y=3× + 7 , y=×- 9 , 3×- 9 , 3×- y= 1 , 7× + 2y = 37.
An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.
Weight % of Total Underweight 2.5 Satisfactory 90.0 Overweight 7.5a) What is the probability of selecting and finding that all three bags are overweight?b) What is the probability of selecting and finding that all three bags are satisfactory?
Answer:
a) 0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.
b) 0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory
Step-by-step explanation:
The condition of the bags in the sample is independent of the other bags, which 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) What is the probability of selecting and finding that all three bags are overweight?
2.5% are overweight, which means that [tex]p = 0.025[/tex]
3 bags means that [tex]n = 3[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.025)^{3}.(0.975)^{0} = 0.000016[/tex]
0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.
b) What is the probability of selecting and finding that all three bags are satisfactory?
90% are satisfactory, which means that [tex]p = 0.9[/tex]
3 bags means that [tex]n = 3[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.9)^{3}.(0.1)^{0} = 0.729[/tex]
0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory
A survey of high schools within a district revealed that for ninth graders, 38% offer no honors classes, 12% offer one
honors class, 25% offer two honors classes, 20% offer three honors classes, and 5% offer four honors classes. A
high school is selected at random. What is the probability that it offers an even number of honors classes?
0.30
O 0.32
O 0.62
O 0.68
Answer:
0.30
Step-by-step explanation:
Find the probability by adding the probabilities together for having two and four honors classes.
25% offer two honors classes and 5% offer four honors classes. Add these together:
25 + 5
= 30
So, there is a 30% probability that the school offers an even number of honors classes.
The correct answer is 0.30.
1) Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of -3. Then graph the line. 2) Write an equation in point-slope form of the line with slope -3/5 that contains(-10 ,8). Then graph the line.
Answer:
An equation in the slope-intercept form is:
y = a*x + b
Where a is the slope, and b is the y-intercept.
a)
Here we have a slope of 6 and a y-intercept of -3
Then the equation is:
y = 6*x - 3
Now we want to graph this.
To graph it, we first need to find two points (x, y) that belong to this equation, then we can graph the points, and connect them with a line.
To find the points, we evaluate in two different values of x.
x = 0
y = 6*0 - 3 = -3
Then we have the point (0, -3)
x = 1
y = 6*1 - 3 = 3
Then we have the point (1, 3)
The graph of this line can be seen in the image below (the red one)
b) Similar to before, here the slope is -3/5, then the equation is something like:
y = (-3/5)*x + b
Now we also know that the line passes through the point (-10, 8)
This means that when x = -10, we must have y = 8
Replacing these two in the equation we get:
8 = (-3/5)*-10 + b
8 = 6 + b
8 - 6 = 2 = b
Then this equation is:
y = (-3/5)*X + 2
The graph can be found in the same way as before, the graph of this function can also be seen in the image below (the green one)
simplify 2x²y²÷m³×m²÷2xy
If the measure of angle 2 is 920 and the measure of angle 4 is 2
what is the value of x?
14.
23
Step-by-step explanation:
the value of x will be 920
which is the best estimate of (-3/5) (17 5/6)?
Answer:
-170 / 10
Step-by-step explanation:
Identify the transformation that occurs to create the graph of m(x)
m(x)=f(5x)
Answer:
m(x) is a dilation of scale factor K = 1/5 of f(x).
Step-by-step explanation:
The transformation is a horizontal dilation
The general transformation is defined as:
For a given function f(x), a dilation of scale factor K is written as:
g(x) = f(x/K)
If K > 1, then we have a dilation (the graph contracts)
if 0 < K < 1, then we have a contraction (the graph stretches)
Here we have m(x) = f(5*x)
Then we have a scale factor:
K = 1/5
So this is a contraction.
Then the transformation is:
m(x) is a dilation of scale factor K = 1/5 of f(x).
6(5x/3 -4/3 - 2)= 6 (3 - 6x/6 +4/6)
Answer:
21/8x
Step-by-step explanation:
10x -20 = -6x+22
+6x-20 = 22
16x-20 = 22
16x +20= +20
16x/16x = 42/16x
x = 21/8x
There are 9 people in an office with 4 different phone lines. If all the lines begin to ring at once, how many groups of 4 people can answer these lines?
A water reservoir is shaped like a rectangular solid with a base that is 60 yards by 30 yards, and a vertical height of 30 yards. At the start of a three-month period of
no rain, the reservoir was completely full. At the end of this period, the height of the water was down to 6 yards. How much water was used in the three-month period?
How much water was used in the three-month period?
Please help :)
Answer:
43200 yd³
Step-by-step explanation:
The water reservoir is a rectangular solid that is a three dimensional shape with six quadrilateral faces (cuboid).
This reservoir has a base of 60 yards by 30 yards, and a vertical height of 30 yards. Therefore:
Volume of the reservoir = area of base * vertical height = 60 * 30 * 30 = 54000 yd³
This reservoir hence have a volume of 54000 yd³ when filled up with water.
After 3 months, the height of the water was down to 6 yards therefore the the volume is:
Volume after 3 months = area of base * vertical height = 60 * 30 * 6 = 10800 yd³
The amount of water used after 3 months = volume of water at beginning - volume of water after 3 months
The amount of water used after 3 months = 54000 - 10800 = 43200 yd³
!!!!Plzzz help!!!!
For your initial post: Discuss your strategy for
establishing identities. Why do you think it is
usually preferable to start with the side
containing the more complicated expression
when establishing an identity?
Answer:
Yes it is very good for establishing identities.
Step-by-step explanation:
Since its a very preferable start it is a very good way to establish identity.
HELP ASAP I WILL GIVE BRAINLIST
Convert 7π OVER 4 radians to degrees. Which quadrant does this angle lie in?
What are the sine, cosine and tangent of the angle 7π over 4? Be sure to show and explain all work.
Answer:
7π/4 radians = 315°, Quadrant IV
sin(315°) = -√2/2
cos(315°) = √2/2
tan(315°) = -1
Step-by-step explanation:
An environmentalist would like to estimate the true mean weight of all cars. To do so, she selects a random sample of
30 cars and determines that the 90% confidence interval for the true mean weight to be 2.8 to 3.4 tons. Which of the
following would increase the margin of error for this confidence interval?
O selecting another sample
O increasing the sample size
O increasing the confidence level
O decreasing the confidence level
If the confidence level will increase, the margin of error will also increases.
What is margin of error?The margin of error is defined a range of values below and above the sample statistic in a confidence interval.
What is confidence interval?The confidence interval is a way to show what is uncertainty is with a certain statistic.
According to the given question
Environmentalist estimating true mean weight or all cars.
For the true mean weights of 2.8 to 3.4 tons the confidence level is 90%.
Since, the confidence level increases, the critical value increases and hence the margin of error increases.
Therefore, if the confidence level will increase, the margin of error will also increases.
Find out more information about confidence interval and margin error here:
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please help with this quadratic equations
Answer:
I don't understand the question
Determine the volume and the surface area of the three dimension figure
Answer:
Volume = 18 cm^3
Surface Area = 58 cm^2
Step-by-step explanation:
Find the volume with the formula V=w*h*l
W= width
H = height
L = length
W= 2cm
H= 1 cm
L= 9 cm
V= w*h*l
V= 2cm * 1 cm * 9cm
V= 18 cm^3
Find the surface area with the formula A= 2(w*l + h*l + h* w)
W= width
H = height
L = length
W= 2cm
H= 1 cm
L= 9 cm
A= 2(w*l + h*l + h* w)
A= 2(2cm*9cm + 1cm*9cm + 1cm* 2cm)
A= 2(29cm)
A= 58cm^2
Cole biked at 5 mph for 1 1/2 hours. Which of the following choices show how far he biked?
Answer:
Should be 5 1/2 if thats on there
Step-by-step explanation:
u take 11/2 and take out the 1 u get 10/2 so u cut 10 in half get 5 then add the one and make it 5 1/2
Find the measure of angle C of a triangle ABC, if angle A=a and angle B= 2a.
*The answer is not 180-3a
The angle C of the triangle ABC is ( π - 3a ).
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
The angle will be calculated as follows:-
We know that the sum of the angles of the triangle is 180 degrees or π in radians.
∠A + ∠B + ∠C = π
a + 2a + ∠C = π
∠C = π - a - 2a
∠C = π - 3a
Therefore angle C of the triangle ABC is ( π - 3a ).
To know more about an angle follow
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Bindi is buying pet food with a coupon for 20% off. The original price of the bag of food is $39.
Which answer gives the best estimate for the price after the discount?
$48
$19
$34
$32
A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures (in degrees Fahrenheit) he observed at his southern Florida home last year. The coldest temperature for any week was 36°F, but he inadvertently recorded the Celsius value of 2°. Assuming that he correctly listed all the other temperatures, explain how this error will affect these summary statistics:a) measures of center: mean and median.b) measures of spread: range, $IQR,$ and standard deviation.
Answer:
nr.herkyrsfdlufshfsyfs
Step-by-step explanation:
dsfsyfksutryrysyrslufzmfyzydzufmzmhfzl
hdhfuthfzhkrskyrsgj
log2(6x) – log2 (x)-2
Answer:
xlog(64)−xlog(2)−2
Step-by-step explanation:
Simplify 6log(2) by moving 6 inside the logarithm.
log(2^6)x − log(2)x − 2
Raise 2 to the power of 6.
log(64)x − log(2)x − 2
Reorder factors in log(64)x − log(2)x −2.
CAN SOMEONE HELP ME ON ANALYZING DOT PLOTS!!!
Answer:
yes
Step-by-step explanation:
but I can't see them here
I need help answering this question.
Answer:
hello dude
x - 9 = - 12
x = 9 -12
x = -3
HAVE A NİCE NİGHT
Step-by-step explanation:
Greetings from Turkey
We have to,
find the required value of x.
Let's start,
→ x - 9 = -12
→ x = -12 + 9
→ x = -3
Thus, -3 is the value of x.
Find two positive numbers whose product is 64 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)
Answer:
Both the numbers are 8.
Step-by-step explanation:
Let the two numbers are p and 64/p.
The sum is given by
[tex]S = p +\frac{64}{p}\\\\\frac{dS}{dp}= 1 - \frac{64}{p^2}\\\\\frac{dS}{dp}=0\\\\\frac{64}{p^2}=1\\\\p= \pm 8[/tex]
So, the sum is minimum for p = 8 0r - 8, so the two numbers 8.
Estimate the student's walking pace, in steps per minute, at 3:20 p.m. by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)
This question is incomplete, the complete question is;
A student bought a smart-watch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded (t) minutes after 3:00 pm on the first day she wore the watch.
t (min) 0 10 20 30 40
Steps 3,288 4,659 5,522 6,686 7,128
a) Find the slopes of the secant lines corresponding to the given intervals of t.
1) [ 0, 40 ]
11) [ 10, 20 ]
111) [ 20, 30 ]
b) Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)
Answer:
a)
1) for [ 0, 40 ], slope is 96
11) for [ 10, 20 ], slope is 86.3
111) for [ 20, 30 ], slope is 116.4
b) the student's walking pace is 101 per min
Step-by-step explanation:
Given the data in the question;
t (min) 0 10 20 30 40
Steps 3,288 4,659 5,522 6,686 7,128
SLOPE OF SECANT LINES
1) [ 0, 40 ]
slope = ( 7,128 - 3,288 ) / ( 40 - 0
= 3840 / 40 = 96
Hence slope is 96
11) [ 10, 20 ]
slope = ( 5,522 - 4,659 ) / ( 20 - 10 )
= 863 / 10 = 86.3
Hence slope is 86.3
111) [ 20, 30 ]
slope = ( 6,686 - 5,522 ) / ( 30 - 20 )
= 1164 / 10 = 116.4
Hence slope is 116.4
b)
Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part .
Since this is recorded after 3:00 pm
{ 3:20 - 3:00 = 20 }
so t = 20 min
so by average;
we have ( [ 10, 20 ] + [ 20, 30 ] ) /2
⇒ ( 86.3 + 116.4 ) / 2
= 202.7 /2
= 101.35 ≈ 101
Therefore, the student's walking pace is 101 per minutes
Can someone pls help asap i will give Brainliest
Answer:
24/145
Step-by-step explanation:
Trigonometric identities are equalities involving trigonometric functions and remains true for entire values of the variables involved in the equation.
Some trigonometric identities are:
sin(a + b) = sinacosb + cosasinb; sin(a - b) = sinacosb - cosasinb
cos(a + b) = cosacosb - sinasinb; cos(a - b) = cosacosb + sinasinb
Given that sin a = 3/5. sin a = opposite/hypotenuse.
Hence opposite = 3, hypotenuse = 5. using Pythagoras:
hypotenuse² = opposite² + adjacent²
5² = 3² + adjacent²
adjacent² = 16
adjacent = 4
Given that sin a = 3/5. a = sin⁻¹(3/5) = 36.86
cos a = cos 36.86 = 4/5
cos b = -20/29; b = cos⁻¹(-20/29) = 133.6
sinb = sin(133.6) = 21/29
sin(a + b) = sinacosb + cosasinb = (3/5 * -20/29) + (4/5 * 21/29) = -12/29 + 84/145
sin(a + b) = 24/145
74. A portion of a board has length x feet. The other part has
length (7x – 9) feet. Express the total length of the board
as a simplified expression in x.
Step-by-step explanation:
Given that,
Length of the one portion of the board = x feetLength of the another portion = (7x – 9) feetAccording to the question,
[tex]\longrightarrow[/tex] Total length = Sum of the length of the two pieces
[tex]\longrightarrow[/tex] Total length = {x + (7x – 9)} feet
[tex]\longrightarrow[/tex] Total length = {x + 7x – 9} feet
[tex]\longrightarrow[/tex] Total length = (8x – 9) feet
Therefore, the total length of the board as a simplified expression in x is (8x – 9) feet.
solve it
[tex]4 \frac{1}{3} \times (3 \frac{1}{3} \times 3 \frac{1}{2} ) \ {}^{7} \div 9 \frac{3}{4} [/tex]
solve it fast
Answer:
[tex]\frac{257357187500}{19683}[/tex]
Step-by-step explanation:
We can convert these mixed fractions to ordinary fractions.
[tex]4(1/3)=\frac{(4*3)+1}{3}=\frac{13}{3}[/tex]
[tex]3(1/3)=\frac{10}{3}[/tex]
[tex]3(1/2)=\frac{7}{2}[/tex]
[tex]9(3/4)=\frac{39}{4}[/tex]
Then we have:
[tex]\frac{13}{3}*(\frac{10}{3}*\frac{7}{2})^{7}*\frac{4}{39}[/tex]
[tex]\frac{257357187500}{19683}[/tex]
I hope it helps you!
Find in the triangle. Round to the nearest degree.
Answer:
D. 34
Step-by-step explanation:
Because this is a right triangle we can use sin, cos, tan.
Use cosine because the values of the adjacent side and hypotenuse are already given.
cos(θ) = 72/87
Because we are solving for the angle measure (and not the measure of the side) we need to use inverse cos.
cos⁻¹ = 72/87
put into a calculator and answer is approximatelyn34 degrees.
PLEASE HELP WILL MARK BRAINLIST AND GIVE 20 POINTS
Answer:
The first one
Step-by-step explanation:
You just need to find the slope in the average of all the dots.
Answer:
the first option, y=3/7x-3
Step-by-step explanation:
the scatterplot begins around y=-3, so therefore the y-intercept is -3. The slope is obviously not higher than 1, so it is y=3/7x-3.
The probability that a certain movie will win an award for acting is 0.15, the probability that it will win an award for direcing is 0.23, and the probability that it will win both is 0.09. Find the probabilities of the following.
a. The movie wins an award for acting, given that it wins both awards.
b. The movie wins an award for acting, given that it wins exactly one award.
c. The movie wins an award for acting, given that it wins at least one award.
Answer:
a) 0.15 / 0.09
b) 0.15 / 1
c) 0.15 / 0.23
