Historically, WoolWord's supermarket has found it sells an average of 2517 grapes per day, with a standard deviation of 357 grapes per day. Consider that the number of grapes sold per day is normally distributed. Find the probability (to 4 decimal places) that: a) the number of grapes sold on a particular day exceeds 2300 ? b) the probability that the average daily grape sales over a three month (i.e. 90 day) period is less than 2500 grapes or more than 3000 grapes per day.
Answers
(a) The number of grapes sold on a particular day exceeds 2300 is:
P(Z > -0.611) ≈ 0.7291
(b) The probability that the average daily grape sales over a 90-day period is less than 2500 grapes or more than 3000 grapes per day is:
P = P1 + P2 ≈ 0.3249 + 0.1003 ≈ 0.4252
We have the information available from the question is:
It is given that the supermarket found it sells an average of 2517 grapes per day, with a standard deviation of 357 grapes per day.
The number of grapes sold per day is normally distributed.
Now, The normal distribution and the properties of the z-score to solve the probability questions:
Mean (μ) = 2517 grapes per day
Standard deviation (σ) = 357 grapes per day
We have to find the probability:
a) The number of grapes sold on a particular day exceeds 2300:
We'll calculate the z-score for 2300 and then use the standard normal distribution table:
We know the formula:
z = (x - μ) / σ
z = (2300 - 2517) / 357
z ≈ -0.611
Now, using the z - table we can find the probability associated with a z-score of -0.611.
P(Z > -0.611) ≈ 0.7291
(b) We have to find the probability that the average daily grape sales over a three month (i.e. 90 day) period is less than 2500 grapes or more than 3000 grapes per day.
Now, According to the question:
We will use the Central limit theorem:
The mean of the sample means will still be 2517, but the standard deviation of the sample means (also known as the standard error of the mean, SEM) can be calculated as:
SEM = σ / √n
Where:
σ => stands for the standard deviation of the original distribution and
√n => is the square of the sample size.
SEM = 357 / √90
SEM ≈ 37.66
Now, We can calculate the z-scores for 2500 and 3000 using the sample mean distribution:
\(z_1\) = (x1 - μ) / SEM = (2500 - 2517) / 37.66
\(z_1\) ≈ -0.452
\(z_2\) = (x2 - μ) / SEM = (3000 - 2517) / 37.66
\(z_2\) ≈ 1.280
By using the z -table:
P1 = P(Z < -0.452)
P2 = P(Z > 1.280)
P1 ≈ 0.3249
P2 ≈ 0.1003
The probability that the average daily grape sales over a 90-day period is less than 2500 grapes or more than 3000 grapes per day is:
P = P1 + P2 ≈ 0.3249 + 0.1003 ≈ 0.4252
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Related Questions
Heather, Eric, and Chang sent a total of 116 text messages over their cell phones during the weekend. Chang sent 3 times as many messages as Eric. Eric sent 9 more messages than Heather. How many messages did they each send?
Answers
Answer:
Step-by-step explanation:
Declaration
Let Heather's number of messages = x
Let Eric's number of messages = x + 9
Let Chang's number of messages = 3(x +9)
Equation
x + x + 9 + 3(x + 9) = 116
Solution
x + x + 9 + 3(x + 9) = 116 Remove the brackets
x + x + 9 + 3x + 27 = 116 Combine like terms
x + x + 3x + 9 + 27 = 116
5x + 36 = 116 Subtract 36 from both sides
5x + 36 - 36 = 116 - 36 Combine
5x = 80 Divide both sides by 5
5x/5 = 80/5
x = 16
Answer
Heather = 16
Eric = 16 + 9 = 25
Chang = 3*25 = 75
The shape below is made of two rectangles joined together.
3 cm
4 cm
6 cm
6 cm
15 cm
Find the total area of the shape.
Optional working
Answer:
+
cm²
Answers
The total area of the shape is 102 cm².
Given that, two rectangles with dimensions L1=15 cm, B1=6 cm, L2=4 cm and B2=3 cm.
What is the area of the rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimetres, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle.
We know that, the area of a rectangle = Length × Breadth.
So, the area of rectangle1 = 15 × 6 = 90 cm²
The area of rectangle2 = 4 × 3 = 12 cm²
Total area = 90+12 =102 cm²
Therefore, the total area of the shape is 102 cm².
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(a) 26 is what percent of 40? 65% (b) 85% of 80 is what number?
Answers
b) 68
26:40 as x:100
26/40 = x/100
Cross multiply
2600 = 40x
x = 65
———————
85% of 80
0.85 is the decimal equivalent of 85%
80 x 0.85 = 68
1.Let ????=(1,−3). Calculate the length of ????????→, where ????=(0,0). (Use symbolic notation and fractions where needed.)
2.Give an equation for the cylinder passing through (0,2,7)(0,2,7) with the vertical line through (1,0,0)(1,0,0) as its central axis.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
Answers
The length of the vector ????????→ is √10. the equation of the cylinder passing through (0,2,7) with the vertical line through (1,0,0) as its central axis is (x - 1)² + y² = 1/5(7 - 2z)².
For the first problem, we need to find the length of the vector from (1, -3) to (0, 0). Using the distance formula, we have
√[(0 - 1)² + (0 - (-3))²] = √[1 + 9] = √10
Therefore, the length of the vector is √10.
For the second problem, we can start by finding the equation of the line passing through (1,0,0) and (0,2,7). This line has direction vector (-1, 2, 7) and passes through (1,0,0), so its vector equation is
r = <1, 0, 0> + t<-1, 2, 7>
Next, we need to find the equation of a circle with radius r centered at the point (1,0,0). This circle lies in a plane perpendicular to the line passing through (1,0,0) and (0,2,7), so we can use the cross product of the direction vector of the line and the vector from (1,0,0) to (0,2,7) to find a normal vector to the plane
n = (-1, 2, 7) x (-1, 0, 0) = <0, 7, 2>
The equation of the plane is then
0(x - 1) + 7y + 2z = 0
Simplifying this equation, we get
7y + 2z = 7
Finally, we can combine the vector equation of the line and the equation of the plane to get the equation of the cylinder
(x - 1)² + y² = 1/5(7 - 2z)²
This is the equation of the cylinder passing through (0,2,7) with the vertical line through (1,0,0) as its central axis.
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What is the position
number of the term
125 in the sequence
f(n) = 2n+3?
Answers
Answer:
61st term in the sequence
Step-by-step explanation:
125 = 2n + 3
122 = 2n
n = 61
If you roll a 6-sided die 6 times, what is the best prediction possible for the number of times you will roll a one?
Answers
Answer:
yes
Step-by-step explanation:
Consider the PDE au(x, t) = 4 d²u(x, t) 2 Ət əx² For each of BCs and ICs, solve the initial value problem. du(π,t) a) BCs: u(0,t)=0 = = 0 and əx IC: u(x,0) = x ANSWER: f(x)= n=1 u(2,t) = 0 and u(0,t)=0 u(x,0)=sin x ANSWER: f(x)=¹1_sin(2 + nx) na n=1 1+ 2 X b) BCs: IC: 8 (2n-1) T n+1 (-1)041 -4(2n-1)²t sin(2-nπ) nπ 1- 2 e sin (2n-1) 2 na sin X 2 -(nn)²t x -X
Answers
the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.
The given partial differential equation is:
au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)
a) BCs (Boundary Conditions):
We have u(0, t) = 0 and u(π, t) = 0.
IC (Initial Condition):
We have u(x, 0) = x.
To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.
The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:
X(x) * T'(t) = 4 * X''(x) * T(t) / a
Dividing both sides by X(x) * T(t) gives:
T'(t) / T(t) = 4 * X''(x) / (a * X(x))
Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².
T'(t) / T(t) = -λ²
X''(x) / X(x) = -λ² * (a / 4)
Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.
Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.
Now, applying the boundary conditions:
1) u(0, t) = 0:
Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.
2) u(π, t) = 0:
Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.
Now, let's find the expression for u(x, t) using the initial condition:
u(x, 0) = X(x) * T(0) = x
Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:
C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x
This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.
Therefore, the solution for the initial value problem is:
u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)
where λ = ± sqrt(-4n² / a), and n is a non-zero integer.
Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.
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The picturegram shows information about CDs sold in a shop.
1 . How manny CDs were sold on Wednesday | Key = 3 |
2. How manny more CDs were sold on Thursday than Wednesday?
**If you know the answer let me know!**
Answers
Answer:
i believe number 1 is 18 and number 2 is 9.
Step-by-step explanation:
if one full circle represents 6 CDs then on wednesday 18 Cds were sold because 6+6+6=18 and on thursday they sold 9 more Cds than on wednesday because they sold 6+6+6+6+3 which equals 9.
Question 5 (1 point)
The mallard duck walks 9,500 ft per year. How many inches is that per day?
Answers
Answer:
LOL, change ft to inches and then divide by 365
Answer:
312.3 Inches/Day
Step-by-step explanation:
I did it on a test and also 9,500 divided by 365 (year) times 12 (12 inches in one foot)=312.3
As you can see in the photo below I chose 312.3
Please helpppp
A plane, initially traveling 150 mi./hr.
100 east of north, suddenly enters a
region where the wind is blowing at
50 mi./hr. from the southwest.
What is the plane's resultant direction?
[?]° compass heading
Round to the nearest hundredth.
Enter
Answers
Answer:
Resultant is 50 mi/hr in the north east direction
Step-by-step explanation:
Plane is traveling north east at 150 mi/hr.
Now a wind is blowing from the south west at 100 mi/hr.
Now, north east and south west are directly opposite directions and such the angle between the resultant speed of the plane in flight and the wind will be;
150 - 100 = 50 mi/hr
Since the north east speed is greater than the south east speed, then the direction will be north east.
Thus, resultant is 50 mi/hr in the north east direction
7(3+5) = 8 + ___
What number or expression could fill in the blank that would make this true
Answers
Answer:
_ = 48
Step-by-step explanation:
7 (3 + 5) = 8 + _
7 x 3 + 7 x 5 = 8 + _
21 + 35 = 8 + _
56 = 8 + _
_ = 56 - 8
_ = 48
Hope that helps!
Answer: x = 48
PEMDAS
7 (3 + 5) = 8 + x
7 (8) = 8 + x
56 = 8 + x
isolate x by subtracting 8
48 = x
First to answer and get right gets brainliest!!!!!
Is (8, 7) a solution of y > 4x − 6?
Yes or No
Answers
Answer:
no
Step-by-step explanation:
8>28-6 that is false
You are a doctorate student in biology doing a dissertation about the insect Desmolithica Geogebra. This insect causes serious damage to plums, apricot and flowering cherries. The female insect lays as many as thirty to sixty eggs on the leaves of the host trees. The time when the insect larva hatches from its egg up to the moment in finding its host tree is called the searching period. Once the insect finds the plum, it squirms into the fruit and begin to ruin it. After approximately four weeks, the insect will crawl back under the bark of the plum tree or directly to the soil where it forms a cocoon. The observation regarding the behavior of the insect demonstrate the length of the searching period S(t), and the percentage of the larvae that survive this period N(t), depend on the air temperature denoted by t. The data from the observations suggest that if the air temperature is measure in degree celsius, where 20
Answers
In this dissertation about the insect Desmolithica Geogebra, the searching period S(t) of the insect depends on the air temperature denoted by t and is directly proportional to t-20.
The percentage of the larvae that survive this period N(t) is inversely proportional to t-20 and depends on t.
These statements can be mathematically represented as:
S(t) ∝ (t - 20)
and
N(t) ∝ 1/(t - 20)
For S(t) and N(t) to be directly and inversely proportional to (t - 20), respectively, we need to assume that the relationship is linear.
That is, S(t) and N(t) can be represented by linear equations of the form:
S(t) = m(t - 20)
and
N(t) = k/(t - 20)
where m and k are constants that depend on the particular observation regarding the behavior of the insect.
These constants can be determined by using the data from the observations.
The dissertation can further explain the significance of these relationships in understanding the behavior of the insect, as well as in developing strategies to control or prevent the damage caused by the insect.
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Find all the values of k for which the equation 2x^2+x+4k has (a) two real solutions, (b) one real solution, and (c) no real solutions.
Answers
the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.
How to solve the question?
The given equation is 2x² + x + 4k.
(a) For the equation to have two real solutions, the discriminant b² - 4ac must be positive.
Therefore, for this equation, b² - 4ac > 0
=> 1 - 4(2)(4k) > 0
=> 1 - 32k > 0
=> k < 1/32
Hence, all values of k less than 1/32 will give the equation 2x² + x + 4k two real solutions.
(b) For the equation to have one real solution, the discriminant b² - 4ac must be zero.
Therefore, for this equation, b² - 4ac = 0
=> 1 - 4(2)(4k) = 0
=> 1 - 32k = 0
=> k = 1/32
Hence, only the value of k equal to 1/32 will give the equation 2x² + x + 4k one real solution.
(c) For the equation to have no real solutions, the discriminant b² - 4ac must be negative.
Therefore, for this equation, b² - 4ac < 0
=> 1 - 4(2)(4k) < 0
=> 1 - 32k < 0
=> k > 1/32
Hence, all values of k greater than 1/32 will give the equation 2x² + x + 4k no real solutions.
In conclusion, the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.
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A trailer will be used to transport several 40-kilogram crates to a store. The greatest amount of weight that can be loaded onto the trailer is 1,050 kilograms. An 82-kilogram crate has already been loaded onto the trailer. What is the greatest number of 40-kilogram crates that can also be loaded onto the trailer?
Answers
The greatest number of 40-kilogram crates that can be loaded onto the trailer = 24
Let us assume that n represents the greatest number of 40-kilogram crates that can be loaded onto the trailer.
The greatest amount of weight that can be loaded onto the trailer is 1,050 kilograms.
Here, 82-kilogram crate has already been loaded onto the trailer.
From this information, we can formulate an equation as,
1050 = 82 + (40 × n)
We solve above equation for n.
40n = 1050 - 82
n = 968 / 40
n = 24.2
As the number of crates can not be a decimal number.
n ≈ 24
This is the greatest number of 40-kilogram crates that can be loaded onto the trailer.
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37. Find the equation of the line that is parallel to y=2x-4 and passes through the point (-7,-2). You may express the equation in slope-intercept or standard form.
Answers
The required equation in slope-intercept or standard form is y = 2x+12.
It is required to find the equation in slope-intercept or standard form.
What is slope?Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it.
Given:
The equation of the line that is parallel to y=2x-4.
Parallel lines have the same slope, We know the equation will be
y = 2x + b.
Use the point (-7,-2) to sub in for (x, y) to solve for b.
-2 = 2(-7) + b
-2=-14+b
12=b
So, the equation will be y = 2x+12
Therefore, the required equation in slope-intercept or standard form is y = 2x+12.
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Find Y. Round to the nearest tenth
Answers
Answer:
32.7 degress
Step-by-step explanation:
In this question we are to find the value of the angle
The best way to do with the information given is the cosine rule
Mathematically that would be;
y^2 = x^2 + z^2 -2xzCosY
where x = 90 ft , y = 55ft and z = 50 ft
Plugging the values we have;
55^2 = 90^2 + 50^2-2(90)(50)CosY
-7575 = -9000cosY
cosY = 7575/9000
cosY = 0.841666666667
Y = cos^-1 0.841666666667
Y = 32.68 degrees which is 32.7 to the nearest tenth
Answer:
32.7
Step-by-step explanation:
What is the probability that a test correctly rejects a false null hypothesis called?.
Answers
Power is the probability that a test correctly rejects a false null hypothesis.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes—how likely they are—whenever we're uncertain of how an event will turn out.
Power is inversely related to the probability of making a type 2 error (β) which is rejecting the alternative hypothesis when it is true.
The equation of power is:
Power=1-β
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What is the surface area of a cube that’s measured 8 inches
Answers
Answer:
2
Step-by-step explanation:
Haven't done this in awhile but I think it's 2 because if you cube 2 it comes to 8. L x W x H = 8 | 2 x 2 x 2 = 8
A pizza was cut into 12 pieces. After lunch, 5/12 of a pizza was left over. Then Santa ate 1/4 of a pizza. What part of the pizza was left when Santa finished eating?
Answers
To answer this question, we have to substract 1/4 (which is the part of the pizza Santa ate) from 5/12 (the part of the pizza that was left over).
\(\frac{5}{12}-\frac{1}{4}=\frac{20-12}{48}=\frac{8}{48}=\frac{1}{6}\)1/6 of the pizza was left when Santa finished eating.
4-14 Practice Problems
3 of 33 of 3 Items
Question
Robert wants to join a gym.
Gym A: $15 joining fee and $30 monthly charge.
Gym B: No joining fee and $35 monthly charge.
Enter the number of months it will take for the total cost for both gyms to be equal.
It will take
months for the gyms to cost the same total amount.
Answers
Answer:
5 months
Step-by-step explanation:
Equation A: 15+30x
Equation B: 35x
In 5 months Gym a will cost 15+30(5) or $175 and Gym B will also cost $175.
Basically all you have to do is apply reasonable numbers until you find out where the costs will meet up.
-(x-7)-x=-8(6+x)+6x Solve for x :)
Answers
Answer:
No Solution.
Step-by-step explanation:
-(x-7)-x=-8(6+x)+6x
-x+7-x=-48-8x+6x
-x-x+7=-48-2x
-2x+7=-48-2x
-2x-(-2x)+7=-48
-2x+2x+7=-48
7=-48
no solution
A stereo store is offering a special price on a complete set ofcomponents (receiver, compact disc player, speakers, cassette deck)ie one of each. A purchaser is offered a choice ofmanufacturer for each component:Receiver: Kenwood, Onkyo, Pioneer, Sony, SherwoodCD Player: Onkyo, Pioneer, Sony, TechnicsSpeakers: Boston, Infinity, PolkCassette Deck: Onkyo,
A stereo store is offering a special price on a complete set ofcomponents (receiver, compact disc player, speakers, cassette deck)ie one of each. A purchaser is offered a choice ofmanufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
CD Player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Cassette Deck: Onkyo, Sony, Teac, Technics
A switch board display in the store allows a customer to hooktogether any selection of components (consisting of one of eachtype). Use the product rules to answer the followingquestions.
a. In how many ways can one component of each type beselected?
b. In how many ways can components be selected if boththe receiver and the cd player are to be sony?
c. In how many ways can components be selected if noneis to be sony?
d. In how many ways can a selection be made if at leastone sony component is to be included?
e. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component? Exactly onesony component?
Answers
a. One component of each type can be selected in 5 * 4 * 3 * 4 = 240 ways.
b. If both the receiver and CD player are Sony, components can be selected in 1 * 1 * 3 * 4 = 12 ways.
c. If none is Sony, components can be selected in 4 * 3 * 3 * 3 = 108 ways.
d. With at least one Sony component, a selection can be made in 240 - 108 = 132 ways.
e. Probability of at least one Sony component is 132/240 ≈ 0.55. Probability of exactly one Sony component is 12/240 = 0.05.
a. To determine the number of ways one component of each type can be selected, we multiply the number of choices for each component.
Receiver: 5 options (Kenwood, Onkyo, Pioneer, Sony, Sherwood)
CD Player: 4 options (Onkyo, Pioneer, Sony, Technics)
Speakers: 3 options (Boston, Infinity, Polk)
Cassette Deck: 4 options (Onkyo, Sony, Teac, Technics)
Using the product rule, the total number of ways to select one component of each type is:
5 * 4 * 3 * 4 = 240 ways.
b. If both the receiver and the CD player are required to be Sony, we fix the choices for those components to Sony and multiply the remaining choices for the speakers and cassette deck.
Receiver: 1 option (Sony)
CD Player: 1 option (Sony)
Speakers: 3 options (Boston, Infinity, Polk)
Cassette Deck: 4 options (Onkyo, Sony, Teac, Technics)
Using the product rule, the total number of ways to select components with Sony as the receiver and CD player is:
1 * 1 * 3 * 4 = 12 ways.
c. If none of the components can be Sony, we subtract the choices for Sony from the total number of choices for each component and multiply the remaining options.
Receiver: 4 options (Kenwood, Onkyo, Pioneer, Sherwood)
CD Player: 3 options (Onkyo, Pioneer, Technics)
Speakers: 3 options (Boston, Infinity, Polk)
Cassette Deck: 3 options (Onkyo, Teac, Technics)
Using the product rule, the total number of ways to select components with none of them being Sony is:
4 * 3 * 3 * 3 = 108 ways.
d. To calculate the number of ways to select components with at least one Sony component, we subtract the number of ways to select components with none of them being Sony from the total number of ways to select components.
Total ways to select components: 5 * 4 * 3 * 4 = 240 ways
Ways to select components with none of them being Sony: 108 ways
Number of ways to select components with at least one Sony component: 240 - 108 = 132 ways.
e. If someone flips the switches randomly, we need to calculate the probability of selecting a system with at least one Sony component and exactly one Sony component.
Total ways to select components: 240 ways
Ways to select components with at least one Sony component: 132 ways
Ways to select components with exactly one Sony component: 12 ways (from part b)
Probability of selecting a system with at least one Sony component: 132/240 ≈ 0.55
Probability of selecting a system with exactly one Sony component: 12/240 = 0.05
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Write an equation of The line that passes through the given point and is parallel to the given line (4;5);y=-3/2x+3
Answers
9514 1404 393
Answer:
y = -3/2x +11
Step-by-step explanation:
The slope of the parallel line is the same as the slope of the given line, so ...
m = -3/2
The y-intercept of the parallel line can be found from ...
b = y -mx
b = 5 -(-3/2)(4) = 11
So, the desired equation is ...
y = mx +b
y = -3/2x + 11
_____
Additional comment
Since you know the slope and a point on the desired line, you can write down the equation directly using the point-slope form. No additional math is required.
y -5 = -3/2(x -4)
what is the greatest common factor of 39, 42, and 33
Answers
Answer:
The greatest common factor of 39, 42, and 33 is 3
Step-by-step explanation:
Answer: The greatest common factor of 39,42, and 33 is 3
Step-by-step explanation:
We first find the factors of the numbers
39=1x39, 3x13 (1,3,13,39)
42=1x42, 2x21, 3x14, 6x7(1,2,3,6,7, 42)
33=1x33, 3x11(1,3,11.33)
The common factors are the factors that appear in the three numbers which are 1 and 3
The greatest common factor therefore is 3
A) make a mark at (-3. 5,-4)
b) make a mark at (0,-4. 5
Answers
Answer:
see attached
Step-by-step explanation:
Points are plotted on a coordinate grid by recognizing the meaning of the numbers in the ordered pair.
The first number is the x-coordinate, the horizontal distance from the y-axis. The second number is the y-coordinate, the vertical distance from the x-axis. Positive numbers indicate "right" or "up". Negative numbers indicate "down" or "left."
A)The mark is 3.5 units left of the y-axis and 4 units down from the x-axis.
__
B)The mark is neither left nor right of the y-axis, so is on the y-axis. It is 4.5 units down from the x-axis.
Try it
Proving the Parallelogram Side Theorem
Given: ABCD is a parallelogram.
Prove: AB CD and BC = DA
A
□
Hint
Angles Segments Triangles Statements Reasons
ASA
CPCTC
reflexive property
given
Statements
✓ 3. BC || DA
4. draw AC
✔✓ 5. AC AC
SE
6. BCA and DAC
are alt. interior angles
7.
DAC
✓8. ZDCA and
are alt. interior angles/
DCA
✓9.
Reasons
3. def. of parallelogram
4. unique line postulate
5. reflexive property
6. def. of alt. interior angles
7. alternate interior angles theorem
8. def. of alt. interior angles
9. alternate interior angles theorem
Answers
Therefore, we have proved that in parallelogram ABCD, AB is congruent to CD and BC is congruent to DA.
What is parallelogram?A parallelogram is a four-sided polygon (a flat, closed shape) with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles of a parallelogram are also equal. Parallelograms can have different shapes and orientations, but they always have these defining properties of parallel sides and equal opposite angles and sides. Examples of shapes that are parallelograms include rectangles, squares, and rhombuses.
Given: ABCD is a parallelogram.
Draw diagonal AC.
1. By definition of a parallelogram, BC || DA.
2. By the Unique Line Postulate, there is exactly one line through A that is parallel to BC.
3. By the Reflexive Property of Congruence, AC is congruent to itself.
4. By the definition of alternate interior angles, angle BCA is congruent to angle DAC.
5. By the Alternate Interior Angles Theorem, angle DAC is congruent to angle ZDCA.
6. By the definition of alternate interior angles, angle DCA is congruent to angle ZDCA.
7. By ASA (Angle-Side-Angle) congruence, triangle ABC is congruent to triangle CDA.
8. By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), AB is congruent to CD and BC is congruent to DA.
Therefore, we have proved that in parallelogram ABCD, AB is congruent to CD and BC is congruent to DA.
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the value of X and the relationship between the angles
Answers
Answer:
they are corresponding angles, x=7
Step-by-step explanation:
75=11x-2
77=11x
x=7
Part B: x=7. Set 75 equal to 11x-2 then solve for x
Several steps go into making a doughnut. The dough must be mixed, formed into a doughnut shape, allowed to rise, fried in oil, glazed, and cooled. For each of these steps, there is a possibility for wasted time and materials. What methods might a doughnut restaurant like Krispy Kreme use to decrease lead times and wasted materials? Please explain.
Answers
To decrease lead times and wasted materials, a doughnut restaurant like Krispy Kreme can use methods such as streamlining the production process, implementing precise measurement and mixing techniques, automating proofing, adopting efficient frying techniques, utilizing glazing automation, and optimizing cooling and packaging processes.
To decrease lead times and wasted materials, a doughnut restaurant like Krispy Kreme can implement the following methods:
1. Streamlined Production Process: By optimizing the workflow and layout of the kitchen, Krispy Kreme can reduce unnecessary movement and improve efficiency. This can include organizing the ingredients and equipment in a logical sequence, minimizing the distance between workstations, and ensuring a smooth flow from one step to the next.
2. Precise Measurement and Mixing: Accurate measurement of ingredients and precise mixing techniques can help minimize wasted materials. Using automated measuring systems or standardized measuring tools can ensure consistency and reduce errors. Additionally, adopting efficient mixing methods, such as high-speed mixers, can decrease mixing time and enhance productivity.
3. Proofing Automation: Implementing automated proofing systems can help control the rising process more precisely. These systems can monitor temperature, humidity, and time to ensure optimal conditions for dough proofing. By automating this step, Krispy Kreme can reduce the risk of over-proofing or under-proofing, which can lead to dough waste.
4. Efficient Frying Techniques: Utilizing advanced frying equipment with precise temperature control and oil circulation can reduce cooking time and minimize the amount of oil required. Maintaining consistent frying conditions can also result in evenly cooked doughnuts and reduce the number of rejects.
5. Glazing Automation: Introducing automated glazing systems can help minimize glaze waste and improve consistency. These systems can accurately apply the desired amount of glaze, reducing excess usage and ensuring uniform coating on each doughnut.
6. Cooling and Packaging Optimization: Efficient cooling methods, such as rapid cooling systems or specialized cooling tunnels, can expedite the cooling process without compromising the quality of the doughnuts. Additionally, optimizing packaging processes, including automated packaging machines, can enhance productivity and reduce material waste.
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Which inequality is represented by this graph?
PLS HELP I NEED AN ANSWER ASAP
Answers
Answer:
D
Step-by-step explanation:
It's x is greater than or equal to 4