Answer: A total of 30 teachers
Step-by-step explanation:
20% = 6 (science) teachers
20x5= 100
6x5=30 teachers
Hope this helps you!
Answer:
30 teachers
20% is 2/10 of 100
20 x 5 = 100
6 x 5 = 30
Therefore, 30 teachers.
What is the slope given points 3/5 and (- 2 4?
The slope of the points (3, -5) and (-2, 4) is -9/5.
Slope in general term means that the elevation or the steepness of any curve. We use slope in order to find the equation of the line between two points. The formula for finding the slope between two points (x₁, y₁) and (x₂, y₂) is expressed as
m = (y₂ - y₁)/(x₂ - x₁)
where m is the slope between the points, y₂ - y₁ is difference between the y coordinates and x₂ - x₁ is the difference between the x coordinates for the same y coordinates.
We have (x₁, y₁) = (3, -5) and (x₂, y₂) = (-2, 4)
So, the slope will be
m = (4 + 5)/(-2 -3)
m = 9/(-5)
m = -9/5 which is the required slope.
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Complete Question:
What is the slope given the points (3, -5) and (-2, 4)?
What is an example of range?
For example, if the given data set is {2, 3, 5, 8, 10, 3, 12, 6, 15}. Then the range will be 15 – 2 = 13.
In the given question, we have to find an example of range.
As we know that;
The group of all possible dependent values that a function or relation can produce from its domain values is known as its range. It consists of every potential output.
The difference between both the highest and lowest numbers in a collection or set is known as the range.
For example, if the given data set is {2, 3, 5, 8, 10, 3, 12, 6, 15}
The largest number of the given set is 15.
The smallest number of the given set is 2.
Then the range will be 15 – 2 = 13.
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Jamie swims 1/2 of the length of the swimming pool every 1/4 of a minute
Answer:
Jamie swims 1/2 the length of the swimming pool every 1/4 of a minute. This means that Jamie swims 1/8 of the length of the pool in one second. If the pool is 25 meters long, it would take Jamie 200 seconds, or about 3 minutes and 20 seconds, to swim the length of the pool. This is just an estimation, as the actual time it would take Jamie to swim the length of the pool would depend on factors such as Jamie's swimming ability and the speed at which they swim.
jeremy can row 3 miles in 12 hours. How long will it take him to row 1 mile
By using division, it can be calculated that
Jeremy can row 1 mile in 4 hours
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem on division
Jeremy can row 3 miles in 12 hours
Jeremy can row 1 mile in [tex]12 \div 3[/tex] = 4 hours
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Given right triangle def, what is the value of sin(e)? three-fifths three-fourths four-fifths four-thirds
The value of sin(e) in the given right angle triangle DEF is 3/5
Given the Right angle DEF,
It is not specified whether angle D= angle F =90°.
Based on the alternatives presented, either base and altitude =3 or 4 and
5 is the hypotenuse.
Case 1. When ∠D=90° In Δ E D F
Sin (E) =altitude/hypotenuse
= 3/5 OR 4/5 [ if base=3, then altitude =4 and if Base =4, Altitude=3]
Case 2. When ∠F=90°, In ΔEFD
Sin (E) =altitude/hypotenuse
= 3/5 or 4/5 [Depending on whether Base =3 then altitude =4, OR Altitude =3 , then Base =4]
Looking at all of the possibilities, 3/5 and 4/5 are accurate.
However, the solution is 3/5, so whether you pick angle D or angle F as 90°, take Altitude=3, Hypotenuse =5, and Base=4.
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Answer:
A. 3/5
Step-by-step explanation:
For right triangle, c^2 = a^2 + b^2
given c = EF = 10, a = DE = 8, b = DF
10^2 = 8^2 + DF^2
DF^2 = 100 - 64 = 36
DF = 6
sin(E) = opposite/hypotenuse = 6/10 = 3/5
Solve the system of linear equations
x + y = 4 2x + 3y = 0 A. x = -6, y = 2 B. x = -1, y = 5 C. x = , y = D. x = 12, y = -8
D. x=12 and y=-8
What is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Given:
[tex]x+y=4\\2x+3y=0[/tex]
from first equation,
[tex]x=4-y[/tex]
substituting this value x in another equation,
[tex]2(4-y)+3y=0\\8-2y+3y=0\\y=-8[/tex]
putting this value of y in [tex]x=4-y[/tex]
[tex]x=4-(-8)\\x=12[/tex]
hence D is the correct option.
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mina 15. a car gets $12$ miles per gallon uphill and $24$ miles per gallon downhill. if the car goes to the top of pike's peak and back ($48$ miles uphill followed by $48$ miles downhill), what is the car's gas mileage, in miles per gallon, for the entire trip?
If the car goes to the top of spike's peak and back, the mileage of the car is 16 miles per gallon
The mileage of car in uphill = 12 miles per gallon
The mileage of car in downhill = 24 miles per gallon
The total distance traveled in up hill = 48 miles
The number of gallon of gas used = 48/12
= 4 gallon
The total distance traveled in down hill = 48 miles
The number of gallon of gas used = 48 / 24
= 2 gallon
Total distance traveled = 48 + 48
= 96 miles
Total number of gallons of gas = 4 + 2
= 6 gallon
The mileage = Total distance / The number of gallon
= 96 / 6
= 16 miles per gallon
Therefore, the mileage of the car is 16 miles per gallon
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What is a synonym for the word split?
Synonym for the word split is given by many words like tear, to break apart, bisect or divide it into parts and so.
Explanation:
Synonym of the given word split is given by:
Many words represents the synonym of the word split.
Tear, separating , fragment , cleave are few words representing the synonym of the word splittingMeaning of the word split in two is given by dividing it into two equal parts, break one part into two equal parts.Bisecting a angle or a line segment into parts is also a splitting.Separating one part of any object from the other is also splitting.For example split number 12 is equal to 3 × 2 × 2.Therefore, the synonym of the given word split is given by cleave, tear, divide it into two equal parts.
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need help asap please!
Answer:
[tex]\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}[/tex]
[tex]\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]
[tex]\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]
[tex]\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=2x-1[/tex]
where:
x is the value rolled on the six-sided die.The sides of the die are labelled 1 to 6.----------------------------------------------------------------------------------------------------
f(1) means the value of the function when x = 1.
Therefore, substitute x = 1 into the given function to find f(1):
[tex]\begin{aligned}x=1 \implies f(1)&=2(1)-1\\&=2-1\\&=1\end{aligned}[/tex]
[tex]\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}[/tex]
----------------------------------------------------------------------------------------------------
f(4.5) means the value of the function when x = 4.5.
Therefore, substitute x = 4.5 into the given function to find f(4.5):
[tex]\begin{aligned}x=4.5 \implies f(4.5)&=2(4.5)-1\\&=9-1\\&=8\end{aligned}[/tex]
As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6. Therefore, rolling a "4.5" does not make sense.
[tex]\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]
----------------------------------------------------------------------------------------------------
f(10) means the value of the function when x = 10.
Therefore, substitute x = 10 into the given function to find f(10):
[tex]\begin{aligned}x=10 \implies f(1)&=2(10)-1\\&=20-1\\&=19\end{aligned}[/tex]
As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6. Therefore, rolling a "10" does not make sense.
[tex]\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]
----------------------------------------------------------------------------------------------------
The domain of a function is the set of all possible x-values.
As the faces of the six-sided die are labelled 1 to 6, the only possible values of x are 1, 2, 3, 4, 5 and 6.
[tex]\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}[/tex]
The domain can also be written as:
[tex]\{x \in \mathbb{N} \; | \; 1 \leq x \leq 6 \}[/tex]
or [tex]\{x \in \mathbb{Z} \; | \; 1 \leq x \leq 6 \}[/tex]
i need help 50 points, please answer correctly
The values of x in the cyclic quadrilateral are 6.67 and 25 and the angle
m∠ ACB is 115°
Cyclic QuadrilateralA cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral. The circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle.
1)
Let's solve to find the value of x
Using proportions;
12/8 = 10 / x
x = 20 / 3
x = 6.67
2) To find x;
(4x + 15)° + (6x + 3)° + 92° = 360°
Sum of angles in a circle is 360°
4x + 15 + 6x + 3 + 92 = 360
10x + 110 = 360
10x = 250
x = 25
To find the value of m ∠ACB in the quadrilateral, we have to evaluate the value of x in the expression = 4x + 15
m∠ ACB = 4(25) + 15
m ∠ ACB = 115°
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What value of x is in the solution set of the inequality –5x – 15 > 10 20x? –2 –1 0 1
We have -2 from the values in the provided solution set, which is the necessary value.
what is solution set?
A solution set is a group of values in mathematics that satisfy a specified set of equations or inequalities. A constrained optimization problem's viable zone is its solution set of constraints.
Given: - 5x - 15 > 10 + 20x
Let's eliminate the variable x in order to solve the inequality.
5 times both sides,
- 5x - 15 + 5x > 10 + 20x + 5x
- 15 > 10 + 25x
Subtracting 10 from both sides
- 15 - 10 > 10 - 10 + 25x
- 25 > 25x
Dividing both sides by - 25
-1 > x
x < - 1
We have -2 from the values in the provided solution set, which is the necessary value.
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Answer:
B
Step-by-step explanation:
The bureau of labor statistics classifies people who would like to work but have given up looking for a job as:______.
People who are looking for a job are unemployed that is the term used by the bureau of labor statistics which classified people who would like to work but have given up .
Step to Step explanation:
People who are jobless and looking for a job are considered in the category of unemployed by the bureau of labor statistics.People in the certain age range and are not working and are looking for a job comes in the category of unemployed.labor force is made by combination of employed and unemployed.Therefore, the people who would like to work but given up who are looking for a job are unemployed classified by bureau of labor statistics.
The complete question is:
The bureau of labor statistics classifies people who would like to work but have given up looking for a job as:______.
a. Unemployed
b. A discouraged worker
c. Not in the labor force
d. Employed
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four fair coins are to be flipped. what is the probability that all four will be heads or all four will be tails? express your answer as a common fraction.
The probability that all four will be heads or all four will be tails is 1/8.
What is probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.Total number of outcomes = 2⁴
Probability of all four will be tails:
P(TTTT) = 1/2⁴
Probability of all four will be heads:
P(HHHH) = 1/2⁴
P(TTTT or HHHH)
= P(TTTT) + P(HHHH)
= 1/2⁴ + 1/2⁴
= 1/16 + 1/16
= 2/16
P(TTTT or HHHH) = 1/8
Hence, the probability that all four will be heads or all four will be tails is 1/8.
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Your mother gave you $13. 31 with which to buy a preent. Thi covered 3 fourth of the cot. How much did the preent cot?
If $13.31 in three fourth of the cost then the cost of the present is $17.747 .
In the question ,
it is given that ,
the amount of money that mother gave to buy the present is = $13.31 ,
the part of cost that the amount covered is = three fourth ,
that means the fraction is 3/4 = 13.31
So , the cost of the present will be = (13.31*4)/3
Simplifying further ,
we get ,
= 53.24/3
Simplifying further ,
we get ,
= 17.746666
rounding off ,
we get,
≈ 17.747
Therefore , the cost of the present is $17.747 .
The given question is incomplete , the complete question is
Your mother gave you $13.31 with which to buy a present. This covered 3 fourth of the cost. How much did the present cost ?
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13. 6x + 2y = 14
please help
Emily is 1.65 meters tall. At 3 p.m., she measures the length of a tree's shadow to be 28.15 meters. She stands 22.9 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Two or more figures are said to be similar if and only if there are common properties of the sides and/or angles of the figures. The height of the tree is 8.85 meters.
How to calulate the height ?Similar shapes have some common properties with respect to either their length of sides or measures of the internal angles. The relationship between similar sides can be expressed as a form of ration. But similarity of two or more shapes does not mean that the shapes are congruent.
In the given question, the construction gives similar triangles. Let the height of the tree be represented by h. Thus by similar properties of the sides of the triangles, we have;
[tex]\frac{1.65}{h}[/tex] = [tex]\frac{5.25}{28.15}[/tex]
h = [tex]\frac{1.65*28.15}{5.25}[/tex]
= 8.8471
h = 8.85 meters
Thus, the height of the tree is 8.85 meters.
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g of the following is the shortest length? question 5 options: 400 pm 4.0 x 10-10 cm 4.0 nm 4.0 x 10-4 m
The shortest length possible in the given question is 4.0×[tex]10^{-10}[/tex] cm .
What is Length?Distance is measured by length. The quantity of length has the dimension of distance in the International System of Quantities. Most measurement systems choose a base unit for length from which all other units are derived. The metre serves as the fundamental unit of length in the International System of Units.
Most people interpret length to mean an object's longest dimension. Nevertheless, depending on the object's position, this is not always the case.
There are several terms for the length of a fixed object, including height, which is also known as vertical length or vertical extent, and width, breadth, or depth. When a base exists from which vertical measurements can be taken, height is used.
Nanometer(nm)- In the International System of Units (SI), a nanometer (American spelling) is a unit of length that is equal to 1000 picometres and one billionth (short scale) of a meter (0.000000001 m).
now , for find the shortest length we can covert all the given units into centimeter,
1 pm = [tex](10)^{-10}[/tex] cm
1 nm = [tex](10)^{-7}[/tex] cm
1 m = 100 cm
we have , 400 pm = 4× [tex](10)^{-8}[/tex] cm
4.0 nm = 4 × [tex](10)^{-7}[/tex] cm
4.0 x [tex](10)^{-4}[/tex]m = 4 × [tex](10)^{-2}[/tex] cm
and 4.0 x [tex](10)^{-10}[/tex] cm
hence , clearly it is shown that shortest length is 4.0 x [tex](10)^{-10}[/tex] cm .
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I need help. I can’t figure this out
∠1 ≅ ∠3 is congruent by AAA postulate where ∠1 and ∠2 form a linear pair and m∠2 + m∠3 = 180
Define congruent.If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
Given,
∠1 and ∠2 form a linear pair
m∠2 + m∠3 = 180
Statements Reasons
∠1 and ∠2 Linear pair
∠1 and ∠3 Linear pair theorem
m∠2 and m∠3 Given
∠3 and ∠2 Definition of supplementary angle
∠1 ≅ ∠3 AAA postulate
∠1 ≅ ∠3 is congruent by AAA postulate where ∠1 and ∠2 form a linear pair and m∠2 + m∠3 = 180
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Two students were climbing stairs at school. Student 1 has a weight of 700 n. Student 2 has a weight of 650 n. How much power would each student have if each took 6 s to climb a 4 m tall flight of stairs?.
The effort you put in while ascending the stairs is equal to the sum of the force you exerted (your weight) and the elevation you moved.
Which is: Work (in joules) is equal to your weight in newtons divided by the stairs' height in meters.
Your Body Weight It goes without saying that moving a heavy object up a flight of stairs takes more strength than moving a light object. However, you still need to push your body weight against gravity even if you don't carry anything. Therefore, the more weight you have, the more power you need to climb the stairs.
Student 1 would have a power of 467 W, while Student 2 would have a power of 433 W. The fourth option—student 1 would have a power of 467 W, while student 2 would have a power of 433 W—is the correct one.
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which type of variable does not change during an experiment, and serves as a comparison point for all data points?
Control variables are the type of variable that does not change during an experiment, and serves as a comparison point for all data points.
Control variables are also called constant variables or control variables.
A control variable in an experiment is a variable that is held constant or controlled by the researcher.
A control variable is a variable or item that the researcher wants to keep constant throughout the study so as not to affect the results.
A typical study design measures the influence of an independent variable on the dependent variable. In order for this to be done properly, it is important to control another external or standardized variable. Experimentation is not as simple as changing factors and recording results. In practice, any study has many different factors that can affect its results. A control variable is a way to keep some of these factors constant so that comparisons are unbiased and transparent.
In many experiments, even slight variations in some factors can lead to inaccurate or skewed results. Voxco's Experimental Research Toolkit aims to give researchers greater control over variables to help them achieve the results they want.
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what do we know about the sizes of the matrices a and b if both of the products ab and ba are defined?
The size of a matrix is its dimension,
AB and BA are of size 4 x 4 and 2 x 2 respectively
Matrix A has dimension 4 x 2 and matrix B has dimension 2 x 4
Matrix:
In mathematics, a matrix (multiple matrices) is a rectangular array or table of numbers, symbols, or formulas, arranged in rows and columns, used to represent mathematical objects or properties of such objects .
Product of Matrix:
Multiplication of two matrices is defined only if the number of columns in the left matrix equals the number of rows in the right matrix. If A is an m-by-n matrix and B is an n-by-p matrix, then its matrix product AB is an m-by-p matrix whose entries correspond to the corresponding rows of A in the matrices.
A column of B whenever a product of different sizes is such that it is defined. The product AB can be defined without BA being defined. That is, if A and B are m-by-n and n-by-k matrices, respectively, and m ≠ k. In general, even if both products are defined, they need not be the same. So, AB ≠ BA,
Product AB:
The dimensions of AB are the rows of matrix A multiplied by the columns of matrix B.
Matrix A has 4 rows and Matrix B has 4 columns.
Therefore, the dimension of the matrix AB is 4 x 4.
Product BA:
The dimensions of matrix BA are the rows of matrix B multiplied by the columns of matrix A.
Matrix B has 2 rows and Matrix A has 2 columns.
Therefore the dimension of the matrix BA is 2 x 2.
Therefore, the sizes of AB and BA are 4 x 4 and 2 x 2 respectively.
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keiko tosses one penny and ephraim tosses two pennies. what is the probability that ephraim gets the same number of heads that keiko gets? express your answer as a common fraction.
The probability that Ephraim gets the same number of heads that Keiko gets is 3/8.
What is probability?
The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.
Here, we
Let K(n) be the probability that Keiko gets n heads, and let E(n) be the probability that Ephriam gets n heads.
K(0) = 1/2
K(1) =1/2
K(2) = 0 (Keiko only has one penny!)
E(0) = 1/2 ×1/2 = 1/4
E(1) = 1/2 ×1/2 + 1/2 ×1/2 = 1/2 (because Ephraim can get HT or TH)
E(2) = 1/2 ×1/2 = 1/4
The probability that Keiko gets 0 heads and Ephriam gets 0 heads is K(0)×E(0). Similarly for 1 head and 2 heads.
We get
P = K(0)× E(0) + K(1)×E(1) + K(2)× E(2)
P = 1/2 ×1/4 + 1/2 ×1/2 +0
P = 3/8
Hence, the probability that Ephraim gets the same number of heads that Keiko gets is 3/8.
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When would you allow a split infinitive and why?
When an adverb requires emphasis or wouldn't fit anyplace else in the sentence, an infinitive should be split. Split infinitive might occasionally help to clarify a sentence's meaning.
In the given question we have to explain, when we allow a split infinitive and why.
When an adverb requires emphasis or wouldn't fit anyplace else in the sentence, an infinitive should be split.
A split infinitive might occasionally help to clarify a sentence's meaning. It is not apparent if the requesting was done softly or whether the leaving should be done quietly in the sentences "I requested her gently to leave" or "I asked her to leave quietly."
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What is the slope of the line that passes through the points (−4,−6) and (1,−6)? Write your answer in simplest form.
Answer:
0
Step-by-step explanation:
The [tex]y[/tex] coordinates are the same, meaning the line is horizontal. Thus, the slope is 0.
40% of the students like music, and 12% of the students like music and dance.what percent of those that like music also like dance?
the students that like music also like dance is 30%.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
40% of the students like music
12% of the students like music and dance.
p(A)=0.4
p(A∩B)=.12
p(A|B)= p(A∩B)/p(A)
=0.4/0.12= 0.3
Hence the students that like music also like dance is 30%.
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Alinewithaslopeof–2passesthroughthepoint (2, –9) . What isitsequationin slope -intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form.
The slope-intercept form of the line is y = - 2x - 5.
What is the slope of a line?
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the Δy and Δx coordinates, respectively. Consequently, it is possible to write the change in y coordinate with respect to the change in x coordinate as m = Δy/Δx.
Given that the slope of the line is -2.
The line passes through the point (2,-9).
The equation of line that passes through (x₁, y₁) with slope m is
y - y₁ = m (x - x₁).
y - (-9) = -2(x -2)
y +9 = -2x + 4
y = -2x - 5
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Are the congruent statements true
Answer:
7. No
8. Yes
Step-by-step explanation:
7. No
For example, sides RS and TQ are not given as congruent, but this statement of congruence makes them congruent.
8. Yes
AB is congruent to CD
BD is congruent to DC
AD is congruent to CD
Triangle ABD is congruent to triangle CDB has all the corresponding parts in the correct order.
is referred to as "energy possessed by an object as a result of its MOTION".
Group of answer choices?
Kinetic Energy is referred to as "energy possessed by an object as a result of its MOTION".
What is Kinetic Energy?
The energy that an item or particle has as a result of its motion is known as kinetic energy. An object accelerates and gains kinetic energy when work—the transfer of energy—is done on it by exerting a net force.
An object in motion always has a velocity, or "v," at any given moment. This energy is referred to as "kinetic energy," and it comes from:
Kinetic Energy = 12×m×v2
Here, m = Mass of the object in motion
Kinetic energy is a type of power that a moving object or particle possesses. An item accumulates kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force. A moving object or particle has kinetic energy, which depends on both its mass and its rate of motion. The type of motion can be vibration, rotation on an axis, translation (or travel along a path from one place to another), or any combination of these.
A body's translational kinetic energy is equal to 1/2mv2, which is the product of its mass, m, and square of its velocity, v.
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1945 men and 2849 women regiter to audition for a inging competition. The number of participant who are not ucceful in their audition what’ five time the number of thoe who are ucceful. How many participant were ucceful
1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799 participants were successful.
The successful participants can be calculate by solving a linear equation as follows
First, it's crucial to understand linear equations.
Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.
Linear equations are those with one degree.
In this case, a linear equation must be resolved.
1945 for the men's total
Women are present in 2849.
Participants in total: 1945 + 2849 = 4794
Let x be the proportion of participants that were successful.
Men who failed were 5 times as numerous.
Participants in total: 5x + x = 6x
Due to the issue,
The linear formula is
6x = 4794
x = 4794/6
x = 799
799 of the participants had success.
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Challenge: Using the 2 functions shown, circle the choice that must be true. Show your work!
The choice that is true are:
f(0) > g(0)
f(6) = g(12)
f(-4) = g(-4)
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 4x + 2
g(x) = (5/2)x - 4
Now,
f(0) = 2
g(0) = -4
f(0) > g(0)
f(6) = 24 + 2 = 26
g(12) = (5/2) x 12 - 4 = 30 - 4 = 26
f(6) = g(12)
f(-4) = -16 + 2 = -14
g(-4) = -10 - 4 = -14
f(-4) = g(-4)
f(2) = 8 + 2= 10
g(2) = 1
f(2) > g(2)
Thus,
f(0) > g(0) is true
f(6) = g(12) is true
f(-4) = g(-4) is true
g(2) > f(2) is not true
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