Answer:
[tex]y = \frac{1}{2} x - 3[/tex]
Step-by-step explanation:
The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y-intercept.
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Using the gradient formula above,
gradient of line
[tex] = \frac{ - 1 - ( - 7)}{4 - ( - 8)} [/tex]
[tex] = \frac{ - 1 + 7}{4 + 8} [/tex]
[tex] = \frac{6}{12} [/tex]
[tex] = \frac{1}{2} [/tex]
Substitute m= ½ into the equation:
y= ½x +c
To find the value of c, substitute a pair of coordinates.
When x= 4, y= -1,
[tex] - 1 = \frac{1}{2} (4) + c[/tex]
-1= 2 +c
c= -1 -2 (-2 on both sides)
c= -3
∴ The equation of the line is y= ½x -3.
A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.1. If the distribution is approximately normal, find the probability that there will be fewer than 69 broken pretzels in a run.
Answer:
0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal 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.
A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.1.
This means that [tex]\mu = 73.5, \sigma = 5.1[/tex]
Find the probability that there will be fewer than 69 broken pretzels in a run.
This is the p-value of Z when X = 69.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 73.5}{5.1}[/tex]
[tex]Z = -0.88[/tex]
[tex]Z = -0.88[/tex] has a p-value of 0.1894
0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.
Choose which method to use: Law of Sines or Use Law of Cosines.
Answer:
we have
b=3mm
c=5mm
a=?
angle =62°
By using cosine rule.
a²=b²+c²-2bc cos angle
a²=3²+5²-2×3×5 cos 62°
a²=19.92
a=√19.92
a=4.5
I had choose cosine rule.
If 25% of a number is 50 and 35% of the same number is 70, find 10% of that number.
Answer:
10%×200=20
Step-by-step explanation:
25%×200=50
35%×200=70
A quiz consists of six multiple choice questions. Each question has four choices. A student who forgot to study guesses randomly on every question. What is the probability that the student answers at most four questions correctly?
Answer:
0.9945 = 99.45% probability that the student answers at most four questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student answers correctly, or he/she does not. The probability of the student answering a question correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A quiz consists of six multiple choice questions.
This means that [tex]n = 6[/tex]
Each question has four choices. Student guesses randomly.
This means that [tex]p = \frac{1}{4}[/tex]
What is the probability that the student answers at most four questions correctly?
This is:
[tex]P(X \leq 4) = 1 - P(X > 4)[/tex]
In which
[tex]P(X > 4) = P(X = 5) + P(X = 6)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{6,5}.(0.25)^{5}.(0.75)^{1} = 0.0053[/tex]
[tex]P(X = 6) = C_{6,6}.(0.25)^{6}.(0.75)^{0} = 0.0002[/tex]
[tex]P(X > 4) = P(X = 5) + P(X = 6) = 0.0053 + 0.0002 = 0.0055[/tex]
[tex]P(X \leq 4) = 1 - P(X > 4) = 1 - 0.0055 = 0.9945[/tex]
0.9945 = 99.45% probability that the student answers at most four questions correctly
greatest common factor of 27q^2 - 9
Answer:
9(3q^2−1)
Step-by-step explanation:
hamburger eaten monthly
Answer:
Full question?
Step-by-step explanation:
HELP HELP HELP HELP
What is the equation of the trend line in the scatter plot ?
Answer:
(0,9),(9,2)
Step-by-step explanation:
Find the area of each figure. Round to the nearest tenth if necessary.
Answer:
1. semicircle=14.1372mm
parallelogram=40 mm
54.1372 mm^2
2. 180 ft
hope this helps
have a good day :)
Step-by-step explanation:
can anyone help with this problem?
Answer:
The numerator factors to
[tex](x + 2)(x - 1)[/tex]
The denomenator factors to
[tex](x + 4)(x - 1)[/tex]
What is the solution to A=7x+40
9514 1404 393
Answer:
x = (A -40)/7
Step-by-step explanation:
Maybe you want to solve for x.
A = 7x +40 . . . . . given
A -40 = 7x . . . . . subtract 40
(A -40)/7 = x . . . divide by 7
The value of x will be ...
x = (A -40)/7
thirty years later the washington monument was finally completed, and the angle of elevation to the top of the monument from the same marker was 70o. to the nearest foot, how many feet were added to the phase 1 structure of the washington monument?
Answer:
Congress immediately tabled its expected contribution of $200,000 to the Society, effectively halting the appropriation. During its tenure, the Know-Nothing Society added only two courses of masonry, or four feet, to the monument using rejected masonry it found on site, increasing the height of the shaft to 156 feet
Step-by-step explanation:
To the nearest tenth, what is the area
of the figure below? Use 3.14 for it.
I need help! :) +no links please and thank you!
Answer:
Step-by-step explanation:
(14×2)+(14×4)
7×(3+5)
c, e and g
A car travels at the rate of 60 miles per hour and averages 30 miles per gallon of gasoline. Which of the following is the best
approximation of the number of gallons of gasoline that will be used in 8 hours of traveling at 60 miles per hour?
0.06 gallons
16 gallons
3.75 gallons
7.5 gallons
480 gallons
On a coordinate plane, a single transformation will be performed on square RSTU.
Select three transformations of square RSTU that would result in a congruent figure.
A a translation 3 units up and 8 units to the right
B a rotation of 270 counterclockwise about the origin
C a dilation by a scale factor of 1 with respect to the origin
a dilation by a scale factor of 1.5 with respect to the origin
E
a dilation by a scale factor of -2 with respect to the origin
Answer:the answer is ABC
Step-by-step explanation:
I had this on my exit ticket and my teacher reviewed the question and told me it was correct
Gary has 4 pencils 12 markers and 24 crayons, what is the ratio of pencils?
Answer:
1:10 [simplified from 4:40)
Step-by-step explanation:
4 pencils+ 12 marker+ 24 crayons=40
4 pencils: 40 items
1 pencil : 10 items
i dunno if this was right but there you gooo lol</3
HELP ME WITH THIS PLEASE. THANK YOU
Answer:
I think it's 2
Step-by-step explanation:
Answer:
1/11 is correct.
Step-by-step explanation:
You can see that the 3 is spun 2 times, but we need to know how many times he spun in total.
2 + 3 + 2 + 4 + 5 + 2 + 1 + 3 = 22
2/22 = 1/11
Have a nice day!
In how many ways can a
president, vice president, and
treasurer be selected for a
club if the club has 40
members?
[?] ways
Note: „Pr =
(n-r)!
n!
PLEASE HELP
Answer:
59,280
Step-by-step explanation:
the answer is base in my previous learning.. hope it helps..
1. What is the slope of the line through the points (-4, 2) and (—16,-6) PLEASE HELP
Answer:
2/3
(-4, 2) and (-16, -6)
slope = m = (y2 - y1) / (x2 - x1) = (-6 - 2) / (-16 - -4) = -8 / -12 = 2 / 3 = 0.667
I hope you got it right :)
If we attempt to create a square using the tiles that represent the algebraic expression x^2 +bx,
1. How many x-tiles would you add to the length of the x-square tile?
2. How many unit tiles would you need to complete the square?
I dont understand the question
Help and explain please.
Answer:
a2 + b2 = c24 + b2 = 49b = [tex] \sqrt{45} [/tex]The height of a triangle is 7 ft more than its base. If the area of the triangle is 30 ft2, what is the length of the base?
2 ft
5 ft
9 ft
12 ft
Answer:
see below
Step-by-step explanation: 5 27 7 16
area = 1/2 bh
height of a triangle is 7 ft more than its base
base = b
height = b + 7
area = 30
area = 1/2 b(h)
30 = 1/2 b(b + 7)
30 = 0.5(b²+ 7b)
30 = 1/2 b²+ 3.5b solve for b
1/2 b²+ 3.5b = 30
1/2 b²+ 3.5b - 30 = 0
b²+ 7b - 60 = 0 factor
(b +12)(b - 5) = 0 when b = -12 or 5 base length can't be negative
b = base = 5
area = 1/2 bh 1/2×2(9) = 9
area = 1/2 bh 1/2×5(12) = 60
area = 1/2 bh 1/2×9(16) = 56
area = 1/2 bh 1/2×12(19) = 114
The sales manager gathered information on the numbers of sales calls made and the number of copiers sold for a random sample of sales representative. Is there a positive correlation between calls made and copiers? Test at the 0.05 level of significance. Determine the 90% prediction interval for 60 number of calls made. *
Calls,X Sold. Y
20 40
20 50
40 60
50 90
40 80
20 40
40 60
30 60
Answer:
b
Step-by-step explanation:
If something cost $60 and it has a markdown of 40% what is the sale price
Answer:
Your total is now $36
Step-by-step explanation:
Multiply 60 times 40%
and it will show that you saved $24
subtract $60 - $24
there's your answer.
The relationship between two quantities that increase or decrease together is called A. indirect variation B. variation C. indirect option D. direct variation E. direct option
Answer:
D. direct variation
Step-by-step explanation:
Answer:
yes it is direct variation
Step-by-step explanation:
well I'm sorry I Don't know if it's going to be step by step but my own understanding is that what ever happens on one side will affect the other side so if there is an increase in A there will be an increase in B so there's a form of equilibrium. so let's say we throw two stones A and B into a fast flowing river we expect that the water will flow so the more the velocity of the river the faster the stone will flow so as the river is flowing the stone is floating as well but an indirect variation as the river increases it's velocity the stone decreases it's movement so in direct variation as the river increases it's velocity the stone does as well. I hope this is well detailed and I answered your question , thank you
What is the sum? Complete the equation.
-5 + (20)
Answer: The answer is 15
HOPE THIS HELPS AND HAVE A VERY GOOD DAY
PLEASE I NEED HELP ASAP!!
Answer:
Option C
Step-by-step explanation:
System of equations have been given as,
y - 4x = 16
y = 4x + 16 ------(1)
By comparing with slope-intercept form of the linear equation,
y = mx + b
Here, m = slope of the line
b = y-intercept
Therefore, m₁ = 4
2y = 8x + 16
y = 4x + 8 -------(2)
Slope of the line m₂ = 4
m₁ = m₂
Therefore, both the lines are parallel and both will not intersect each other.
Hence, there will be no solution of the system of equations.
Option C will be the correct option.
A sewing class has 185 yards of fabric to make quilts. Each quilt requires 8 yards of fabric. How much fabric will remain after all the quilts are made?
About 0.34 of the length of a cat is its tail. Write this decimal as a percent.
Give the coordinates of point D.
A. (-2,-4)
B. (-4,2)
C. (-4,-2)
D. (4, -2)