The function distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
The right response is: The information is categorical and univariate.
The only variable in the data set is the preferred sports among ninth graders. As it includes several categories or groupings, the variable is categorical (i.e., baseball or softball, basketball, lacrosse, soccer, and field hockey). The distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).
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help please!!!!!!!!$!!!
Which of these is a pythagorean triple?
20, 48, 52
10, 26, 89
1, 2, 3
15, 18, 21
The triplets 20, 48, 52 is a Pythagorean triplet.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
We know, Any three numbers to be a Pythagorean triplet,
The sum of the squares of any smaller side must be equal to the square of the third side.
Now, 20² + 48² = 52².
400 + 2304 = 2704
2704 = 2704.
So, The first option 20, 48, 52 it self is a Pythagorean triplet and we don't need to check further options.
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(Quick!) Can you show work as well please?
The value of x would be equal to 20 degrees.
What is linear pair?Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
We are given the parameters as;
7x and (x + 20)
The sum of angle is equal to 180.
7x + (x + 20) = 180
8x + 20 = 180
8x = 180 - 20
8x = 160
x = 160/8
x = 20
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Two hikers, Alan and Ben, are 12.6 miles apart and walking towards each other. They meet in 3 hours. Find the rate of each hiker if Ben walks 0.8 mph faster than Alan.
Alan's rate of speed is _____ mph. (Round to one decimal place.)
Ben's rate of speed is ___ mph. (Round to one decimal place.)
In response to the supplied query, we may state that Ben's speed, equation rounded to one decimal place, is x + 0.8 = 2.5 mph.
What is equation?Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.
Rate times distance
Let x represent Alan's speed in mph. Ben's speed will then be x + 0.8 mph.
They will have travelled 12.6 kilometres in total when they finally cross paths. The formula is as follows:
[tex]12.6 = (x + x + 0.8) × 3\\12.6 = 6x + 2.4 \s10.2 = 6x \sx = 1.7[/tex]
Alan is moving at a speed of 1.7 mph, decimal place included.
Ben's speed, rounded to one decimal place, is x + 0.8 = 2.5 mph.
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Answer:
Alan's rate of speed is 1.7 mph.
Ben's rate of speed is 2.5 mph.
Step-by-step explanation:
We can use the distance-rate-time formula to solve the given problem.
[tex]\boxed{\sf Distance=rate \times time}[/tex]
Create a distance equation for each of the hikers.
AlanDistance = dSpeed = rTime = 3 hoursTherefore, the equation for Alan's distance in terms of r is:
[tex]\implies \sf d = 3r[/tex]
BenDistance = dSpeed = r + 0.8 (as Ben walks 0.8 mph faster than Alan)Time = 3 hoursTherefore, the equation for Ben's distance in terms of r is:
[tex]\implies \sf d = 3(r+0.8)[/tex]
Alan and Ben are 12.6 miles apart and walking toward each other.
Therefore, their combined distances will equal 12.6 miles.
Set the sum of the found expressions for distance equal to 12.6 and solve for r:
[tex]\implies \sf d_{Alan}+d_{Ben}=12.6[/tex]
[tex]\implies \sf 3r+3(r+0.8)=12.6[/tex]
[tex]\implies \sf 3r+3r+2.4=12.6[/tex]
[tex]\implies \sf 6r+2.4=12.6[/tex]
[tex]\implies \sf 6r=10.2[/tex]
[tex]\implies \sf r=1.7[/tex]
Therefore:
Ben = r = 1.7 mphAlan = r + 0.8 = 1.7 + 0.8 = 2.5 mphSolutionAlan's rate of speed is 1.7 mph.
Ben's rate of speed is 2.5 mph.
ami has 9 cups of sand. she shares the sand equally among 12 friends. how much sand does each friend recieve
Answer:4/3
Step-by-step explanation:
Use pythagorean theorem to answer.
The unknown side 'x' is found using pythagorean theorem as: x = 12.69.
Explain about the Pythagorean theorem?The Pythagorean Theorem has a name for Pythagoras of Samos, a religious figure and mathematician who held the view that everything in the cosmos is made up of numbers.
The Pythagoras equation applies to any triangle with a 90° angle solely on a single side.The Pythagorean Theorem states that a right triangle's hypotenuse (the side across from the right angle) has a square that is equal to the sum of its legs.Pythagorean Theorem is also known as:
a²+ b² = c²
Given sides are:
13, 3 and x.
Then,
3²+ x² = 13²
x² = 13² - 3²
x² = 169 - 9
x² = 160
x = √160
x = 12.69
Thus, the unknown side 'x' is found using pythagorean theorem as: x = 12.69.
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Which function is equivalent to y=3(x−2)^2+6?
Answer:
The function y = 3(x - 2)^2 + 6 is in vertex form, which is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola.
In this case, the vertex is (2,6), and the coefficient "a" is 3, so we can write the equivalent function in standard form as follows:
y = 3(x - 2)^2 + 6
y = 3(x^2 - 4x + 4) + 6
y = 3x^2 - 12x + 18
Therefore, the equivalent function in standard form is y = 3x^2 - 12x + 18.
4. Write the function rule for g(x) from f(x) = √x. Shift up 5, then vertical stretch by a factor of 2, followed by a shift to the right 3 units.
This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.
The function rule for g(x) from f(x) = √x can be found by applying the given transformations to f(x). First, we shift up 5 units by adding 5 to the function. Then, we apply a vertical stretch by a factor of 2 by multiplying the function by 2. Finally, we shift to the right 3 units by replacing x with (x - 3) in the function. The resulting function rule for g(x) is:
g(x) = 2√(x - 3) + 5
This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.
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16x^2 - 81=
Factor completely
Answer:
Below
Step-by-step explanation:
(4x- 9)(4x + 9) Just by looking.....
Kyle’s handful of trail mix has 2 almonds, 4 peanuts, 3 raisins, and 5 sunflower seeds. If he picks one item from the handful of trail mix at random, what is the probability that the item is a peanut?
StartFraction 1 over 14 EndFraction
StartFraction 1 over 7 EndFraction
StartFraction 2 over 7 EndFraction
Two-fifths
The answer is Start Fractiοn 2 οver 7 End Fractiοn.
What is Algebraic expressiοn ?Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.
Kyle's handful οf trail mix cοntains a tοtal οf 2 + 4 + 3 + 5 = 14 items.
The prοbability οf picking a peanut is the number οf peanuts in the handful divided by the tοtal number οf items in the handful:
prοbability οf picking a peanut = number οf peanuts / tοtal number οf items
prοbability οf picking a peanut = 4 / 14
Simplifying the fractiοn by dividing bοth the numeratοr and denοminatοr by 2, we get:
prοbability οf picking a peanut = 2 / 7
Therefοre, the answer is StartFractiοn 2 οver 7 EndFractiοn.
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A 2-gallon container of window cleaner costs $34.24. What is the price per quart?
Answer: $4.28 per quart
Step-by-step explanation:
So there is 4 quarts in one gallon. Since there is 2 gallons that means there is 8 quarts total. now you want to take $34.24 and divide it by 8 and you will get $4.28
I need help on this asap!!
Answer: if under 15 miles, then use Red cab company. if over 15 miles, then use Yellow cab company
Step-by-step explanation:
first, need to identify equations for the each cab company.
let X be the mile driven and Y be the fare cost
red cab cost: Y= 1.25X + 3.50
yellow cab cost: Y = 1.15X + 5
I like to use the combination method to eliminate one variable
multiply -1 to one of the equation so -1[ Y= 1.25X + 3.50 ] = -Y = -1.25X -3.50
combine (add) them and eliminate the Y value
-Y = -1.25X - 3.50
Y = 1.15X + 5
-------------------------
0 = -0.1X + 1.5
0.1X = 1.5
X = 1.5/0.1 = 15
input X = 15 to the original equation(s) to find Y
Y = 1.15(15) + 5 = 17.25 +5 = 22.25
Y= 1.25(15) + 3.50 = 18.75 + 3.5 = 22.25
X = 15 miles and Y = $ 22.25
these values represents the red and yellow cab companies will charge the same amount when going exact 15 miles.
What if X is under or over 15 miles?
if X = 10 (under 15 miles)
red cab cost: Y= 1.2(10) + 3.50 = 12 + 3.50 = 15.50 (cheaper)
yellow cab cost: Y = 1.15(10) + 5 = 11.50 + 5 = 16.50
You can test out the X when greater than 15 miles
Conclusion.
if under 15 miles, then use Red cab company. if over 15 miles, then use Yellow cab company
Find the measure of the missing arc lengt. pt. 2
Answer:
100°
Step-by-step explanation:
You want the missing arc measure in the geometry where two chords cross at 85° and they intercept one arc of measure 70°.
Crossing chordsThe angle where chords cross is the average of the two arcs that they intercept. Here, that means ...
85° = (AE +BC)/2
Solving for BC, we get ...
2(85°) = AE +BC
BC = 170° -AE = 100°
The missing arc measure is 100°.
Given: PQ ≈ QS and QS = ST
Prove: PQ = ST
Proof:
Answer:
Proof:
Using the given information, we know that PQ is approximately equal to QS and QS is exactly equal to ST.
Since a value that is approximately equal to another value can be treated as equal in many cases, we can say that PQ is roughly equal to ST.
To prove that PQ is exactly equal to ST, we must use the transitive property of equality.
Transitive Property of Equality: If a = b and b = c, then a = c.
Using the transitive property, we can say:
PQ ≈ QS and QS = ST → PQ ≈ ST
Since PQ is approximately equal to ST and they have the same units of measurement, we can round the values to the same number of decimal places and say:
PQ ≈ ST ≈ rounded value
Therefore, PQ is exactly equal to ST because they have the same rounded value.
Does anyone know how to answer this?
Following surgery, a patient has been receiving a pain relief medication intravenously. The concentration C� (in milligrams per liter) of the medication in the patient's bloodstream t� hours after this process started is given by
C(t)=60t+12t+6,t≥0�(�)=60�+12�+6,�≥0
a) The patient will not receive pain relief unless the concentration of the medication is 1010 or more milligrams per liter. Use this function to determine the time interval for which the concentration of the medication, C� , will be greater than or equal to 1010 milligrams per liter.
The time interval for which the patient will receive pain relief is hours. (Express your answer in interval notation and round any decimals to the nearest tenth of an hour).
The time interval for which the patient will receive pain relief is [1.3, 8.3] hours.
To determine this, we can use the equation C(t) = 60t + 12t + 6, where t is the number of hours after the surgery. Setting C(t) = 1010 and solving for t, we get t = 13.3, so the patient will receive pain relief for t > 13.3 hours, or [1.3, 8.3] hours.
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-3a + 6b = a + 4b what does b equal???
The amount of orange juice that can be obtained from a single orange is normally distributed. A manufacturing company selects an srs of size n
The shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population is approximately Normal
If the amount of orange juice that can be obtained from a single orange is Normally distributed, then the distribution of the sample mean of orange juice obtained from a sample of size 5 from this population will also be Normally distributed.
The mean of the sample mean distribution will be equal to the population mean, which is the mean amount of orange juice that can be obtained from a single orange.
The standard deviation of the sample mean distribution, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size.
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The given question is incomplete, the complete question is:
The amount of orange juice that can be obtained from a single orange is Normally distributed. A manufacturing company selects an SRS of size n = 5 from the population of all oranges in their inventory and calculates the sample mean amount of orange juice that is obtained. What is the shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population?
A line / is said to be tangent to a circle Cat a point P if and only if I meets Cat P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line / passing through P, show that lis tangent to the circle at P if and only if /is perpendicular to the line OP.
Yes, a line / is said to be tangent to a circle at a point P if and only if it meets the circle at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line / passing through P, we can show that / is tangent to the circle at P if and only if it is perpendicular to the line OP.
To show this, first consider a line / that is perpendicular to the line OP. Since the line OP is the line connecting the point P and the center of the circle, O, the line / must intersect the circle at P and nowhere else. This means that / is tangent to the circle at P.
Now, consider a line / that is not perpendicular to the line OP. Since / is not perpendicular to the line OP, it will either intersect the circle at two points or not at all. Since it is not tangent to the circle, it cannot intersect the circle at only one point, P. Therefore, we have shown that a line / is tangent to a circle at a point P if and only if it is perpendicular to the line OP.
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Angle relationships are an important part of furniture design and construction. You will calculate missing angles needed to construct pieces. In each drawing, some measurements are provided. Use angle relationship rules to find the missing angle measurements. Show your work in the boxes below. Note: Drawings are not to scale, so a protractor cannot be used! You may make a few assumptions common to construction:
Angles that appear to be right angles are right angles. Pieces that appear symmetrical are symmetrical.
The measurement of the third angle is 100°.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Given ,
The measurement of one angle in triangle is 30°.
And other angle in triangle is 50°
We have to find,
The measurement of the third angle.
According to the question,
It is a triangle the sum of three angles is 180 degrees.
Now,
Sum of the all the interior angle in right triangle = 180°
30° + 50° + ∠c = 180°
80° + ∠c = 180°
∠c = 180° - 180° = 100°
Hence, The required measurement of the third angle is 100°.
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Let's relax a bit before we keep answering! What's your fav song and singer?
shirt by sza and fav singer ariana grande!
thanks so much!
Answer:
Love The Way You Lie - Eminem
Exit
3-2: Practice & Problem Solving week of 2/27
Find the least common multiple (LCM) for the pair of numbers.
45,7
The LCM of 45 and 7 is
Answer:
315
Step-by-step explanation:
The LCM for 45 and 7 is 315
One way to find the LCM of 7 and 45 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 7?What are the Factors of 45?
Here is the prime factorization of 7:
7171
And this is the prime factorization of 45:
32×5132×51
When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 7, 3, 5
the base of a parallelogram is one third its height if the area is 768 square cm find the base and height
The base and height of the parallelogram is B = 16 cm and H = 48 cm
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the area of the parallelogram be represented as A
Now , area of parallelogram A = bh
And , base of a parallelogram is one third its height
So , B = ( 1/3 )H
And , area of parallelogram is A = 768 cm²
On simplifying , we get
768 = ( 1/3 )H²
Multiply by 3 on both sides , we get
H² = 2304
Taking square roots on both sides , we get
H = 48 cm
So , the height of the parallelogram is 48 cm
And , the base of the parallelogram is 16 cm
Hence , the base and height of the parallelogram are 16 cm and 48 cm respectively
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please help with my this just write the letters in the order it should go in please
The correct match of the accounting terms such as assets, debits, and credit, would be:
Asset - ODebit - KCredit - RCapital - G Liabilities - QCash payments - NProfit - BCash receipts - DOwner's equity - LTransactions - ESole trader - CIncome - Q Expenses - HAccounting equation - F Loss - J Bank - M Subsidiary journal - AWhat are some accounting terms ?This is a matching exercise that matches various accounting terms with their definitions. Here are the meanings of the terms:
Asset: Possessions of the business that can be used to generate income.Debit: An entry on the left-hand side of the ledger that records an increase in assets or a decrease in liabilities.Book of first entry: Also known as a subsidiary journal, this is a book where transactions are first recorded before being transferred to the general ledger.Profit: This is the excess of income over expenses. When income is greater than expenses, the business makes a profit.Sole trader: This refers to a business that is owned and operated by one person.Cash receipts: This refers to transactions that generate cash for the business, such as sales.These are some terms in accounting which are used to ensure that proper records are taken.
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A lighthouse casts a 144-foot shadow. A nearby lamppost that measures 5.5 feet casts an 9-foot shadow. What is the height (in feet) of the lighthouse?
Therefore, the height (in feet) of the lighthouse is 88 feet.
What is an illustration of height?A person's or something's height can be described as their vertical position or their vertical extension (how "tall" they are) (how "high" a point is). For example, "The height of the structure is 50 m" or "The height of an airplane in-flight is roughly 10,000 m".
Let's use proportions to solve the problem. We can set up a ratio of the height of the lighthouse to the length of its shadow, and another ratio of the height of the lamppost to the length of its shadow, and then equate the two ratios:
height of lighthouse / length of shadow of lighthouse = height of lamppost / length of shadow of lamppost
Let's plug in the given values:
h / 144 = 5.5 / 9
To solve for the height of the lighthouse, we can cross-multiply and simplify:
9h = 144 × 5.5
9h = 792
h = 88
Therefore, the height of the lighthouse is 88 feet.
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the techniques of shifting, compressing, stretching, an(d)/(o)r reflecting. g(x)=-x^(3)+7
The techniques of shifting, compressing, stretching, and reflecting can be used to transform the function g(x)=-x^(3)+7.
The techniques of shifting, compressing, stretching, and reflecting are used to transform functions. These techniques allow us to move the graph of a function up, down, left, or right, to make it wider or narrower, and to flip it over the x-axis or y-axis.
The function g(x)=-x^(3)+7 can be transformed using these techniques. For example, we can shift the graph of g(x) up by 2 units by adding 2 to the function: g(x)=-x^(3)+7+2=-x^(3)+9. We can also stretch the graph of g(x) vertically by multiplying the function by a constant greater than 1: g(x)=2(-x^(3)+7)=-2x^(3)+14.
Similarly, we can compress the graph of g(x) vertically by multiplying the function by a constant between 0 and 1: g(x)=0.5(-x^(3)+7)=-0.5x^(3)+3.5. We can also reflect the graph of g(x) over the x-axis by multiplying the function by -1: g(x)=-(-x^(3)+7)=x^(3)-7.
These are just a few examples of how the techniques of shifting, compressing, stretching, and reflecting can be used to transform the function g(x)=-x^(3)+7.
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use the image below to find the requested values?
find the measure of hdg
Answer:
<HDG = 39°
Step-by-step explanation:
Red square is a right angle which mean its a 90°
Those two angle <CDG and <HDG are complementary angle which mean they both add up to 90°
<CDG + <HDG = 90°
51° + (3t+15)° = 90°
Solve for t.
3t + 51 + 15 = 90°
3t + 66 = 90°
3t = 24
t = 8
Plug t = 8 into <HDG to find the measurement.
<HDG = 3t + 15
<HDG = 3*8 + 15
<HDG = 24 + 15
<HDG = 39°
Kendra is making hamburgers for her family barbecue. She has bought three packages of ground beef with masses of 0. 652 kg, 0. 545 kg, and 0. 824 kg. If each hamburger she makes has a mass of about 0. 125 kg, how many whole hamburgers can she make?
If each hamburger she makes has a mass of about 0. 125 kg she can make a maximum of 16 hamburgers with the amount of ground beef she has.
To determine how many hamburgers Kendra can make, we need to divide the total mass of ground beef by the mass of each hamburger:
Total mass of ground beef = 0.652 kg + 0.545 kg + 0.824 kg = 2.021 kg
Number of hamburgers = Total mass of ground beef / Mass of each hamburger
Number of hamburgers = 2.021 kg / 0.125 kg = 16.168
Since Kendra can only make whole hamburgers, she can make a maximum of 16 hamburgers with the amount of ground beef she has.
Calculation of how many items can be made with a given amount of material, based on the mass of each item and the total mass of the material available.
In the context of the question, Kendra has three packages of ground beef with different masses and wants to make hamburgers, each with a specific mass. To determine how many hamburgers she can make, we need to calculate the total mass of ground beef available and then divide it by the mass of each hamburger.
This concept can be applied in many different situations, such as determining how many cookies can be made with a given amount of dough or how many pieces of clothing can be made with a certain amount of fabric. It is a useful skill in cooking, baking, and manufacturing, as it helps to ensure that resources are used efficiently and waste is minimized.
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Please show your work.
The slopes of opposite sides are equal, which means that they are parallel. Therefore, JKLM is a parallelogram.
Opposite sides have different slopes, which means that they are not parallel. Therefore, JKLM cannot be a rhombus because a rhombus is a special case of a parallelogram where all four sides are congruent and opposite sides are parallel.
What are parallelograms and rhombus?A parallelogram is a quadrilateral (a four-sided polygon) in which opposite sides are parallel.
A rhombus is a special type of parallelogram in which all four sides are congruent.
To prove that quadrilateral JKLM is a parallelogram, we need to show that opposite sides are parallel.
We can find the slope of each side by using the formula:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope of JK:
(-5 - 1) / (1 - (-3)) = -6/4 = -3/2
The slope of LM:
(4 - (-2)) / (3 - 7) = 6/-4 = -3/2
The slope of KL:
(-2 - (-5)) / (7 - 1) = 3/6 = 1/2
The slope of MJ:
(1 - (-5)) / (-3 - 1) = 6/-4 = -3/2
We can see that the slopes of opposite sides are equal, which means that they are parallel. Therefore, JKLM is a parallelogram.
To prove that JKLM is not a rhombus, we need to show that at least one pair of opposite sides are not congruent.
We can find the length of each side using the distance formula:
Length of JK:
√[(1 - (-5))² + (1 - (-3))²] = √[36 + 16] = √[52]
Length of KL:
√[(-2 - (-5))² + (7 - 1)²] = √[9 + 36] = √[45]
Length of LM:
√[(4 - (-2))² + (3 - 7)²] = √[36 + 16] = √[52]
Length of MJ:
√[(-5 - 1)² + (-3 - 1)²] = √[36 + 16] = √[52]
We can see that all four sides have the same length, which means that they are congruent. Therefore, JKLM is a rhombus.
However, we can also see that opposite sides have different slopes, which means that they are not parallel. Therefore, JKLM cannot be a rhombus because a rhombus is a special case of a parallelogram where all four sides are congruent and opposite sides are parallel.
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The sum of two numbers is 146. The larger number is 16 less than 5 times the smaller number. What are the numbers
The sum of two numbers is 146. The larger number is 16 less than 5 times the smaller number, the two numbers are 27 and 119.
Let's call the smaller number "x" and the larger number "y". We can write two equations based on the information given:
The sum of two numbers is 146: x + y = 146
The larger number is 16 less than 5 times the smaller number: y = 5x - 16
We can use substitution to solve for one of the variables. Using equation 2, we can solve for y in terms of x:
y = 5x - 16
Now we can substitute this expression for y into equation 1:
x + (5x - 16) = 146
Simplifying this equation, we get: 6x - 16 = 146
Adding 16 to both sides, we get: 6x = 162
Dividing both sides by 6, we get: x = 27
Now we can use equation 2 to solve for y:
y = 5x - 16 = 5(27) - 16 = 119
Therefore, the two numbers are 27 and 119.
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You ask your neighbor to water a sickly plant while you are on vacation. Without water it will die with probability 90%: with water it will die with probability 20%. You are 80% certain that your neighbor will remember to water the plant.
1. What is the probability that the plant will die when you return?
2. If it is dead, what is the probability your neighbor forgot to water it?
You ask your neighbor to water a sickly plant while you are on vacation. Without water it will die with probability 90%: with water it will die with probability 20%. You are 80% certain that your neighbor will remember to water the plant. The probability that the plant will die when you return is 34%. If the plant is dead, the probability that the neighbor forgot to water it is approximately 52.94%.
1. The probability that the plant will die when you return can be calculated using the law of total probability. We need to consider both scenarios, where the neighbor remembers to water the plant and where they forget to water the plant.
P(plant dies) = P(plant dies | neighbor remembers) * P(neighbor remembers) + P(plant dies | neighbor forgets) * P(neighbor forgets)
= (0.20 * 0.80) + (0.90 * 0.20)
= 0.16 + 0.18
= 0.34
So the probability that the plant will die when you return is 34%.
2. If the plant is dead, we need to calculate the probability that the neighbor forgot to water it using Bayes' theorem.
P(neighbor forgets | plant dies) = P(plant dies | neighbor forgets) * P(neighbor forgets) / P(plant dies)
= (0.90 * 0.20) / 0.34
= 0.5294
So if the plant is dead, the probability that the neighbor forgot to water it is approximately 52.94%.
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