Answer:
We conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.
Step-by-step explanation:
We are given that slab avalanches studied in a region of Canada had an average thickness of μ = 66 cm.
A random sample of avalanches in spring gave the following thicknesses (in cm);
X: 59, 51, 76, 38, 65, 54, 49, 62, 68, 55, 64, 67, 63, 74, 65, 79.
Let [tex]\mu[/tex] = true mean slab thickness in the Vail region
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 66 cm {means that the mean slab thickness in the Vail region is the same as that in the region of Canada}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 66 cm {means that the mean slab thickness in the Vail region is different from that in the region of Canada}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean thickness = [tex]\frac{\sum X}{n}[/tex] = 61.81 cm
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 10.64
n = sample of avalanches = 16
So, the test statistics = [tex]\frac{61.81-66}{\frac{10.64}{\sqrt{16} } }[/tex] ~ [tex]t_1_5[/tex]
= -1.575
The value of t-test statistics is -1.575.
Now, at a 1% level of significance, the t table gives a critical value of -2.947 and 2.947 at 15 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.
How does a reflection across the y-axis change the coordinates of a shape?
Answer:
When you reflect a shape avross the y-axis, the y-coordinates stay the same, but the x-coordinates turn into its opposites.
Step-by-step explanation:
EXAMPLES:
(3,6)---(reflected over y-axis)--> (-3,6)
(9,2)---(reflected over y-axis)--> (-9,2)
Hope this helped! Brainliest would be really appreciated :)
The graph of a function is shown:
In which interval is the graph decreasing?
Answers:
A - AB
B - BC
C - CD
D - DE
Answer:
Maybe D-DE
Step-by-step explanation:
Because D has been decrease to E
Find The measure of the unknown angle.
1. Add the two known angles:___+___=___
2. Subtract the sum from 180°: 180-___=___
3. The measure of the unknown angle is:____
Answer:
L = 45°
Step-by-step explanation:
1. 82° + 53° = 135°
2. 180° - 135° = 45°
3. Angle L is 45°
I hope this helps.
Find factors of x³-7x-6 A. (x-4)(x-2)(x+1) B. (x-6)(x-1)(x+1) C. (x-3)(x+2)(x+1) D. (x+3)(x+2)(x-1)
Answer:
C. (x-3)(x+2)(x+1)
Step-by-step explanation:
We can use the rational roots test to help factor out the original equation.
The leading term is 1 and the constant is 6
p/q= 6/1
Now we find factors (all these are plus and minus)
1,2,3,6
1
We find the common ones (+1 and -1) and use -1 because it ends up being the root of the function
Factor, (x+1)
Now we have (x+1)(x^2-x-6)
Factor this with whatever method you perfer, I use AC method
Find two that are a product of -6 and add to -1 (-3 and 2)
We get (x+1)(x-3)(x+2)
C
Answer:
[tex]\boxed{C}[/tex]
Step-by-step explanation:
Let's solve all of the option and see which equals x³-7x-6
Option A)
[tex](x-4)(x-2)(x+1)[/tex]
=> [tex](x^2-6x+8)(x+1)[/tex]
=> [tex]x^3+x^2-6x^2-6x+8x+1\\x^3-5x^2+2x+1[/tex]
So, A is not correct
Option B)
[tex](x-6)(x-1)(x+1)\\(x+6)(x^2-1)\\x^3-x+6x^2-6\\x^2+6x^2-x-6[/tex]
This is also not correct
Option C) ← Correct
[tex](x-3)(x+2)(x+1)\\(x^2-x-6)(x+1)\\x^3+x^2-x^2-x-6x-6\\x^3-7x-6[/tex]
This equals to x³-7x-6, So, this is the correct option. No need to do Option D since we have the right option now!
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 6 days. 72% of all of these types of trials are completed within how many days
Answer:
25.5 days
Step-by-step explanation:
Mean number of days (μ) = 22 days
Standard deviation (σ) = 6 days
Z-score for the 72nd percentile (according to tabulated values) = 0.583
The z-score for any number of days, X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
The value of X that is greater than 72% of the trial times is:
[tex]0.583=\frac{X-22}{6}\\ X=25.5\ days[/tex]
Therefore, 72% of all of these types of trials are completed within 25.5 days.
A group of students were asked to choose their favorite course. The results are shown in the two-way frequency table. Which of the following can be concluded from the joint and marginal frequencies of the table? Math is the most popular subject in the 10th grade. History is the least popular subject in the 9th grade. Science is more popular than math among 12th grade students. Students in the 11th grade like English more than students in the 12th grade. The overall favorite course is history.
A.) III and IV only
B.) II and V only
C.) I, III, and V
D.) II and IV only
The answer is C.) I, III, and V
The statement 1, 2, and 5 will be correct hence option (C) will be correct.
What is a frequency table?A frequency table is a list of objects with the frequency of each item shown in the table.
In other words, a frequency table is a table in which we have some data and their frequency.
The frequency of an occurrence or a value is the number of times it happens.
In option (C)
1st statement;
Math is the most popular subject in the 10th grade.
In 10th grade, maths is 104 rest are less so it is correct.
3rd statement;
Science is more popular than math among 12th-grade students.
The number of science lovers in the 12th is 78
The number of maths lovers in 12th is 52
So it is also correct.
5th statement;
Overall favorite course is history.
A number of overall favorite courses is history = 403 which is higher than others hence it is also correct.
So option (C) is correct rest are incorrect.
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These two polygons are similar.
Find the value of z.
z = [?]
Answer:
Definitely 3 hmmm..
Step-by-step explanation:
6/2=3 so 9/z=3
tfo 9/3=3
The missing variables have values of 12, 5, 9, and 3, respectively, for x, y, w and z.
Given that there are two similar polygons with dimension:
Larger polygon = 9, 6, w, 15, x.
Smaller polygon = z, 2, 3, y, 4.
We need to find the missing value of the side length.
According to the definition of the similar polygons, the corresponding sides shows proportionality.
9/z = 6/2 = w/3 = 15/y = x/4
Solving for each variable =
i) Solve for z:
9/z = 6/2
Cross-multiplying:
6z = 9 × 2
6z = 18
Dividing both sides by 6:
z = 18/6
z = 3
ii) Solve for w:
6/2 = w/3
Cross-multiplying:
2w = 6 × 3
2w = 18
Dividing both sides by 2:
w = 18/2
w = 9
iii) Solve for y:
6/2 = 15/y
Cross-multiplying:
6y = 30
Dividing both sides by 6:
y = 5
iv) Solve for x:
6/2 = x/4
Cross-multiplying:
2x = 24
Dividing both sides by 2:
x = 12
Hence the values of the missing variables are x = 12, y = 5, w = 9 and z = 3.
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Help with 18 - 22
18 4 x 1 =
— —
7 2
A. 8
—
7
B. 4
—
14
C. 28
—
2
19. 15 X 2 =
— —
2 20
A. 4
—
300
B. 30
—
40
C. 30
—
4
20. 3 x 7 =
— —
6 8
A. 18
—
56
B. 24
—
42
C. 21
—
48
21. 9 x 1 =
— —
10 2
A. 9
—
20
B. 18
—
10
C. 8
—
18
22. 3 x 2 =
— —
6 4
A. 6
—
24
B. 18
—
8
C. 8
—
18
Answer:
18. b. 4/14
19. b. 30/40
20. c. 21/48
21. a. 9/20
22. a. 6/24
Step-by-step explanation:
So in these questions all we do is multiply the fractions.
18)
[tex]\frac{4}{7} * \frac{1}{2}[/tex]
4*1 = 4
7*2 = 14
b. 4/14
19)
[tex]\frac{15}{2}*\frac{2}{20}[/tex]
15*2 = 30
2*20 = 40
b. 30/40
20)
[tex]\frac{3}{6}*\frac{7}{8}[/tex]
3*7 = 21
6*8 = 48
c. 21/48
21)
[tex]\frac{9}{10}*\frac{1}{2}[/tex]
9*1 = 9
10*2 = 20
a. 9/20
22)
[tex]\frac{3}{6}*\frac{2}{4}[/tex]
3*2 = 6
6*4=24
a. 6/24
Hope this helps :)
Help me fast please
give the coordinates of the
foci,vertices,and convertices of the ellipse with equation x²/169 + y²/25 = 1
Answer:
We can see that for this case the vertex is [tex] V= (0,0)[/tex]
The values for a and b are:
[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]
Then the ellipse have the major axis on x.
In order to find the two foci we need to use the following formula:
[tex] c =\sqrt{a^2 -b^2}[/tex]
And replacing we got:
[tex] c =\sqrt{169-25}= \pm 12[/tex]
And then the two foci are (12,0) and (-12,0)
And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis
Step-by-step explanation:
For this problem we have the following equation given:
[tex]\frac{x^2}{169} + \frac{y^2}{25}= 1[/tex]
If we compare this with the general expression of an ellipse given by:
[tex] \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}= 1[/tex]
We can see that for this case the vertex is [tex] V= (0,0)[/tex]
The values for a and b are:
[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]
Then the ellipse have the major axis on x.
In order to find the two foci we need to use the following formula:
[tex] c =\sqrt{a^2 -b^2}[/tex]
And replacing we got:
[tex] c =\sqrt{169-25}= \pm 12[/tex]
And then the two foci are (12,0) and (-12,0)
And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis
Simplify the expression:
1 – 5b + – b + – 8b – 2b
Answer:
The answer is 1 - 16b.
Step-by-step explanation:
You have to collect like-terms :
[tex]1 - 5b - b - 8b - 2b[/tex]
[tex] = 1 + b( - 5 - 1 - 8 - 2)[/tex]
[tex] = 1 + b( - 16)[/tex]
[tex] = 1 - 16b[/tex]
Answer:
The answer is
1 - 16bStep-by-step explanation:
1 – 5b + – b + – 8b – 2b can be written as
1 - 5b - b- 8b - 2b
Subtract the like terms
That's
We have the final answer as
1 - 16b
Hope this helps you
The amount of time (t) in minutes it takes to make a coffee at Starbucks is related to (n) the number of coffees they purchase. The equation is t =2n-3. How long does it take if a customer buys 5 coffees ?
Answer:
7 minutesStep-by-step explanation:
Given the expression for time
[tex]t =2n-3[/tex]
say a customer buys 5 coffees, hence n=5
substituting n=5 into the function time it takes to prepare a coffee we have the time it will take to prepare 5 coffees
[tex]t= 2(5)-3\\t=10-3\\t=7[/tex]
Hence it will take 7 minutes to prepare 5 coffees
The length of a rectangle is six times its width. The area of the
rectangle is 294 square centimeters. Find the dimensions of the
rectangle.
Answer:
length= 42
width = 7
Step-by-step explanation:
Select the correct answer. Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing diameters of the circle. He labels the ends the diameters A, B, C, D, E, and F, and he uses a straightedge to draw the chords that form a hexagon. Which statement is true? A. Vincent’s construction method produces a hexagon that must be regular. B. Vincent’s construction method produces a hexagon that must be equilateral but may not be equiangular. C. Vincent’s construction method produces a hexagon that must be equiangular but may not be equilateral. D. Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.
Answer:
B.
Step-by-step explanation:
Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular. The correct option is D.
What is a regular polygon?A regular polygon is a polygon that is equiangular and equilateral. Therefore, the measure of all the internal angles and the measure of all the sides of the polygon are equal to each other.
Given that Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing the diameters of the circle.
Now as it can be seen as the paper is folded as shown in the below image but it does not create a hexagon that is equilateral and equiangular.
Hence, Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.
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Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for
itself since the time it takes to produce the product using the new machine is significantly less than the
production time using the old machine. To test the claim, independent random samples were taken from
both machines. You are given the following results.
New Machine Old Machine
Sample Mean 25 23
Sample Variance 27 7.56
Sample Size 45 36
As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain your
Answer:
Step-by-step explanation:
We will develop a test to compare the mean of two population
Population 1.
population mean μ₀₁ = 25 ; Sample variance 27 ; and sample size n = 45
Population 2.
population mean μ₀₂ = 23 ; Sample variance 7,56; and sample size n = 36
As our major interest is to investigate if the new machine uses less time for the same production, the test will be a one tail test ( left test)
Test Hypothesis
Null Hypothesis H₀ ⇒ μ₀₂ - μ₀₁ = 0
Alternative Hypothesis Hₐ ⇒ μ₀₂ - μ₀₁ < 0
We will use confidence of 90 %, therefore α = 10 % α = 0,1
α = 0,1
We get z score of z = 1,28 or z = - 1,28 ( left tail)
And compute z(s) = ( μ₀₂ - μ₀₁ ) /√ (s₁)²/n₁ + (s₂)²/n₂
z(s) = - 2 / √(729/45) + (57,15/36)
z(s) = - 2 / √16,2 + 1,59
z(s) = - 2 / 4,2178
z(s) = - 0,4742
As |z(s)| < |z(c)|
We are in the acceptance region. If we lok at 90 % as Confidencial Interval α = 0,1 and α/2 = 0,05 in this case
₀,₉CI ( μ₀₂ - μ₀₁) = [ -2 ± z(0,05)√ (s₁)²/n₁ + (s₂)²/n₂ )
From z Table z ( 0,05 ) ⇒ z score z = 1,64
And √ (s₁)²/n₁ + (s₂)²/n₂ ) = √(729/45) + (57,15/36) = 4,2178
₀,₉CI ( μ₀₂ - μ₀₁) = [ -2 ± 1,64 *4,2178]
₀,₉CI ( μ₀₂ - μ₀₁) = ( - 8,917 ; 4,917 )
We can see that 0 is a possible value in the ₀,₉CI ( μ₀₂ - μ₀₁) so again we cannot reject H₀. Then as we are not quite sure about the strengths of the new machine over the old one we should not recomend to purchase the new machine
What value of x is I the solution set of 3(x-4)>5x+2
Answer:
-7 > x
Step-by-step explanation:
3(x-4)>5x+2
Distribute
3x-12>5x+2
Subtract 3x from each side
3x-12-3x>5x-3x+2
-12 > 2x+2
Subtract 2 from each side
-12-2>2x+2-2
-14 > 2x
Divide by 2
-14/2 > 2x/2
-7 > x
Answer:
[tex]\boxed{x<-7}[/tex]
Step-by-step explanation:
3(x-4)>5x+2
Expand brackets.
3x - 12 > 5x+2
Subtract 3x and 2 on both sides.
-12 - 2 > 5x - 3x
-14 > 2x
Divide both sides by 2.
-7 > x
Switch sides.
x < -7
Determine whether each red path in the vector field is positive, negative, or zero
If the path is perpendicular to the field it is zero.
If the path is along the field it is positive or negative depending on it's direction.
See the attached picture.
solve the nonlinear system of equations. State the number of solutions.
Answer:
Step-by-step explanation:
Hello,
Question 15
We can search x such that:
[tex]x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }[/tex]
There is 1 solution.
Question 16
Again, we search x such that:
[tex]x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }[/tex]There are two solutions.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Simplify (4x)². Rewrite the expression in the form k ⋅ xⁿ
Answer:
16x²
Step-by-step explanation:
(4x)²4² *x²16*x² 16x²Dan's mean average on 5 exams is 86 determine the sum of his score
Answer: 430
Step-by-step explanation:
An average of 5 scores can be found via: (the sum of the scores)*5. Thus, simply multiply 86*5 to get that the sum of his scores is 430
Hope it helps <3
please answer me question 3 solving part
Answer:
1. D
2. B
3. A
Step-by-step explanation:
Question 1:
The pair of <JKL and <LKM can be referred to as linear pairs. They are two adjacent angles that are formed from the intersecting of two lines.
Question 2:
Given that <KLM = x°
<KML = 50°
<JKL = (2x - 15)°
According to the exterior angle theorem, exterior ∠ JKL = <KLM + KML.
2x - 15 = x + 50
Solve for x
2x - x = 15 + 50
x = 65
Therefore, <KLM = 65°
QUESTION 3:
<JKL = 2x - 15
Plug in the value of x
<JKL = 2(65) - 15
= 130 - 15
<JKL = 115°
In an ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even. (Round your answer to four decimal places.) (a) What is the probability that a subject would guess exactly 18 correct in a series of 36 trials
Answer: The answer is 0.1350
Step-by-step explanation:
Given data
n=36
p=1/2
q=1/2
X=18
O=3
U = 18
a. With n = 36 and p = q = 1/2, you may use the normal approximation with µ = 18 and o = 3. X = 18 has real limits of 17.5 and 18.5 corresponding to z = -0.17 and z = +0.17. p = 0.1350.
The probability that a subject would guess exactly 18 correct in a series of 36 trials is 0.1350.
Given that,
ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even.
We have to determine,
What is the probability that a subject would guess exactly 18 correct in a series of 36 trials?
According to the question,
Number of trials n = 36
The probability must per whether a number randomly generated by a computer will be odd is 1/2 or even is 1/2.
By using the normal approximation,
[tex]\mu = 18 \ and \ \sigma = 3[/tex]
Therefore,
X = 18 has real limits of 17.5 and 18.5 corresponding to z = -0.17 and z = +0.17.
p = 0.1350
Hence, the probability that a subject would guess exactly 18 correct in a series of 36 trials is 0.1350.
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ASAP!!! NEED HELP!!!! Max is stacking logs at his campground for firewood. After his first load of logs, he has 8 logs on the stack. After his seventh load of logs, he has 62 logs on the stack. Use sequence notation to represent the arithmetic function. ANSWER CHOICES: A. an = 8 + 6(n − 1) B. an = 62 + 6(n − 1) C. an = 8 + 9(n − 1) D. an = 62 + 9(n − 1)
Answer: Choice C. an = 8 + 9(n-1)
===========================================
Work Shown:
a1 = 8 is the first term
a7 = 62 is the seventh term
an = a1+d(n-1) = nth term of arithmetic sequence
a7 = a1+d(7-1) ... plug in n = 7; solve for d
62 = 8+d(6)
62 = 6d+8
6d+8 = 62
6d = 62-8
6d = 54
d = 54/6
d = 9 is the common difference
an = a1 + d(n-1)
an = 8 + 9(n-1) is the nth term of this arithmetic sequence
Answer:
Choice C. an = 8 + 9(n-1)
Step-by-step explanation:
I just took the test
Translate the phrase into a variable expression. Use the letter sto name the
variable. If necessary, use the asterisk (*) for multiplication and the slash
(1) for division.
the product of 60 and the number of seconds...
Answer:
The statement
the product of 60 and the number of seconds is written as
60 * s
Hope this helps you
Please help me!! Need help with geometry! Thank you so much!!
Answer:
b
Step-by-step explanation:
A, b, c, and d are all points. the line segements are: ab, bc, cd, da, and ac
Shawna spent half of her weekly allowance playing arcade games. To earn more money her parents let her clean the windows in the house for $4.37. What is her weekly allowance if she ended with $11.18?
Answer:
$13.62
Step-by-step explanation:
By working backward we can see that before she cleaned the windows she had $6.81.
We know that she spent half her allowance on the arcade and the $6.81 she had before cleaning the windows is the other half.
So, if you multiply by 2 you get that here weekly allowance is $13.62.
Answer:
$13.62
Step-by-step explanation:there
One variable in a study measures how many serious motor vehicle accidents a subject has had in the past year. Explain why the mean would likely be more useful than the median for summarizing the responses of the 60 subjects.
Answer:
The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5 or greater or much lesser than the average. It would not give an approximate value of occurrences.
Step-by-step explanation:
Mean is the averaage of all the values.
Median is the value of the data which gives an estimate of the middle value. Middle values can be different than the average values.
The mean is
1) rigorously defined by a mathematical formula.
2) based on all the observations of the data
3) affected by extreme values
The meadian is
1) computed for open end classes like income etc.
2) not rigorously defined
3) is located when the values are not capable of quantitative measurment.
4) is not affected by extreme values.
The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5 or greater or much lesser than the average. It would not give an approximate value of occurrences.
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green and 2 red marbles. Find probability that both marbles are white. Round to nearest thousandth
Find the solution(s) of the quadratic equation 2x2 – 3x – 35 = 0
Answer: x = 5, x = -7/2
Step-by-step explanation:
2x² - 3x - 35 = 0
Step 1: Find two values whose product = 2(-35) and sum = -3: -10 & 7
Step 2: Replace the b-value of -3x with -10x + 7x:
2x² - 10x + 7x - 35 = 0
Step 3: Factor the first two terms and the second two terms:
2x(x - 5) +7(x - 5) = 0
Step 4: Write the factored form:
Notice that the parenthesis are identical. This is one of the factors. The outside values are the other factor:
Parenthesis: (x - 5)
Outside: (2x + 7)
Factored form: (x - 5)(2x + 7) = 0
Step 5: Set each factor each to zero and solve for x:
x - 5 = 0 2x + 7 = 0
x - 5 [tex]x=-\dfrac{7}{2}[/tex]
The solutions of the quadratic equation given as 2x² - 3x - 35 = 0 are x=5 and x =-3.5.
Given that:
2x² - 3x - 35 = 0
This is a quadratic equation.
It is required to find the solutions of this equation.
The solution of the quadratic equation of the form ax² + bx + c = 0 can be found using the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
From the given equation:
a = 2
b = -3
c = -35
Substitute to the quadratic formula.
[tex]x=\frac{-(-3)\pm \sqrt{(-3)^2-4(2)(-35)}}{2(2)}[/tex]
[tex]=\frac{3\pm \sqrt{9+280}}{4}[/tex]
[tex]=\frac{3\pm \sqrt{289}}{4}[/tex]
[tex]=\frac{3\pm 17}{4}[/tex]
So, the solutions are:
[tex]x=\frac{3+ 17}{4}=5[/tex], and [tex]x=\frac{3-17}{4}=-3.5[/tex]
Hence, the solutions are x =5, -3.5.
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It takes four painters working at the same rate 1.25 work-days to finish a job. If only three painters are available, how many work-days will it take them to finish the job, working at the same rate? Express your answer as a mixed number.
Answer:
.9375 days
Step-by-step explanation:
1.25 / 4 = 0.3125
0.3125 x 3 - 0.9375
Type the slope-intercept equation
of the line that passes through
the points (-1,3) and (2,-3).
y = [? ]x + [ ]
Answer:
y= -2x +1
Step-by-step explanation:
slope- intercept form:
y= mx +c, where m us the gradient and c is the y-intercept.
Let's find the value of m first using the gradient formula.
Gradient= [tex] \frac{y1 - y2}{x1 - x2} [/tex]
[tex]m = \frac{ - 3 - 3}{2 - ( - 1)} \\ m = \frac{ - 6}{2 + 1} \\ m = \frac{ - 6}{3} \\ m = - 2[/tex]
y= -2x +c
To find the value of c, substitute a pair of coordinates.
When x= -1, y=3,
3= -2(-1) +c
3= 2 +c
c= 3 -2
c= 1
Thus the equation of the line is y= -2x +1.