The number of ways can a group of three students be chosen is 20 ways
What are Combinations?The number of ways of selecting r objects from n unlike objects is given by combinations
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the number of ways of selecting students be A
Now , the total number of students = 6
And , to choose 3 students out of 6 without regard to order. The formula for combinations is
n C r = n! / r!(n-r)!
where n is the total number of items, and r is the number of items to choose
6 C 3 = 6! / 3!(6-3)! = 20
Hence , there are 20 ways to choose a group of three students out of six
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The correct number of ways to choose a group of three students from six is [tex]\boxed{20}.[/tex]
To solve this problem, we can use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In our case, we have six students and we want to choose three of them to participate in the spelling bee. The order in which we choose the students does not matter since all three will participate equally.
The formula for calculating combinations is given by:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to that number.
For our problem:
[tex]- $n = 6$[/tex] (total number of students)
[tex]- $k = 3$[/tex] (number of students to choose)
Plugging these values into the formula, we get:
[tex]\[ C(6, 3) = \frac{6!}{3!(6-3)!} \][/tex]
Calculating the factorials, we have:
[tex]\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]
[tex]\[ 3! = 3 \times 2 \times 1 = 6 \][/tex]
[tex]\[ (6-3)! = 3! = 6 \][/tex]
Now, we substitute these values into the combination formula:
[tex]\[ C(6, 3) = \frac{720}{6 \times 6} \][/tex]
[tex]\[ C(6, 3) = \frac{720}{36} \][/tex]
[tex]\[ C(6, 3) = 20 \][/tex]
Therefore, there are 20 different ways to choose a group of three students from six for the spelling bee.
What is 2+2.
15 points
Get it right
ITS 4!! THE ANSWE IS 4!!! BRAINLIEST?!?!
Geometry help? : which triangle could NOT be similar to triangle ABC ?
I think that the answer is the 4th triangle hope this helped.
That would be triangle DEF and the last one (M - -)
The corresponding sides compared with triangle ABC are not in same ratio
A car can travel 105 miles on 7 gallons of gas. How far can it travel on 9 gallons
Find how far the car can travel on one gallon of gas, by dividing total miles by number of gallons:
105 miles / 7 gallons = 15 miles per gallon.
Now multiply that by the number of gallons to find total miles:
15 miles per gallon x 9 gallons = 135 total miles.
An expression involves subtracting two numbers from a given first number under what circumstance will the value of the expression be negative
Final answer:
The value of an expression will be negative when the sum of the two numbers subtracted from a given first number is greater than the initial number itself, resulting in a negative outcome after applying the appropriate rules for addition and subtraction.
Explanation:
The value of an expression involving the subtraction of two numbers from a given first number will be negative under specific conditions. When the combination of the two numbers to be subtracted is larger than the first number, the result will be negative. To understand this, let's consider the basic rules of addition and subtraction with positive and negative numbers:
When two positive numbers add, the result has a positive (+ve) sign. For example, 3+2 = 5.When two negative numbers add, the result has a negative (−ve) sign. For example, -4 + (-2) = -6.When two numbers having opposite signs add, subtract the smaller number from the larger number, and the result has the sign of the larger number. For example, -5 + 3 = -2.In subtraction, we change the sign of the number being subtracted and then apply the rules of addition:
5 - (+3) = 5 - 3 = 2, where the sign of 3 is changed from positive to negative before adding.2 - (-6) = 2 + 6 = 8, where the sign of -6 is changed to positive before adding.Therefore, to have a negative result, the magnitude of the sum of the two numbers being subtracted should exceed the first number and, reflecting the sign rules, should result in a negative value. For instance, if the first number is 1 and the two numbers to subtract are 3 and 5, the expression would be 1 - (3 + 5) = 1 - 8 = -7, resulting in a negative value.
The driver of a car travels 150 miles to reach his destination. If he travels 60.0 mi/h for 100.0 miles and 55.0 mi/h for the remaining 50.0 miles, how long does it take for him to reach his destination
I think the answer is 2.7 hours
Using the formula Time = Distance ÷ Speed, we find that the driver would spend approximately 1.67 hours on the first 100 miles and 0.91 hours on the last 50 miles. Adding these two times gives a total travel time of approximately 2.58 hours.
Explanation:The first thing you need to do is calculate the time spent in each part of the trip. To calculate time, we use the formula Time = Distance ÷ Speed. For the first 100 miles at 60 mi/h, it takes: Time = 100 miles ÷ 60 mi/h = 1.67 hours. Moving on to the next 50 miles at 55 mi/h, it takes: Time = 50 miles ÷ 55 mi/h = 0.91 hours.
Adding these two times together gives us the total time for the trip: 1.67 hours + 0.91 hours = 2.58 hours. So, the driver would take approximately 2.58 hours to reach his destination if he traveled 100 miles at 60 mi/h and the remaining 50 miles at 55 mi/h.
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find an equation of a line containing the points (-6,1) and (2,-5).
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 6, 1 ) and (x₂, y₂ ) = (2, - 5 )
m = [tex]\frac{-5-1}{2+6}[/tex] = [tex]\frac{-6}{8}[/tex] = - [tex]\frac{3}{4}[/tex]
the partial equation is
y = - [tex]\frac{3}{4}[/tex] x + c
to find c substitute either of the 2 given points into the partial equation
using (- 6, 1 ), then
1 = [tex]\frac{9}{2}[/tex] + c ⇒ c = 1 - [tex]\frac{9}{2}[/tex] = - [tex]\frac{7}{2}[/tex]
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← equation of line
Please help with geometry homework!!!!!
Answer: First option 120 sq.in
Solution:
Perimeter of the base of the prism: p=20"=20 in
Height of the prism: h=6"=6 in
Lateral area of the prism: Al=?
Al=p*h
Replacing the known values in the formula above:
Al=(20 in)*(6 in)
Al=120 sq.in
The line for which equation has a negative slope?
A. y = 6
B. y = -5x
C. y = 2x + 5
What is the slope of the line represented by -14y = 7x ?
A. −2
B. 1/2 negative
C. 2
Question 3
What is the approximate solution of the following system of equations?
graph of lines y equals negative x minus 5 and y equals x plus 9
(2, -7)
(-7, 2)
(7, 2)
(-7, -2)
answer is (-7,2)
y = -x -5
y= x+9
Both equations have y on the left hand side
So we equate both equations
We replace -x-5 for y in the second equation
-x -5 = x+9
Subtract x on both sides
-2x -5 = 9
Now add 5 on both sides
-2x = 14
Divide by -2 from both sides
x = -7
Now plug in -7 for x in the first equation
y = -x -5
y = -(-7) -5= 7-5 = 2
So answer is (-7,2)
1. You have the following system of equations:
[tex]\left \{ {{y=-x-5} \atop {y=x+9}} \right.[/tex]
2. Therefore, you have that [tex]y=y[/tex], then:
[tex]-x-5=x+9[/tex]
3. Solve for [tex]x[/tex]:
[tex]-5-9=x+x\\2x=-14\\x=-7[/tex]
3. Now, substitute this value into one the original equations:
[tex]y=x+9\\y=-7+9\\y=2[/tex]
The answer is: (-7,2)
A local club team is holding tryouts for six spots on the soccer team. Since there is not much time before a very important tournament they need to select the best players. Which method would be the best to ensure they select the "most talented" soccer players?
The method would be the best to ensure they select the "most talented" soccer players is They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top six from the list.
The correct option is (A).
A. This method involves observing the players during tryouts and then ranking them from the most skilled to the least skilled. By selecting the top six players from this ranked list, the team is more likely to pick the most talented individuals based on their performance and skills demonstrated during the tryouts.
Option B (selecting the first six that show up) may not necessarily guarantee selecting the most talented players as eagerness to show up early does not always correlate with soccer skills.
Option C (selecting randomly from a hat) is not ideal because it does not take into account the players' actual skills and performance during tryouts. It relies solely on chance.
Option D (selecting the top three and bottom three) may overlook potentially talented players who fall in the middle range. Additionally, selecting the bottom three solely based on being the least skilled may not be fair or accurate.
Therefore, option A is the most suitable method for ensuring the selection of the "most talented" soccer players.
complete question given below:
A local club team is holding tryouts for six spots on the soccer team. Since there is not much time before a very important tournament they need to select the best players. Which method would be the best to ensure they select the "most talented" soccer players?
A. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top six from the list.
B. The first day of tryouts they select the first six that show up as they figure those are the most eager for a spot.
C. They place all of the names of the people trying out in a hat and theselect six out of the hat. Those are the ones that are chosen.
D. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top three and the bottom three from the list.
Utilize open tryouts, structured evaluations, scouting, fitness assessments, game simulations, background checks, objective evaluation, expert consultation, feedback, and review.
To ensure the selection of the most talented soccer players for the local club team, the following method can be adopted:
1. **Open Tryouts**: Organize open tryouts where any interested player can participate. This allows for a wide pool of talent to be assessed.
2. **Structured Evaluation**: Develop a structured evaluation system that includes various aspects of soccer skills such as dribbling, passing, shooting, defending, and game intelligence. Each player should be assessed on these criteria.
3. **Scouting**: Utilize scouts who have a keen eye for talent to observe players in local leagues, school teams, or other relevant competitions. They can provide insights into players who may not have attended the tryouts.
4. **Physical Fitness Assessment**: Soccer requires a good level of physical fitness. Conduct physical fitness assessments to gauge players' endurance, speed, agility, and strength.
5. **Game Simulations**: Organize scrimmages or small-sided games during tryouts to see how players perform in real-game situations. This can reveal their decision-making abilities, teamwork skills, and adaptability.
6. **Background Checks**: Consider players' past performances, achievements, and behavioral aspects. Look for players who demonstrate dedication, discipline, and a positive attitude.
7. **Objective Evaluation**: Ensure that the selection process is fair and transparent, with scores and assessments being recorded objectively. Avoid biases based on personal preferences or relationships.
8. **Consult Coaches and Experts**: Involve experienced coaches or soccer experts in the selection process. They can provide valuable insights and perspectives on players' potential and suitability for the team.
9. **Feedback and Review**: Provide feedback to players after the tryouts, highlighting areas of improvement and offering guidance for future development. Additionally, periodically review the selected players' performance to ensure they continue to meet the team's standards.
By combining these methods, the local club team can maximize the chances of selecting the most talented soccer players for their upcoming tournament.
Draw 3 rows with 2 counters in each row. Write a word problem to that can be acted out using these counters
A triangle has side lengths of 6, 8, and 5. Is it a right, acute or obtuse triangle
Write three numbers that are greater than 12,000 but less than 13,000
The answers to your question are,
12,001, 12,562, 12,999
-Mabel <3
12,001, 12,562, 12,999 .
Is your answers, hope this helps.
~hEcKiNsHoBe
Can someone Please help with this Geometry question, thanks!
The length of CD is -9 to 7 = 16 units long
CE is 1/4 of that length, so 16 x 1/4 = 4 units long.
Add 4 to C: -9 + 4 = -5
Point E would be located at -5.
Find the slope. If you don't know the answer, don't waste my points, please.
One month julia collected 8.4 gallons of rainwater. That month she used 5.2 gallons of rainwater to water her garden and 6.5 gallons of rainwater to water flowers.How much was the supply of rainwater increased or decreased by the end of the month
Given
One month julia collected 8.4 gallons of rainwater.
she used 5.2 gallons of rainwater to water her garden
6.5 gallons of rainwater to water flowers
Find out how much was the supply of rainwater increased or decreased by the end of the month.
To proof
As given in the question
One month julia collected 8.4 gallons of rainwater
she used 5.2 gallons of rainwater to water her garden and 6.5 gallons of rainwater to water flowers
Total water she used in the month = 5.2 gallons + 6.5gallons
= 11.7 gallons
Let the supply of rainwater increased or decreased by the end of the month
be x .
Than the equation become in the form
x + 8.4 = 11.7
x = 3.3 gallons
Therefore the supply of rainwater increased or decreased by the end of the month is 3.3 gallons.
Hence proved
Total rainwater collected by Julia = 8.4 gallons
Water used for watering garden = 5.2 gallons
Water used for watering flowers = 6.5 gallons
Hence, total water used by Julia = [tex]5.2+6.5=11.7[/tex] gallons
11.7 gallons were used and only 8.4 gallons were collected , so supply of rainwater decreased by [tex]11.7-8.4=3.3[/tex] gallons
Which equations are correct? Select each correct answer. −5a4(2a2+4)=−10a6−20a4 −4x2(2x2+5)=−8x4−20x2 −6y4(4y2+2)=−24y8−12y4 −4b3(5b2+3)=−20b6−12b3
1. Consider the expression [tex]-5a^4(2a^2+4)=-10a^6-20a^4.[/tex]
Start with left side and use dustributive property :
[tex]-5a^4(2a^2+4)=-5a^4\cdot 2a^2-5a^4\cdot 4=-10a^6-20a^4.[/tex]
This option is true.
2. Consider the expression [tex]-4x^2(2x^2+5)=-8x^4-20x^2.[/tex]
Start with left side and use dustributive property :
[tex]-4x^2(2x^2+5)=-4x^2\cdot 2x^2-4x^2\cdot 5=-8x^4-20x^2.[/tex]
This option is true.
3. Consider the expression [tex]-6y^4(4y^2+2)=-24y^8-12y^4.[/tex]
Start with left side and use dustributive property :
[tex]-6y^4(4y^2+2)=-6y^4\cdot 4y^2-6y^4\cdot 2=-24y^6-12y^4\neq -24y^8-12y^4.[/tex]
This option is false.
4. Consider the expression [tex]-4b^3(5b^2+3)=-20b^6-12b^3.[/tex]
Start with left side and use dustributive property :
[tex]-4b^3(5b^2+3)=-4b^3\cdot 5b^2-4b^3\cdot 3=-20b^5-12b^3\neq -20b^6-12b^3.[/tex]
This option is false.
Answer: A, B - true, C, D - false.
Answer
−5a⁴(2a²+4)=−10a⁶−20a⁴ is correct.
−4x²(2x²+5)=−8x⁴−20x² is correct.
−6y⁴(4y²+2)=−24y⁸−12y⁴ is NOT correct.
−4b³(5b²+3)=−20b⁶−12b³ is NOT correct.
Explanation
Equation 1
−5a⁴(2a²+4)=−10a⁶−20a² ⇒ −5a⁴(2a²+4) = ( −5a⁴×2a²)+ ( −5a⁴×4)
= -10a⁶ - 20a⁴
−5a⁴(2a²+4)=−10a⁶−20a² is correct
Equation 2
−4x²(2x²+5)=−8x⁴−20x² ⇒ −4x²(2x²+5) = (-4x²×2x²) + (-4x²×5)
= -8x⁴ - 20x²
−4x²(2x²+5)=−8x⁴−20x² is correct.
Equation 3
−6y⁴(4y²+2)=−24y⁸−12y⁴ ⇒ −6y⁴(4y²+2) = (−6y⁴×4y²) + (-6y⁴×2)
= -24y⁶ - 12y⁴
−6y⁴(4y²+2)=−24y⁸−12y⁴ is NOT correct.
Equation 4
−4b³(5b²+3)=−20b⁶−12b³ ⇒ −4b³(5b²+3) = (−4b³×5b²) + (-4b³×3)
= -20b⁵ - 12b³
−4b³(5b²+3)=−20b⁶−12b³ is NOT correct.
RS=6y+5,ST=2y-3, and RT=12y-14
Find Y.
._______.___.
R S T
Note that RT is the whole line segment, and RS and ST are parts of it
RS = 6y + 5
ST = 2y - 3
RT = 12y - 14
Set the equation
RS + ST = RT
(6y + 5) + (2y - 3) = 12y - 14
Simplify. Combine like terms
6y + 2y + 5 - 3 = 12y - 14
(6y + 2y) + (5 - 3) = 12y - 14
8y + 2 = 12y - 14
Note the equal sign. What you do to one side, you do to the other. Isolate the variable (y). Subtract 12y from both sides, and 2 from both sides.
8y (-12y) + 2 (-2) = 12y (-12y) - 14 (-2)
8y - 12y = -14 - 2
Simplify. Combine like terms
(8y - 12y) = (-14 - 2)
-4y = -16
Isolate the y. Divide -4 from both sides
-4y/-4 = -16/-4
y = (-16)/-4
y = 4
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4 is your answer for y.
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hope this helps
The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.654
What percent of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers?
Answer:
42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.
Step-by-step explanation:
The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.654
For finding the percent of the variation in one variable explained by the other variable, we just need to take square of the correlation coefficient.
Here, [tex]r=0.654[/tex]
So, [tex]r^2 = (0.654)^2 = 0.427716[/tex]
Now, for converting it into percentage, we will multiply it by 100.
So, [tex]0.427716*100\% = 42.7716 \%[/tex]
Thus, 42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.
Final answer:
About 42.8% of the variation in the bags of trash collected can be attributed to the number of volunteers, as indicated by the squared correlation coefficient (0.654²).
Explanation:
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. When squared to calculate the coefficient of determination (r²), it represents the proportion of the variance in the dependent variable that is predictable from the independent variable. In the given scenario, with a correlation coefficient of 0.654, the coefficient of determination would be 0.654², which calculates to approximately 42.8%. This percentage indicates that about 42.8% of the variation in the number of bags of trash collected (y) can be explained by the variation in the number of volunteers (x).
What is the explicit formula for this geometric sequence
27,9,3,1
Answer:
an=27*(1/3)^(n-1)
Step-by-step explanation:APEX
The correct option is B.
Geometric Progression,A geometric progression is a sequence in which every next term of the sequence is found out by multiplying the previous term by a fixed ratio.
Any nth term of the sequence is found out the formula,
[tex]a_n = a_1 \times r^{n-1}[/tex],
where,
[tex]a_n[/tex] is the nth term,
[tex]a_1[/tex] is the first term,
r is the fixed common ratio.
Given to us,Sequence, 27, 9, 3, 1.
the first term, [tex]a_1[/tex]= 27,
As we can see from the series 27, 9, 3, 1. the series is a geometric series,
And can be written as [tex]3^3,\ 3^2,\ 3^1\ ,3^0[/tex].
therefore, will follow the formula of a geometric series.
[tex]a_n = a_1 \times r^{n-1}[/tex],
Ratiowe know the value of r can be found out using the formula,
[tex]r = \dfrac{a_{n}}{a_{n-1}}}[/tex]
taking n =2,
[tex]r = \dfrac{a_{2}}{a_{2-1}}} = \dfrac{a_{2}}{a_{1}}}= \dfrac{9}{27} = \dfrac{1}{3}[/tex]
SubstitutingSubstituting the values in the formula of geometric progression we get,
[tex]a_n = a_1 \times r^{n-1}\\a_n = 27\times {\dfrac{1}{3}}^{n-1}\\a_n = (27)\times ({\dfrac{1}{3}})^{n-1}[/tex]
Therefore, the correct option is B.
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please help asap 25 pts
[tex]4(k+5)=2(9k-4)\qquad|\text{use distributive property}\\\\(4)(k)+(4)(5)=(2)(9k)+(2)(-4)\\\\4k+20=18k-8\qquad|\text{subtract 20 from both sides}\\\\4k=18k-28\qquad|\text{subtract 18k from both sides}\\\\-14k=-28\qquad|\text{divide both sides by -14}\\\\\boxed{k=2}\to\boxed{d.}[/tex]
Without using a calculator, determine between which two consecutive integers the square root lies _/29
5 and 6
√25 = 5 and √36 = 6
5 < √29 < 6
Naomi starts the engine on her small private airplane. The engine drives a propeller with a radius of 8 feet and its centerline 13 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 700 revolutions per minute. The height of one propeller tip as a function of time is given by h = 13 + 8 sin(700t), where h is the height in feet and t is the time in minutes. Use degrees to find h when t = 4 minutes.
Answer:
5.13 feet
Step-by-step explanation:
Engine is driving the propeller with a radius of 8 feet and its centerline 13 feet above the ground.
And the speed is 700 revolutions per minute, the height of one propeller tip as a function of time is given by:
[tex]h=13+8 \sin(700t)[/tex]
We have been asked to find the value of height, 'h', when t=4 minutes.
Plugging the value of time, 't', in the equation, we already know that we need to use degrees (not radians) we get:
[tex]h=13+8 \sin (700 \times 4)[/tex]
[tex]h=13+8 \sin (2800)[/tex]
[tex]h=13+8 \times (-0.984)[/tex]
[tex]h=13+(-7.872)[/tex]
[tex]h=13-7.872[/tex]
[tex]h=5.128\approx 5.13[/tex]
So the height of one propeller tip at t=4 minutes is 5.13 feet.
The question is in the attached below , thank you for helping me .
I' just going to type some of it so if there is someone in the future can find it
3. AB ~= CE
4. CE ~= AC
5. Definition of isosceles triangle
6. Transitive Property of Congruence
What is 0.79 x 3.7 with an explanation?
My answer for 0.79 x 3.7 is 2.923. It is 2.923 because when you do the problem on paper that is what you get. Also not to be rude or nothing im good at math.
[tex]Solution, 0.79\cdot \:3.7=2.923[/tex]
[tex]Steps:[/tex]
[tex]\mathrm{Multiply\:without\:the\:decimal\:points,\:then\:put\:the\:decimal\:point\:in\:the\:answer}, 79\cdot \:37=2923[/tex]
[tex]79\cdot \:37, \mathrm{Line\:up\:the\:numbers}, \begin{matrix}\space\space&7&9\\ \mathrm{x}&3&7\end{matrix}[/tex]
[tex]\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}, \begin{matrix}\space\space&\textbf{7}&\textbf{9}\\ \mathrm{x}&3&\textbf{7}\end{matrix}[/tex]
[tex]\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:9\cdot \:7=63[/tex][tex]\mathrm{Carry\:}6\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}3\mathrm{\:in\:the\:result\:line}[/tex][tex]\frac{\begin{matrix}\space\space&6&\space\space\\ \space\space&7&\textbf{9}\\ \mathrm{x}&3&\textbf{7}\end{matrix}}{\begin{matrix}\space\space&\space\space&3\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:6+7\cdot \:7=55[/tex], [tex]\mathrm{Carry\:}5\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}5\mathrm{\:in\:the\:result\:line}, \frac{\begin{matrix}\space\space&5&\textbf{6}&\space\space\\ \space\space&\space\space&\textbf{7}&9\\ \mathrm{x}&\space\space&3&\textbf{7}\end{matrix}}{\begin{matrix}\space\space&\space\space&5&3\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:digit,\:}5\mathrm{,\:to\:the\:result}, \frac{\begin{matrix}\space\space&5&6&\space\space\\ \space\space&\space\space&7&9\\ \mathrm{x}&\space\space&3&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&\textbf{7}&\textbf{9}\\ \space\space&\mathrm{x}&\textbf{3}&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&2&\space\space\\ \space\space&\space\space&7&\textbf{9}\\ \space\space&\mathrm{x}&\textbf{3}&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\\ \space\space&\space\space&7&\space\space\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&2&\textbf{2}&\space\space\\ \space\space&\space\space&\textbf{7}&9\\ \mathrm{x}&\space\space&\textbf{3}&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\\ \space\space&3&7&\space\space\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&2&2&\space\space\\ \space\space&\space\space&7&9\\ \mathrm{x}&\space\space&3&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\\ 2&3&7&\space\space\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&7&9\\ \space\space&\mathrm{x}&3&7\end{matrix}}{\begin{matrix}0&5&5&3\\ 2&3&7&0\end{matrix}}[/tex]
553+2370=2923, =2.923
Consider two functions: g(x)=x2 and the linear function f(x) with slope 1 and y-intercept of 0.
Which statements are true?
Select each correct answer.
f(−1) is equal to g(−1) .
f(1) is equal to g(1) .
f(x) is greater than g(x) on the interval (0,1) .
g(x) has a greater y-intercept than f(x) does.
ANSWER
The correct answers are option B and C
EXPLANATION
A linear function with slope [tex]m=1[/tex] and y - intercept [tex]0[/tex] has equation, [tex]f(x)=x[/tex]
Option A
[tex]f(-1)=-1[/tex]
[tex]g(-1)=(-1)^2=1[/tex]
Therefore [tex]f(-1) \ne g(-1)[/tex]
Option B
[tex]f(1)=1[/tex]
[tex]g(1)=(1)^2=1[/tex]
Therefore [tex]f(1) = g(1)[/tex]
Option C
[tex]f(0.5)=0.5[/tex]
[tex]g(0.5)=(0.5)^2=0.25[/tex]
Therefore [tex]f(x) > g(x)[/tex]
on [tex](0,1)[/tex] See graph also.
Option D
At y-intercept, [tex]x=0[/tex]
This implies that,
[tex]f(0)=0[/tex]
[tex]g(0)=(0)^2=0[/tex]
Therefore g(x) does not have a greater y-intercept.
The function f(x) with a slope of 1 and a y-intercept of 0 is compared with the quadratic function g(x)=x^2. f(1) is equal to g(1) and f(x) is greater than g(x) on the interval (0,1).
Explanation:The function g(x)=x^2 is a quadratic function, and the function f(x) with a slope of 1 and a y-intercept of 0 is a linear function. Let's evaluate the given statements:
f(-1) is equal to g(-1). To evaluate this, substitute -1 into both functions: f(-1) = -1(1) + 0 = -1, and g(-1) = (-1)^2 = 1. Since -1 is not equal to 1, this statement is false.f(1) is equal to g(1). Again, substitute 1 into both functions: f(1) = 1(1) + 0 = 1, and g(1) = 1^2 = 1. Since 1 is equal to 1, this statement is true.f(x) is greater than g(x) on the interval (0,1). To determine this, we need to compare the values of f(x) and g(x) on the interval (0,1). Evaluating both functions at x = 0.5, we get f(0.5) = 0.5(1) + 0 = 0.5 and g(0.5) = 0.5^2 = 0.25. Since 0.5 is greater than 0.25, this statement is true.g(x) has a greater y-intercept than f(x) does. The y-intercept of g(x) is 0, and the y-intercept of f(x) is also 0. Therefore, this statement is false.In summary, the true statements are: f(1) is equal to g(1), and f(x) is greater than g(x) on the interval (0,1).
Learn more about Comparing linear and quadratic functions here:https://brainly.com/question/13081013
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which of the binomials below is a factor of this expression? 121A2-64B2
A. 121A+8B
B. 11A+32B
C. 121A +32B
D. 11A+8B
Answer: 11A + 8B
Step-by-step explanation:
What is 6x+2=9x-1 ahngfhwejgfjhygfweugfuweg
By simplifying both sides of the equation, then isolating the variable.
x = 1
Answer:
x=1
Step-by-step explanation:
1. Move the terms: move the variable to the left hand side and change it sign
2. Move the constant to the right hand side and change its sign
3. Collect like terms
4. Calculate the difference
5. Divide both sides of the equation by -3, therefore x = 1
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What is 8+0.0+0.05+0.009+0.0006 in standard form
A sugar bowl holds 237 grams. You have a one kilogram bag of sugar. Estimate how many bowls of sugar you can fill from the bag.
Answer:
The required number of bowls are 5.
Step-by-step explanation:
Given : A sugar bowl holds 237 grams. You have a one kilogram bag of sugar.
To find : Estimate how many bowls of sugar you can fill from the bag?
Solution :
1 bowl can hold 237 gram of sugar.
We have, 1 kg of sugar or 1000 gram of sugar.
According to question,
237 gram of sugar can hold in 1 bowl.
So, 1 gram of sugar can hold in [tex]\frac{1}{237}[/tex] bowl.
1000 gram of sugar can hold in [tex]\frac{1000}{237}[/tex] bowl.
1000 gram of sugar can hold in [tex]4.21[/tex] bowl.
Which means, The required number of bowls are 5.
As 4 bowls have [tex]237\times 4=948[/tex] grams of sugar.
Sugar left is 1000-948=52 grams
That 52 grams is filled into 5th bowl.