Answer:
Let A represent the cost of purchasing a pool membership from the Aquatics Club and let S represent the cost of purchasing a pool membership from the Swimming Hole. Then, we can write the following system of inequalities:
A ≤ y
A = 75 + 20x
S ≤ y
S = 15 + 65x
The first two inequalities represent the cost of purchasing a membership from the Aquatics Club, while the last two represent the cost of purchasing a membership from the Swimming Hole. The inequalities ensure that the cost of purchasing a membership from either company does not exceed Alfonso's budget of y dollars.
(x+2)^2=-16 This equation had no solution, why not?
Answer:
It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).
Step-by-step explanation:
The normalized form of the equation
(x+2)^2= - 16
x^2 + 4x + 4 = - 16
x^2 + 4x + 20 = 0
We have in the form ax^2 + abx + c = 0
a = 1
b = 4
c = 20
Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64
Discriminant is negative, therefore, no Real solutions.
pls helllpppp i beg u i reallly need this tysmmm
In linear equation, value of expression is -5 and 0.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
-6d + 4a + 5c/5
1)
d = 1 , a = 1 , c = 3
= -6d + 4a + 5c/5
= -6 * 1 + 4 * -1 + 5 * -3/5
= -6 -4 - 15/5
= -25/5
= -5
2)
d = -10, a = -5 , c = -8
= -6d + 4a + 5c/5
= -6 * -10 + 4 * -5 + 5 * -8/5
= 60 -20 - 40/5
= 60-60/5
= 0
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three cards are drawn with replacement from a standard deck of 52 cards. find the the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability of drawing a diamond, then a black card, and then a face card from a standard deck of 52 cards with replacement is 3/104 or 0.028846 .
What is the probability?The probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card is given by the expression, `(13/52) × (26/52) × (12/52)`.
In a standard deck of 52 cards, there are 13 diamonds, 26 black cards (13 clubs and 13 spades), and 12 face cards (4 Jacks, 4 Queens, and 4 Kings).
To calculate the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card, we use the formula of probability:
`P(E) = n(E) / n(S)`
where, P(E) = Probability of an event
n(E) = Number of favorable outcomes
n(S) = Total number of outcomes
Total number of outcomes = 52
First card will be a diamond
Number of diamonds in a deck of 52 cards = 13
Total number of outcomes after drawing the first card = 52
Probability of drawing a diamond in the first attempt = P(diamond)`= 13/52
Probability of drawing a black card in the second attempt, given that the first card is a diamond= `P(black/diamond)`= (26/52) = `(1/2)`
Probability of drawing a face card in the third attempt, given that the first card is a diamond and second card is a black card= `P(face/diamond and black)`= `(12/52)` = `(3/13)`
Therefore, probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card`= P(diamond) × P(black/diamond) × P(face/diamond and black) = (13/52) × (1/2) × (3/13)= 3/104`
Therefore, the required probability is 3/104 or 0.028846 rounded to the nearest millionth.
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the weights of bunches of bananas in the grocery store are normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. a random sample of four bunches is taken and the mean weight is recorded. which of the following is the mean of the sampling distribution for the mean of all possible samples of size four? a.0.89 b.1.27 c.3.54 d.5.53
The mean of the sampling distribution will be 3.54. Thus, the correct option is C.
The population means is equal to the mean of the sampling distribution for all feasible samples of size 4. In this instance, 3.54 pounds is shown as the population means.
This suggests that the mean weight of the population of banana bunches will be 3.54 pounds if we pick several random samples of size four, compute the mean weight for each sample, and then average those sample means.
The Central Limit Theorem, which asserts that the sampling distribution of the sample means approaches a normal distribution centered on the population mean as the sample size grows, is a fundamental idea in statistics.
Thus, the correct option is C.
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A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume decreases at a rate of 4 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 27 cubic meters.
The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.
To find the rate of change of an edge of the cube, given that the volume decreases at a rate of 4 cubic meters per minute when the volume is exactly 27 cubic meters, follow the solution below:Let the length of the edge of the original cube be L.Let the volume of the original cube be V, such that V = L³.The rate of change of volume is given as -4 m³/min; the negative sign is used to indicate a decrease in volume, and this is obtained when the derivative of the volume with respect to time is multiplied by the negative sign.Let V₀ be the original volume of the cube, and V₁ be the volume after t minutes. Thus, V₁ = V₀ - 4t m³. We are told that V₁ = 27 m³, hence:V₀ - 4t = 27 ⇒ V₀ = 27 + 4t m³Substituting V₀ in terms of t into the expression V = L³, we have:L³ = 27 + 4tTaking the derivative of both sides with respect to t, we have:3L²(dL/dt) = 4 ⇒ dL/dt = 4/(3L²)Substituting L from the expression L³ = 27 + 4t, we have:L = (27 + 4t)^(1/3)Therefore, the rate of change of an edge of the cube is given by the derivative of L with respect to t:dL/dt = 4/(3L²) = 4/(3(27 + 4t)^2/3) ≈ 0.048 m/min (to 3 decimal places)Answer: The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.
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Write this value in order , starting with the smallest 0. 2 1/2 2℅
0, 2%, 2 1/2 The values are ordered from smallest to largest, with 0 being the smallest, followed by 2%, and then 2 1/2.
0 is the smallest value because it represents nothing. It is the absence of a quantity, and therefore, it is always the smallest value.
2% is larger than 0 because it represents a percentage of a whole. Percentages are fractions out of 100, so 2% means 2 out of 100. It is larger than 0, but smaller than 2 1/2.
2 1/2 is the largest value because it represents a whole number and a fraction. It is larger than 2%, because 2 1/2 is equal to 250 out of 10,000 or 25 out of 1,000, which is a larger quantity than 2 out of 100.
Understanding the relative size of different values is an important skill in many areas, including mathematics, science, and finance. Being able to order values from smallest to largest helps us make sense of data and information, and it allows us to make informed decisions based on the relative size of different quantities. It is important to learn how to do this accurately and efficiently in order to be successful in these fields.
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What is the slope of the line passing through the points (4, -6) and (2, 3)?
Answer:
m = -9/2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (4, -6) (2, 3)
We see the y increase by 9, and the x decrease by 2, so the slope is
m = -9/2
Can someone please help me with these, I wasn’t able to attend school cause I have Covid and I don’t know what’s going on. Please please help me
Answer: The answer for the first question goes as follows: Which one(s) have both pairs of opposite sides that are parallel? Rectangle, Rhombus, and square. Which one(s) have both pairs of opposite sides that are congruent? Rectangle, square, and rhombus. Which one(s) have all four sides congruent? Square and rhombus.
The answers to the second question are:
Circumference = pi * diameter. So, the distance around it is 100pi.Area of a circle = pi * r^2. So the area of the theater is 7854.0 ft^2.Step-by-step explanation:
Essentially, all of these parallelograms have different properties and properties that they share. For example, a property they share by the definition of a parallelogram is that all of them have two pairs of opposing sides that are parallel. Another property they share from the definition of a parallelogram is that opposite sides are congruent.
As such, rectangles, squares, and rhombuses have the properties that all parallelograms have because they are all parallelograms. However, they also have their own properties.
Rectangles: A rectangle has the properties of a parallelogram, as well as the property of having all of its angles be right angles. This also makes all of its angles congruent.Rhombuses: Rhombuses have the properties of a parallelogram, and they also have all four of their sides congruent. Squares: Squares are like rhombuses and rectangles put together. They have all of their angles as right angles and they have all four of their sides congruent.Second Question Explanation:
1. The question is describing a theater that has a circular base. Therefore, you can use the formula for the circumference of a circle, pi * diameter, to find the circumference (or distance around) the theater. The diameter is given to you: 100 ft. So just multiply that by pi.
2. The question is asking for the area of the theater. This means that you can use the formula for the area of a circle, A = pi * r^2. Note that it is asking you for the area, not the volume, so you would find the area of the circle, not the volume of the hemisphere. r represents the radius of the circle/theater. The diameter is given as 100 ft, and the radius is half of the diameter, so it is 50 ft. Now just plug the radius into the equation and you get the answer I showed.
Jen’s assignment is to read at least 85 pages of a novel. Jen has read 31 pages. How many pages p does Jen have left to read? Write an inequality that represents this situation. Then solve the inequality
Jen has 54 pages left to read to meet her assignment requirement.
The inequality that represents this situation is p ≥ 85 - 31
To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.
The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:
p = 85 - 31
p = 54
Therefore, Jen has 54 pages left to read.
To represent this situation with an inequality, we can use:
p ≥ 85 - 31
This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).
Solving for p:
p ≥ 85 - 31
p ≥ 54
This means that Jen must read at least 54 more pages to meet her assignment requirement.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
The correct answer is p=62
3. Find the distance from A to B. A(-2,2) B (4,-2)
The distance from points A(-2, 2) to B (4, -2) is equal to √52 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given points into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-2))² + (-2 - 2)²]
Distance = √[(6)² + (-4)²]
Distance = √(36 + 16)
Distance = √52 units.
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give the position of C on this number line
The position of C on the number line is 1/8th position.
Define the term number line?A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.
From the given number line, there are total 8 points between 0 to 1
That means, it's fractions of 8.
Location of point C is on the 1st point,
So, position of C on this number line = (1/8) ÷ (1-0) = 1/8
Therefore, In the number line, C is located in the 1/8th place.
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Please help me as I’m struggling
Therefore , the solution of the given problem of pie chart comes out to be number of adults who selected math (15) outnumbered the number of minors. (10).
Explain pie charts.
A pie chart, also referred to as a circle diagram, is a graphical representation of each of the values of a particular variable or a method to condense a collection of nominal data. (e.g. percentage distribution). A circle with many parts makes up this kind of chart. Each segment represents a particular group.
Here,
for a two-way table: Party A, Party B, and Party C
Men make up 12 8 % of the population while women make up 16 %.
Total 28 15 19
32 ladies make up the group, to start with.
b) 16 female voters plan to support Party A.
Math, English, and science are studied by adults aged 15 to twenty-one and by children aged ten to ten.
Total 25 24 31
15 people selected math.
b) Reeshma is mistaken. The number of adults who selected math (15) outnumbered the number of minors. (10).
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*9. The consultancy Imagination Inc. Is working with its manufacturing client Parts-R-Us to improve their on-time
performance. The firm can earn a bonus of up to $1,000,000 based on how much the on-time performance actually
improves. It's current (baseline) on-time performance is 90%.
The company typically completes approximately 1,000 orders per month, with approximately 100 orders delayed. The
bonus payment is prorated according to the following criteria:
• The on-time performance improvement is calculated based on a reduction in late events or an improvement in on-
time performance.
• No bonus is earned for the first 25% reduction in late events, say from 100 to 75. Maximum bonus is earned once
Parts-R-Us achieves 95% on-time performance.
Please answer the following:
Write down a formula to
determine the total bonus
amount to be received
Using your formula, show
how much bonus would be
paid if Parts-R-Us achieves
94% on-time performance
Parts-R-Us could be eligible for a $0 bonus if it achieves an on-time performance rate of 94% or more.
The company would have to maintain an order delivery rate of 95% in order to qualify for the bonus. If achieved, the bonus would be as follows: Bonus = 94% * (1 - 100).
The following is the calculation for the bonus:
Bonus = P * (1 - D)
Where:
P represents the proportion of orders that are delivered on time.
D represents the total number of orders placed late.
In the event that Parts-R-Us achieves an on-time performance rate of 94%, the bonus would be as follows:
Bonus = 94% * (1 - 100)
Bonus = $0
If the company only managed to complete its tasks 94% of the time, it will not be eligible for a bonus.
In order to qualify for the maximum bonus, Parts-R-Us would have to maintain an on-time delivery rate of 95%.
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please help!!
4.
Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.
a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given.
b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other?
c. What is the measure of the angle between the bikers?
d. What is the relationship between the measure of the angles and the paths the bikers took?
e. Classify the triangle the paths created.
f. How many miles did they travel together?
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
How to solve:The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
They cover almost equal distances from their starting points:
24 miles ≈ √12²+21² miles
b) They encounter each other.
c) The angle at one vertex measures 30 degrees.
d) e) As shown in the attached picture, it is an almost right triangle.
f) Together, they cover a total distance of 57 miles (12+21+24).
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1,500 decagrams = 150 kilograms.
True?
False?
Answer: FALSE
Step-by-step explanation:
1500 decagram = 15 kg
1 decagram = 0.01 kg
1500 decagram = 1500/0.01 kg
= 1500/100 kg
1500 decagram = 15kg
Nonresponse bias occurs when ________.
A) the population has been divided into strata
B) portions of the population are excluded from the sample
C) cluster sampling is used instead of stratified random sampling
D) those responding to a survey or poll differ systematically from the nonrespondents
Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.
Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.
Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.
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Find the greatest common factor and the least common multiple of the following terms. Submit all
solution steps and your final answers to earn full credit.
8a³b5
16a²b7
Answer:
To find the greatest common factor, we need to find the largest factor that divides both terms evenly. We can factor each term as follows:
8a³b5 = 2³ * a³ * b5
16a²b7 = 2⁴ * a² * b7
The greatest common factor is the product of the lowest exponent of each prime factor that appears in both terms. Therefore, the greatest common factor is:
GCF = 2³ * a² * b5 = 8a²b5
To find the least common multiple, we need to find the smallest multiple that both terms share. We can start by writing out the prime factorization of each term:
8a³b5 = 2³ * a³ * b5
16a²b7 = 2⁴ * a² * b7
The least common multiple is the product of the highest exponent of each prime factor that appears in either term. Therefore, the least common multiple is:
LCM = 2⁴ * a³ * b7 = 16a³b7
So, the greatest common factor is 8a²b5 and the least common multiple is 16a³b7.
Find the surface area of the rectangular prism.
6 km
4 km
4 km
Answer: 88km is your answer
Step-by-step explanation: We just had this on a test
Enter the correct answer in the box
Function is shown on the graph in function is the parent quadratic function what is the equation of transtormed function in terms of ?
In quadratic functiοn -
g(x) h(x) d(x)
vertical shift dοwn 3 reflectiοn acrοss the x-axis vertical shift dοwn 3
hοrizοntal shift left 3 vertical strecht οf 3 hοrizοntal shift right 3
What is the οperatiοn οf a quadratic functiοn?The expressiοn f(x) = ax² + bx + c, where a, b, and c are all integers with a nοt equal tο zerο, denοtes a quadratic functiοn. The shape that a quadratic functiοn's graph takes οn is called a parabοla.
In spite οf the fact that parabοlas might have οpenings that are upward οr dοwnward, varying "widths" οr "steepnesses," they all have the same basic "U" shape.
Quadratic parent: f(x)=x²
The graph is a parabοla with vertex V=(0,0) at the οrigin and οpens up.
When x=1→f(1)=1²→f(1)=1
1) g(x)
The graph οpens up, then there is nοt a reflectiοn acrοss the x-axis.
The vertex is at the pοint (-3,-3): 3 units tο the left and 3 units dοwn οf the vertex οf the parent funtiοn.
When x is 1 unit tο the right frοm the vertex g(x)=1
Then the transfοrmatiοns were applied tο the cuadratic parent functiοn are:
1.1) vertical shift dοwn 3.
1.2) hοrizοntal shift left 3.
2) h(x)
The graph οpens dοwn, then there is a reflectiοn acrοss the x-axis.
The vertex is at the οrigin (0,0).
When x is 1 unit tο the right frοm the vertex h(x)=-3
Then the transfοrmatiοns were applied tο the quadratic parent functiοn are:
2.1) reflectiοn acrοss the x-axis.
2.2) vertical strecht οf 3.
3) d(x)
The graph οpens up, then there is nοt a reflectiοn acrοss the x-axis.
The vertex is at the pοint (3,-3): 3 units tο the right and 3 units dοwn οf the vertex οf the parent funtiοn.
When x is 1 unit tο the right frοm the vertex d(x)=1
Then the transfοrmatiοns were applied tο the cuadratic parent functiοn are:
3.1) vertical shift dοwn 3.
3.2) hοrizοntal shift right 3.
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The complete question is -
The given graphs show functions which have been transformed from the quadratic parent, f(x) = x2. Determine which transformations were applied to the quadratic parent function to result in each graph.
PART X: Lost at sea
Suddenly, during your race, a powerful thunderstorm strikes. A wave washes over your boat, shorting out your navigation devices. They wouldn't be much use anyhow, because the lightning is interfering with all communications in the area.
When the storm ends and the sea is calm, you're safe, because you observed all safety precautions, but you have no idea how far off course you are. However, you do know:
* The height of a nearby landmark, which you remember from the tourist center you visited yesterday.
> Mykonos: The light in the Armenistis Lighthouse is 604 feet above sea level.
* The length of your thumb - it's about 2 inches long.
* That you can estimate lengths of less than a foot pretty accurately (to the nearest inch).
1. First, you close one eye and hold your thumb up to block your view of the landmark. You move your thumb nearer and farther from your eye until it just covers the landmark.
Make a sketch showing overlapping triangles ΔEBT and ΔELH to illustrate this situation, where your eye is E, the base of your thumb is B, the tip of your thumb is T, the bottom of the landmark is L, and the top of the landmark is H.
2. Explain why ΔEBT~ΔELH
3. When your thumb covers the landmark, you estimate that it is 10 inches from your eye. Label your drawing with the known measurements.
4. Solve for EL, the distance from your eye to the landmark. Show all work and justify each step.
Answer: 1. Here is a sketch of the overlapping triangles ΔEBT and ΔELH:
H
/|
/ |
/ |
/ |
/ θ |
/____|L
E
|
|
|
|
T
|
|
|
|
B
2. ΔEBT~ΔELH because they have the same shape (both are right triangles with angle θ in common) and their corresponding sides are proportional. Specifically, angle θ is shared by both triangles, angle EBT is a right angle, and angle ELH is a right angle. Therefore, by the Angle-Angle Similarity Theorem, the two triangles are similar. Corresponding sides are proportional because EB/EL = BT/LH (by definition of similar triangles).
3. We are given that BT (the length of the thumb) is about 2 inches. We are also told that the distance from the eye to the landmark (EL) is unknown, but that the distance from the eye to the thumb (EB) is 10 inches (estimated by the person). We are given that LH (the height of the landmark) is 604 feet, or 604*12=7248 inches (since there are 12 inches in a foot). Therefore, we can label the diagram as follows:
7248
/|
/ |
/ | EL
/ |
/ θ |
/____|L
E
|10
|
|
|
T
| 2
|
|
|
|
B
4. To solve for EL, we use the fact that the triangles are similar: EB/EL = BT/LH. Substituting in the known values, we get:
10/EL = 2/7248
5. Multiplying both sides by EL and dividing both sides by 2, we get:
EL = 7248*5 = 36240 inches
Therefore, the distance from the eye to the landmark is 36240/12 = 3020 feet (rounded to the nearest foot).
Step-by-step explanation:
60 identical machines in a factory pack 150 crates of limes per day
between them.
a) Write the ratio of the number of machines to the number of crates
packed per day in the form 1: n.
b) How many crates of limes would 70 of these machines pack per day?
Give any decimals in your answers to 1 d.p.
a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:
Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day
Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.
b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:
1 machine : 2.5 crates/day = 70 machines : x crates/day
Solving for x, we get:
x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day
Therefore, 70 of these machines would pack 175 crates of limes per day.
Step-by-step explanation:
a) The ratio of the number of machines to the number of crates packed per day can be written as:
60 : 150
To simplify this ratio, we can divide both sides by 10:
6 : 15
Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:
1 : 2.5
Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.
b) If 60 machines can pack 150 crates per day, then one machine can pack:
150/60 = 2.5 crates per day
So, 70 machines can pack:
70 × 2.5 = 175 crates per day
Therefore, 70 machines can pack 175 crates of limes per day.
I need some help with this
the solid is really just a right-cylinder missing a chunk.
so a full circle is 360°, now from the one in the picture above we're missing 90°, that means the cylinder is only using 270°, 360-90=270.
Well, 270° is just 3/4 of a full circle, and since the circle extends all the way down the solid cylinder, we can also say that's 3/4 of the volume of the cylinder, so hmmm let's just get the full volume of the cylinder with a radius of 6 and a height of 12 and then only grab 3/4 of it.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2(12)\implies V=432\pi \\\\\\ \stackrel{\textit{now let's just grab }\frac{3}{4}}{432\pi \cdot \cfrac{3}{4}}\implies 324\pi ~~ \approx ~~ \text{\LARGE 1017.88}[/tex]
4.1.60-(15)+(-13 4.2.-2(3)+27 ÷(-3)
Answer:
-15
Step-by-step explanation:
4.1.60 - (15) + (-13) = 32
4.2. -2(3) + 27 ÷ (-3) = -2(3) - 9 = -15
which one do you think is the correct Triangle Congruence Theorem?
These theories are all true and can be used to demonstrate the congruence of two triangles.
what is triangle ?Three straight sides and three angles define the two-dimensional geometric form known as a triangle. It is created by joining three non-collinear plane lines. The three places where a triangle's sides intersect are known as the triangle's vertices, and the line segments that make up the triangle's sides are known as its edges or sides. A triangle's inner angles are always added up to 180 degrees. Triangles can be categorised according to their edges and side lengths.
given
Many triangular congruence theorems exist, and they are all true.
The two triangles are congruent if their two sides and included angles match those of another triangle, according to the Side-Angle-Side (SAS) congruence theory.
The Angle-Side-Angle (ASA) congruence theory states that two triangles are congruent if their included sides and two angles are congruent with one another.
The two triangles are congruent if all three sides of one triangle are congruent with all three sides of the other triangle, according to the Side-Side-Side (SSS) congruence theory.
The right triangles are congruent if their hypotenuses and legs are congruent with those of another right triangle, according to the Hypotenuse-Leg (HL) congruence theory.
These theories are all true and can be used to demonstrate the congruence of two triangles.
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Which operation is used to convert 245 liters to milliliters?
O Multiply by 1,000
O Multiply by 10,000
O Divide by 1,000
O Divide by 10,000
A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Ybe the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by 3. f(x) = { 3/2(x^2 +y^2) 0
Answer:
Step-by-step explanation:
Edith's van can safely carry a maximum land of 920 kilograms.
She wants to use her van to carry
30 sacks of potatoes, each of mass 25 kilograms to the nearest kilogram
and
20 sacks of carots, each of mass 7. 5 kilograms to 1 decimal place
Can she definitely use her van safety in one journey?
You must show your working
(4 marks)
Yes, she can definitely use her van safety in one journey. The total weight is the weight of potatoes plus the weight of carots.
Given,
Number of sacks of potatoes = 30
Mass of each potato = 25
Total weight of Potatoes = 30 * 25
= 750
Number of sacks of carrots = 20
Mass of each Carot = 7.5
Total weight of Carrot = 20 * 7.5
= 150
(The total weight is the weight of potatoes plus the weight of carrots.)
So, total weight = 750 + 150
= 900
The maximum land which Edith can carry safely in the van is 920 kilograms.
∵ 900 < 920
∴ She can use her van safely.
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In a class of students, the following data table summarizes how many students passed
a test and complete the homework due the day of the test. What is the probability that
a student completed the homework given that they failed the test?
Completed the homework
Did not complete the homework
Passed the test Failed the test
8
2
3
сл
The probability that a student completed the homework given that they failed the test is 3/8.
Describe Probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It involves the measurement and analysis of the likelihood or chance of an event occurring. Probability is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.
The concept of probability is used in many fields, such as statistics, physics, finance, and engineering, to make predictions and decisions based on incomplete information. It provides a framework for analyzing situations in which multiple outcomes are possible and assigns a quantitative value to the likelihood of each outcome.
To find the probability that a student completed the homework given that they failed the test, we need to use conditional probability.
Let A be the event that a student completed the homework and B be the event that a student failed the test.
We want to find P(A | B), the probability that a student completed the homework given that they failed the test.
Using the data from the table, we can see that the total number of students who failed the test is 8 (3 who completed the homework and 5 who did not).
Therefore, P(B) = 8/18 = 4/9 (the probability that a student failed the test)
Out of the 8 students who passed the test, 3 also completed the homework, so P(A and not B) = 3/18 = 1/6.
So, P(A | B) = P(A and B) / P(B) = (1/6) / (4/9) = 3/8.
Therefore, the probability that a student completed the homework given that they failed the test is 3/8.
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SOMEONE HELP ME PLEEASSEEEEE I'M IN DESPAIR PLEASE OMG I DON'T UNDERSTAND HOW TO GRAPH THIS BECAUSE OF THE X-AXIS OMG
Answer:
Proofs attached to answer
Step-by-step explanation:
Cant really graph since we don't have access, but here are some pointers.
