^6-25
Step-by-step explanation:
1. Distribute
(2x^3+5)(2x^3−5)
2(2^3+5)x^3+5(2x^3-5)
2. Distribute
2(2x^3-5)x^3+5(2x^3-5)
4x^6-10x^3+5(2x^3-5)
3. Distribute
4x^6-10x^3+5(2x^3-5)
4x^6-10x^3+10x^3-25
4. Combine like terms
4x^6-10x^3+10x^3-25
4x^6-25
what is tcreefp seaqur unscrambled
Answers
Answer:
perfect square
Step-by-step explanation:
hope this helps plz give brainliest.
draw a graph of the rose curve
Answers
Looking through the options, the answer is option D.
find the common factor and least first 3 possible multitiple of each number using any of the method 25and 75
35and 45
21and 56
54and 72
27and 36
12and 16
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The greatest common factor (divisor) is found in the GCD column of the attached spreadsheet. The GCD is calculated using the spreadsheet function. The least common multiple (LCM) is the product of the numbers, divided by their GCD.
Other multiples shown are 2 times, 3 times, and 4 times the least common multiple.
