The probability that the first two people to leave are science teachers is; 2/15
What is the probability of selection?The parameters about the subject teachers are;
Number of maths teachers = 5
Number of Science Teachers = 6
Number of Social Studies Teachers = 5
Total number of teachers = 5 + 6 + 5
Total teachers = 16
Thus;
Probability that first to leave is a science teacher = 6/15
Probability that after the first leaves, the second to leave will be a science teacher = 5/15
Thus;
P(first two to leave are science teachers) = (6/15) * (5/15)
= 2/15
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Charmaine wants to rent a boat and spend at most $56. The boat costs $6 per hour, and Charmaine has a discount coupon for $4 off. What are the possible numbers of hours Charmaine could rent the boat.
Use t for the number of hours.
Write your answer as an equality solved for t.
determine if (x-3) is a factor of (x^4-13x^2+36) using synthetic division
Answer: x^3+3x^2+22x+66+234/x-3
Step-by-step explanation: I used synthetic division and this is what I got hope this helps
be Maps Desmos) Graphing
Analyzing Intersections of Lines and Planes
y
Z
x
B
Schoology
O
w
A
E
Use the given diagram to answer the question.
Which line is the intersection of two of the planes
shown?
Which line intersects one of the planes shown?
VZv
Which line has points on three of the planes shown?
Note that:
There are three separate planes and three different lines in the diagram. Line X crosses two of the planes, whereas Line Z intersects just one of the planes, and Line Y has points on all three planes.
Line y has points A and B in each of the three planes.
A plane is a flat surface that can be sliced across by a straight line connecting any two locations on the plane.
As a result of the diagram, we may deduce that
Line X is the line that connects two planes.Line Z is the line that intersects one of the planes.Line Y is the line with points on three of the planes displayed.Learn more about Planes:
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A fifth degree polynomial with a root of multiplicity 3 at x = 2, and a root of multiplicity to at x = -3, can be written as the function y=(x - 2) ^a (x - b)^c where:
A=
B=
C=
the y-intercept of this polynomial is (0, )
Note: your answer should be integers.
When a fifth degree polynomial with a root of multiplicity 3 at x = 2, and a root of multiplicity to at x = -3. The polynomial can be written in the form
a = 3, b = -3c = 2How to write the polynomialEach zero's multiplicity is the quantity that indicates how frequently its corresponding factor appears. In other words, the powers are the multiplicities.
The polynomial is expressed as y = (x - 2) ^a (x - b)^c
for x = 2, x - 2, and the multiplicity is 3 hence
(x - 2)³
for x = -3, x + 3 and the multiplicity is will be 2 hence
(x + 3)²
Because of this we can say that
a = 3, b = -3 and c = 2
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$7,300 is invested in an account earning 6.6% interest (APR), compounded
monthly. Write a function showing the value of the account after t years, where the
annual growth rate can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage of
growth per year (APY), to the nearest hundredth of a percent.
Answer:
see below
Step-by-step explanation:
7300 investment
annual rate 6.6% compounded monthly = 6.6/12 months = 0.55% per month
t years = t*12 months
so function is = 7300 * (1+6.6%/12)^12t
APY = (1+0.55%)^12 - 1 = 1.068-1 = 0.068 = 6.8%
What was the closing price for the last trading day?
Answer:
how would i know the closing price ...
i need an answer fast and correct and ill mark for brainiest
The correct orientation and location of triangle DEF is option B (as shown in the attachment to this answer).
Rotation of an object.Rotation is one of the types of solid transformation which involves turning a given object about a reference point or line at a certain required measure of angle. Other types of transformation are: dilation, translation and reflection.
Dilation: This is a process in which the dimensions of an object is either increased or decreased to produce its image.
Translation: This is a procedure that requires moving a given object a number of units in a specified direction.
Reflection: This requires flipping an object over a line to produce an image.
In the question, after rotating triangle ABC 90^o clockwise; the correct orientation and location of triangle DEF is option B.
A sketch of this is attached to this answer for clarity.
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based on the results of the mouse coloration case study, suggest another hypothesis researchers might use to study the role of predators in natural selection.
Researchers might study the role of predators in natural selection by testing the hypothesis that animals with camouflage colorings have a greater chance of survival when they are exposed to predators.
They can do this by setting up an experiment in which they expose animals with different colorings, including camouflage, to predators and then measure the survival rate of the different colorings. This would test if animals with camouflage colorings have a higher chance of survival when they are exposed to predators.
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Sidney made b braided bracelets. she split them evenly among 4 gift boxes. Write an expression that shows how many bracelets were in each box answerlets.
Answer: We can use the distributive property to write an expression that shows how many bracelets were in each box.
Let b be the total number of bracelets that Sidney made.
The number of bracelets in each box can be represented as:
b/4
This expression means that Sidney divided the total number of bracelets she made, represented by b, by 4, the number of gift boxes.
So, the total number of bracelets in each box is b/4 bracelets.
Step-by-step explanation:
a standard football field is 100 yards long from the end zone to the end zone and 160 feet wide. find the area of the field in square yards. hint: read carefully!
To find the football field's area in square yards, we need to multiply the length by the width, both of which are given in different units of measurement (yards and feet).
Steps:
1. Convert the width of the field from feet to yards: 160 feet / 3 feet/yard = 53.33 yards
2. Multiply the length and width of the field to find its area: 100 yards * 53.33 yards = 5,333 square yards. Therefore, the area of the football field is 5333.33 square yards.
The room is square since the length and range of the room are the same. Hence, we can apply the area of the square formula to cipher the area of the given carpet demanded to cover the room. Hence, the answer is 16 square yards.
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The area of the field in square yards will be 16 sq. yards.
To calculate the size of a football field in square yards, multiply the length by the width, which are both given in separate units of measurement (yards and feet).
First, we'll convert the field's width from feet to square yards.
There are 3 feet in 1 yard,
So 160 feet is the same as 160 / 3 = 53.333 yards.
Then we'll multiply the length by the width: 100 * 53.333 = 5333.33 square yards.
Therefore, the area of the football field is 5333.33 square yards.
The room is square since its length and width are equal.
As a result, we can use the area of the square formula to calculate the area of the provided carpet required to cover the room.
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The current population of a small town is
4709
people. It is believed that town's population is tripling every
9
years. Approximate the population of the town
4
years from now.
The number of people in the town in the next four years is 7610.
What is the population growth rate?We know that the population growth rate can be obtained when we apply the exponential growth formula. In this case we would have;
P= Poe^rt
P = Population at time t
Po = Initial population
r = Population growth rate
t = time taken
3(4709) =4709e^9r
3 = e^9r
ln3 = 9r
r = ln3/9
r = 0.12 or 12%
In the next four years;
P =4709e^4 * 0.12
P = 7610
The population can be obtained as 7610.
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Construct segment so that it is perpendicular to segment and segment so that it is perpendicular to segment .
Complete the proof.
The completed proof for the two triangles is as follows -
ST bisects ∠UTV - Given
∠UTS ≅ ∠VTS - Angle Bisection Theorem
∠TUS and ∠TVS are right angles - Given
∠TUS ≅ ∠TVS - All right angles are congruent
ST ≅ ST - Reflexive property of congruence
ΔUTS ≅ ΔVTS - Angle Angle Side (AAS) Theorem
SU ≅ SV - CPCTC Rule
SU = SV - Congruence Theorem
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
Two right angle triangles ΔSUT and ΔSVT are given with line segment ST being the common.
It is given that line segment ST bisects ∠UTV as ST is the common line between the two triangles.
∠UTS ≅ ∠VTS as it is bisected by the line segment ST and it follows the rule of angle bisection theorem.
∠TUS and ∠TVS similar as they both are right-angles which is denoted by the small square symbol in the diagram.
∠TUS ≅ ∠TVS as they both are right-angles and all the right angles are equal and congruent having a measure of 90°.
ST ≅ ST since it is mid line segment of both the triangles and it follows the rule of reflexive property of congruency.
ΔUTS ≅ ΔVTS as they satisfy the AAS theorem, where two angles of a triangle and side between them are equal. Here, ∠UTS ≅ ∠VTS, ∠UTS ≅ ∠VTS and ST ≅ ST.
SU ≅ SV as corresponding parts of the congruent triangles are congruent. So, the CPCTC rule is applied.
SU = SV as they are part of the congruent triangles, so the line segments must be equal.
Therefore, ΔUTS is equal and congruent to ΔVTS.
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Answer: Hope this helps sorry for answering late ^ ^
Step-by-step explanation: i got it right
a software engineer owns 3 pair of pants, 4 shirts, and 3 pair of shoes. How many days can the software engineer go without wearing the same combination of three items?
The number of days a software engineer can go without wearing the same combination of three items will be 36.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
A software engineer owns 3 pairs of pants, 4 shirts, and 3 pairs of shoes. Then the number of different ways is given as,
⇒ ³C₁ × ⁴C₁ × ³C₁
⇒ 3 x 4 x 3
⇒ 36
The number of days a software engineer can go without wearing the same combination of three items will be 36.
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=. A boy walked 7km on a bearing of 060°. Represent this information on a diagram.
A boy walked 7km on a bearing of 60°. Represented this information on a diagram given below.
What are bearing rules in maths?A bearing in mathematics is the angle, measured in degrees and anticlockwise from north. Typically, bearings are given as a three-figure bearing. For instance, 30° clockwise from north is typically expressed as 0°.
"Pieces that aid objects' rotation" are bearings. They support the rotating shaft that moves the machinery. Cars, planes, power generators, and other devices all use bearings.
To lessen friction between two spinning or sliding surfaces, a bearing is a mechanical component.
There are many different types of bearings, including ball and roller bearings, linear bearings, and mounted versions that may use either, and they are used for rotating or linear shaft applications. Bearings are mechanical assemblies that include rolling elements and typically inner and outer races.
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Find three consecutive odd
three times the
integers such that the sum of one times the first,
two times the second, and
third is 334. List the numbers in order from smallest to in largest.
The numbers in order from smallest to in largest are 65.6, 66.6. and 67.6 respectively
What are algebraic expression?Algebraic expression are expressions comprising of terms, variables, coefficients, constants and factors.
These algebraic expressions are also composed of arithmetic operation, such as;
DivisionSubtractionAdditionMultiplicationFloor divisionBracketParenthesesFrom the information given as;
x+1 + 2x + 4 + 2x + 6 = 334
collect like terms
x + 2x + 2x = 334 - 11
add or subtract like terms
5x = 323
Make 'x' the subject of formula
x = 64. 6
The numbers are;
x + 1 = 65.6
x+ 2 = 66. 6
x + 3 = 67. 6
Hence, the numbers are 65.6, 66.6. and 67.6
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which equation can be used to find the scale price, s,of an oil change?
If an oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. The equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).
How to find the sales price?First step is to find the percentage left if he has a coupon for 15% off.
Percentage left = ( 1- 0.15)
Percentage left = 0.85 or 85%
Now let find the sales price
Sales price = 0.85(30)
Sales price = $25.50
Therefore the equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).
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The complete question is:
An oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. Which equation can be used to find the sale price, S, of an oil change?
1. s=0.85 divided by 30
2. s=85 divided by 30
3. s=0.85(30)
4. s=85•30
You are curious about the accuracy of the estimates that the widget store owner gave you. If you wanted to take a random sample of daily customer arrivals, from which of the following is the population you should sample?1 баллThe number of arrivals each day for this widget store and the competing widget store down the street.The number of arrivals each day for all days this specific widget store has been open.The number of arrivals each day for this specific widget over the past month.A random, representative sample of the number of arrivals each day to this specific widget store.
The number of arrivals who came in each day while this particular widget shop was open. Therefore, statement 2 is correct.
The process by which a sample of observations is selected from a population to assume the population is known as random sampling. This process ensures that the results we get from your sample should be close to what we would have gotten if we measured the complete population. So that all the units in the population have an equal chance of being chosen using the simplest random sample.
In the given scenario, the number of arrivals each day for the widget store should have equal chance. To be specific, we should only take into account the number of visitors on the days when the store is open.
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enter the recursive rule for the geometric sequence 2, -6, 18, -54 a1=; an=
The value for a1 in geometric series 2, -6, 18, -54, ..... is a1 = 2, and the recursive formula is a(n) =a^(n-1)·(-3) for n≥2.
What is geometric series?
A geometric series is a collection of terms in mathematics that have an unlimited number and a fixed ratio between each term. A geometric series is typically expressed as a + ar + ar² + ar³ + ..., where r is the common ratio between neighbouring terms and a is the coefficient of each term.
The given geometric series is -
2, -6, 18, -54, ..... (1)
Let A(n) be the geometric series defined in (1).
Then the first term A(1) = 2
The second term A(2) = -6
We need to find the common ratio from one term to the next.
r = common ratio
The formula for r is -
r = subsequent term / previous term = -6/2 = -3
The third term A(3) = 18
The r value for A(3) is -
r = subsequent term / previous term = 18/-6 = -3
The fourth term A(4) = -54
The r value for A(4) is -
r = subsequent term / previous term = -54/18 = -3
The formula for a(n) terms will be -
a(n) =a^(n-1)·(-3)
Therefore, the recursive formula is a(n) =a^(n-1)·(-3).
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Y=21(1.44)^x growth or decay
The exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth when x ∈ N.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex].
Given, An exponential function [tex]Y=21{(1.44)}^x[/tex].
Now, This function can represent growth or decay depending upon the values of 'x'.
If x ∈ N, Then this exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth.
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Can you help me? I could use it.
The ratio of rubies to diamonds is equal to 1:4.
What is a ratio?In Mathematics, a ratio simply refers to a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this scenario, we would assign variables to the number of rubies and number of diamonds as follows;
Let the variable R represent number of rubies.Let the variable D represent number of diamonds.Since the number of rubies is four (4) times the number of diamonds, this can be represented as a ratio as follows;
R = 4D ⇒ R:D = 1:4.
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Please see attached math problem.
a) The table is given below..
b) x + y = 45
c) 5.20x + 9y = 291
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
Cost of small box x = $5.20
Cost of large box y = $9
Now,
Number of boxes sold in one hour = 45
Total amount earned = $291
We can make two equations.
x + y = 45
x = 45 - y
Substituting
5.20x + 9y = 291
5.20 (45 - y) + 9y = 291
234 - 5.20y + 9y = 291
234 + 3.8y = 291
3.8y = 291 - 234
3.8y = 57
y = 15
Now,
x = 45 - y
x = 45 - 15
x = 30
Table:
Categories Value Number Amount
Small box 5.20 30 30 x 5.20 = 156
Large box 9 15 15 x 9 = 135
Thus,
The table is given above.
The equation is x + y = 45
The equation is 5.20x + 9y = 291
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which of the following are correct ways ofg determining of two compound propositions p and q are equailivanet
Two compound propositions p and q are logically equivalent if p↔q is a tautology. Alternatively, p and q are equivalent if and only if the columns in a truth table giving their truth values agree.
Two compound propositions p and q are logically equivalent if and only if p logically implies q and q logically implies p. In other words: two compound propositions are logically equivalent if and only if they have the same truth table.
let us consider,
T be the truth and F be the false of a problem statement.
Then the compound propositions p and q are logically equivalent if :
P q P→q
T T T
F F T
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The complete question is :
What is the correct way of determining of two compound propositions p and q are equivalent.
construct a truth table for p→q if the proposition is tautology.
If RS = x + 5, ST = 14x − 15, and RT = 20, what is RS?
please help as fast as you can.
The Length of RS = 7 units.
Collinear points:The set of points that lie on a straight line is known as Collinear points. In other words, two or more points that lie on the same straight line are said to be Collinear points.
Here we have
RS = x + 5, ST = 14x − 15, and RT = 20
When R, S, and T are considered as 3 collinear points
=> RT = RS + ST
From the given data,
=> 20 = x + 5 + 14x − 15
=> 15x − 10 = 20
=> 15x = 30
=> x = 2
Length of RS = x + 5 = 2 + 5 = 7
Therefore,
The Length of RS = 7 units
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Find the scale factor of W X YI 2 QRST, if both quadrilaterals are similar.
We come to the conclusion that if the scale factor from S to M is 3/2, the scale factor from M to S must be 2/4.
What is the scale factor going from M to S?Assume we have a figure S. If we apply a stretch of scale factor K to our figure S, we may say that all of figure S's dimensions have been multiplied by K.
Following the stretch, we will have a bar of length M, such that:
M = S*K
If the scale factor is 3/2, the following scenario arises:
M = (3/2)*S
In the relationship mentioned above, S can be separated out as follows:
(2/3)*M = S
We now have an equation (similar to the first one).
As of right now, the scaling factor from M to S is 2/3, according to an equation (like the first one).
After that, we draw the conclusion that if the scale factor from S to M is 3/2, the scale factor from M to S must be 2/4.
The complete question is,
Scale factor is 3/2 for the range of S to M. How many are there in the scale from M to S?
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Consider this equation.cos(0)= -2â5/5If 0 is an angle in quadrant II, what is the value of sin(0)?
The value of sin(0) should be considered as the [tex]\frac{\sqrt5}{5}[/tex] in second quadrant.
The values of all trigonometric functions' dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides about any of its acute angles are known as that angle's trigonometric ratios.
Calculation of the value of sin(0):
Since the equation is [tex]cos(o)=\frac{-2\sqrt{5}}{5}[/tex]
by the Pythagorean theorem -
[tex]h^2=p^2+b^2[/tex]
value of perpendicular is = [tex]\sqrt5[/tex].
The trigonometry ratios for a specific angle ‘θ’ is given below:
Trigonometric Ratios:
Sin θ = Perpendicular/Hypotenuse
Cos θ = Base/Hypotenuse
Also in the case when 0 is an angle in quadrant II
So based on this, we can say that value of sin(0) should be considered
as the [tex]\frac{\sqrt5}{5}[/tex].
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simplify 4 x 5p
plssssssss
dont need step by step
Answer:
4 × 5p = 20p
(Multiply the terms; don't have to be like terms)
Reason:
I'm assuming the x refers to multiplication. If so, then 4 x 5 = 4 times 5 = 20. The p doesn't change.
A real world example would be that 5p represents a box with 5 pens inside it. Then imagine 4 such boxes to get 4 x 5 = 20 pens total.
(50 POINTS AND BRAINLYEST)
Recall that the side length of the square was 14 units long. What is the base area of the prism?
Answer:
196 unit squareStep-by-step Explaination:
Area of base section of prism = area of square
Area of square = a²
side = 14 unit
=> (14)²
=> 196 unit square
hope it helps<3due to power failure, components of two states became mixed, given a boc containing both the components and two deectors can tou disginuish the two components
Yes, you can distinguish the two components if you have two detectors. The detectors can measure different properties of the components, such as:
SizeDensityElectrical chargeEven chemical compositionBy using the two detectors and measuring different properties of the components, you can identify which components belong to which state. For example, a detector can measure the size of the components, and another detector can measure the density of the components. If the components from one state have a larger size or a higher density than the components from another state, then the detectors can distinguish between the two components.
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One number is 11 less than another. If their sum is increased by eight, the result is 81. Find the numbers. (Enter your answers as a comma-separated list.)
In a case whereby One number is 11 less than another ,If their sum is increased by eight, the result is 81 the numbers will be 42.
How can the number be determined?The concept that will be used here is summation. A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
Let the first number be wriiten as = x
second number = x-11
The we can add up as :
(x + x -11 + 8) =81
2x -3 =81
2x =84
x = 42
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hash ___ are mathematical functions that create a hash value, also known as a message digest, by converting variable-length messages into a single fixed-length value.
hash functions are mathematical functions that create a hash value, also known as a message digest, by converting variable-length messages into a single fixed-length value.
A hash function converts a given numeric or alphanumeric key into a practical and controllable integer value. The mapped integer value acts as an index in the hash table.
A hash function, in its simplest form, converts a significant number or string into a tiny integer that can be used as the index in the hash table. The pair has the form (key, value), and one can find a value for a given key by using a "function" that converts keys to values.
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