The trip from Winston to Carver takes 8 min longer during rush hour, when the average speed is 75 km/h, than in off-peak hours when the average speed is 90 km/h. the distance between the two towns is 60 km.
Considering the distance between the Winston and carver be "d", since here we got that during off-peak hours, the average speed is 90 km/h. so by using the formula of distance which is distance =speed x time=> d = 90t.
Whereas in rush hour, the average speed is 75 km/h, we also know that the trip takes 8 minutes longer during rush hour. calling the time it takes to travel during rush hour "t+8/60"( since 8 minutes is 8/60 of an hour). Now using the same formula as before:
d = 75(t + 8/60), since here we have two equations for d we can equal them to each other then we get :
90t = 75(t + 8/60)
=>90t = 75t + 10
=>90t-75t=10
=>t = 2/3
Since during the off-peak hours, it takes 2/3 hours or 40 minutes to travel the distance between Winston and carver. now using either equation to find the distance we get
d = 90t = 90(2/3) = 60 km or d = 75(t + 8/60) = 75(2/3 + 8/60) = 60 km
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A savings account pays a 3% nominal annual interest rate and has a balance of $1,000. Any interest earned is deposited into the account and no further deposits or withdrawals are made. If interest is compounded semi-annually (every six months), what interest rate would be used for each calculation?
A. 3%
B. 2%
C. 1.5%
D. 12%
E. 18%
The answer is: C. 1.5%
For 0 <3 days. the number of weeds in large garden is given by the function W that satisfies tbe differential equation dW/dt = 1/12(-318+ 24W). At time t = 2 days, there are 20 weeds in the garden Find d^2W/dt^2 when W = 14.
[tex]3[/tex] days [tex]0[/tex] hours. The answer is three because the function [tex]W[/tex] that solves the differential equation gives the number of weeds in a large garden.
How to explain number?A number is calculated and represented using a decimal, which is an algebra quantity. In handwriting, numerical symbols like "3" are used to represent numbers. A counting system is a logical way of expressing numbers that uses digits or symbols to represent them.
Is the number 111111 lucky?Vets Day and Memorial Day are commonly celebrated on November 11 in the United States and overseas, respectively. The history, mythology, and mathematical importance of this particular time and date are all explained here.
[tex]\frac{dw}{dt}=\frac{1}{12}(-318+24W)[/tex]
[tex]\frac{d^{2}W }{dt^{2} }=\frac{d}{dt}[\frac{1}{12} (-318+24W)][/tex]
When [tex]W=14, \frac{dW}{dt}[/tex]
[tex]=\frac{1}{12}(-318+24*14)[/tex]
[tex]=\frac{18}{12}=1.5[/tex]
[tex]=2\frac{dW}{dt}=2*1.5[/tex]
[tex]=3[/tex]
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Solve each system of equations algebraically. y=x + 15, y= 2x
The solution to the system of equations is (15, 30).
What is system of equations?A group of two or more equations that must be solved all at once is known as a system of equations. The system's equations each show how two or more variables relate to one another. The variables' values that satisfy every equation in the system can be discovered using algebraic techniques.
Algebraic systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. The substitution approach involves solving one equation for one variable in terms of the other variable, and then substituting the result for that variable's expression into the other equation.
The given system of equations are y=x + 15, y= 2x.
Substitute the value of y from equation 2 in equation 1:
x + 15 = 2x
15 = x
Substitute the value of x to get the value of y:
y = 2x = 2(15) = 30
Hence, the solution to the system of equations is (15, 30).
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If Alyssa has 6 shirts, 4 skirts, and 10 pairs of shoes, how many possible outfits can she make?
Answer: 240
You multiply them. 6x4x10 :)
The number of different outfits made by Alyssa as per the given number of shirt , skirts and shoes is equal to 240 outfits.
To find the number of possible outfits Alyssa can make, you multiply the number of choices for each item of clothing:
Number of shirts = 6
Number of skirts = 4
Number of pairs of shoes = 10
Substitute the values and multiply with each other
Total number of possible outfits
= 6 (shirts) × 4 (skirts) × 10 (shoes)
= 240 outfits.
Therefore, Alyssa can make 240 different outfits using her 6 shirts, 4 skirts, and 10 pairs of shoes.
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Which of these following lies between 6. 3 and 6. 6
6. 2
6. 9
6. 05
6. 41
The mayor of a town sees an article that claims the national unemployment rate is
8%. They suspect that the unemployment rate is lower in their town, so they plan to take a sample of 200 residents to test if the proportion of residents that are unemployed in the sample is significantly lower than the national rate. Let p represent the proportion of residents that are unemployed.
Which of the following is an appropriate set of hypotheses for the mayor's significance test?
Choose 1 answer:
The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].
What is Hypothesis test?Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.
Using the appropriate notation, the hypotheses can be expressed as:
$H_0: p = 0.08$
$H_a: p < 0.08$
Therefore, the appropriate set of hypotheses for the mayor's significance test are:
[tex]$$H_0: p = 0.08$$[/tex]
[tex]$$H_a: p < 0.08$$[/tex]
Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate
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Blowlers that score at least 228 point will make it to the next round
Answer:
p ≥ 228
Step-by-step explanation:
p ≥ 228
This inequality means the Bowlers have to score at least 228 points to move on.
Hope this helped!
If Karel starts at Street 1 and Avenue 1, facing East, where will Karel be, and what direction will Karel be facing after running the following code? (Assume the world is 10x10 in size)move();turnLeft();putBall();turnLeft();turnLeft();turnLeft();move();turnLeft();
After running the given code, Karel will be at Street 2 and Avenue 2, facing North.
Here is a step-by-step explanation of what the code does:
move(); - Karel moves one block east, to Street 1 and Avenue 2.
turnLeft(); - Karel turns left to face north.
putBall(); - Karel puts a ball at Street 1 and Avenue 2.
turnLeft(); turnLeft(); turnLeft(); - Karel turns left three times to face south.
move(); - Karel moves one block south to Street 2 and Avenue 2.
turnLeft(); - Karel turns left to face east.
So after executing this code, Karel will be at Street 2 and Avenue 2, facing North.
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Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm?
Answer:
The area of the pool increasing at the rate of 125.6 when the radius is 5 cm
Step-by-step explanation:
Given:
radius of the pool increases at a rate of 4 cm/min
To Find:
How fast is the area of the pool increasing when the radius is 5 cm?
Solution:
we are given with the circular pool
hence the area of the circular pool =
A =[tex]\pi r^2[/tex]-----------------------------(1)
The area of the pool is increasing at the rate of 4 cm/min, meaning that the area of the pool is changing with respect to time t
so differentiating eq (1) with respect to t , we have
[tex]\dfrac{dA}{dt} =\pi \times2r\times\dfrac{dr}{dt}[/tex]
we have to find [tex]\dfrac{dA}{dt}[/tex] with [tex]\dfrac{dr}{dt}[/tex] = 4 cm/min and r = 5 cm
substituting the values
[tex]\dfrac{dA}{dt} =\pi \times2(5)\times4[/tex]
[tex]\dfrac{dA}{dt} =\pi \times 10\times4[/tex]
[tex]\dfrac{dA}{dt} =\pi \times 40[/tex]
[tex]\dfrac{dA}{dt} =40\pi[/tex]
[tex]\dfrac{dA}{dt} =125.6[/tex]
Let f be a differentiable function defined by f(x) = 3x + 2e −3x , and let g be a differentiable function with derivative given by g′(x) = 1 x + 4. It is known that lim g(x) = [infinity].
x→[infinity]
The value of lim f(x) g(X) is:______
x→[infinity]
The value of lim f(x)g(x) as x approaches infinity is 0.
L'Hopital's rule is a mathematical tool used to evaluate limits of functions that are in an indeterminate form.
To find the limit of f(x)g(x) as x approaches infinity, we can use L'Hopital's rule since it is an indeterminate form of infinity times zero. We have:
lim x→[infinity] f(x)g(x) = lim x→[infinity] [(3x + 2e^(-3x))(1/x + 4)]
= lim x→[infinity] [(3 + 2e^(-3x)/x)/(1/x + 4)^(-1)]
Applying L'Hopital's rule to the fraction in the numerator, we get:
lim x→[infinity] [(2e^(-3x)(-3)/x^2)/(1/x + 4)^(-1)]
= lim x→[infinity] [(6e^(-3x)/x^2)/(1/x + 4)]
= lim x→[infinity] [(6e^(-3x)/(x + 4x^2))]
= 0
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Which of the following are key ingredients of a confidence interval based on the Central Limit Theorem?
(1) A summary statistic (e.g. a mean) from your sample
(2) A multiple z, based on a tail area from the normal distribution.
(3) A formula for the standard error of your summary statistic.
a. All of the above (1, 2, and 3)
b. (1) and (2)
c. (1) and (3)
d. (2) and (3)
Option a. (All of the above (1, 2, and 3)) is the right answer to the question regarding the key ingredients of a confidence interval based on the Central Limit Theorem.
A confidence interval is a statistical estimate of a population parameter with a level of confidence or certainty.
The Central Limit Theorem states that the distribution of the means of a sufficiently large sample size from a population with a finite variance will be approximately normal, regardless of the population's actual distribution.
A confidence interval based on the Central Limit Theorem, there are three key ingredients:
1. A summary statistic (e.g. a mean) from your sample
2. A multiple z, based on a tail area from the normal distribution.
3. A formula for the standard error of your summary statistic.
For a given level of confidence, the z-score corresponds to the number of standard deviations from the mean. The standard error of a summary statistic is a measure of the variability of the estimate that is dependent on the size of the sample, the variability of the population, and the type of summary statistic. The standard error of a sample mean is given by the formula σ/√n, where σ is the population standard deviation and n is the sample size.
Thus, all the above points (1, 2, and 3) are the key ingredients of a confidence interval based on the Central Limit Theorem.
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The table below shows the number of gold, silver and bronze medals won by
some countries in the 2016 Paralympic Games.
Work out the ratio of gold to silver to bronze medals won by Belarus.
Give your answer in its simplest form.
Country
Cuba
Malaysia
Belarus
Spain
Gold
8
3
8
9
Silver
1
0
0
14
Bronze
6
1
2
8
The ratio of gold to silver to bronze medals won by Belarus in its simplest form is 4:0:1, which means that Belarus won four times as many gold medals as bronze medals, and no silver medals.
What is simplest form ?In mathematics, the simplest form refers to the most reduced or compact form of an expression.
The simplest form can be achieved by simplifying, reducing, or condensing a mathematical expression or ratio to its smallest possible form using various techniques such as factorization, cancellation, and distribution.
To find the ratio of gold to silver to bronze medals won by Belarus, we need to look at the row corresponding to Belarus in the table:
Country Gold Silver Bronze
Belarus 8 0 2
The ratio of gold to silver to bronze medals won by Belarus is: 8:0:2
However, this ratio is not in its simplest form, because we can simplify it by dividing all of the numbers by the greatest common factor of the three numbers. In this case, the greatest common factor of 8, 0, and 2 is 2, so we can simplify the ratio by dividing each number by 2:
8 ÷ 2 : 0 ÷ 2 : 2 ÷ 2
4 : 0 : 1
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out of total student 3/5 are girls .On a particular day one third boys and 2/5 girls were absent. If total absentees was 280 find total number of students
Answer:
Step-by-step explanation:
Calculate fraction of boys
If girls =3/5, then boys = 1 - 3/5 = 2/5.
Calculate fraction of students absent
Girls - 2/5 of 3/5 = 6/25
Boys - 1/3 of 2/5 = 2/15
6/25+2/15=28/75
Calculate total number of students
If 28/75 = 280
280/28=10
10x75=750
Total number of students = 750
Classify the polynomial
X+2
Urgent !!!
Answer: Quadratic polynomial.
Step-by-step explanation: Polynomials with 2 as the degree.
find the long leg: b =
Answer:
b ≈ 12.1
Step-by-step explanation:
using the tangent ratio in the right triangle
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{7}[/tex] ( multiply both sides by 7 )
7 × tan60° = b , then
b ≈ 12.1 ( to the nearest tenth )
I need help with number 12
The compounding formula is used to create the quarterly compounding formula. To the nearest cent, the compounded balance is $ [tex]12,832.27.[/tex]
What is the compounded quarterly formula?To reflect the quarterly interest computation as the only change, the interest rate is increased by 4*2.
[tex]A = P(1 + r/n)(nt)[/tex]
Assume that we have a $ [tex]10,000[/tex] Initial investment, a 6% yearly interest rate, and a 5-year investment period. We have n = 4 and t = 5 since the interest is compounded every three months.
Plugging in these values, we get:
[tex]A = 10,000(1 + 0.06/4)(4*5)[/tex]
[tex]= 10,000(1.015)^20[/tex]
[tex]= 12,835.72[/tex]
Hence, the final balance is $ [tex]12,835.72[/tex] to the nearest penny.
If the money is compounded continually, we may use the following formula to determine the balance:
[tex]A = Pe(rt)[/tex]
With the identical values as before, we obtain:
[tex]A = 10,000e(0.06 \times5)[/tex]
[tex]= 10,000e(0.3)[/tex]
[tex]= 12,832.27[/tex]
Therefore, So the balance, to the nearest cent, is $ [tex]12,832.27.[/tex]
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Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour
(mph). Given the least-squares regression line, In(Fuel Efficiency) = 1.437 + 0.541 In(Speed), what is the predicted fuel
efficiency for a speed of 30 mph?
17.67 mpg
26.50 mpg
30.00 mpg
37.74 mpg
The predicted fuel efficiency for a speed of 30 miles per hour is given as follows:
26.50 mpg.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is defined as follows:
In(Fuel Efficiency) = 1.437 + 0.541 In(Speed).
The speed is of 30 miles per hour, hence the predicted fuel efficiency is given as follows:
In(Fuel Efficiency) = 1.437 + 0.541 x In(30).
In(Fuel Efficiency) = 3.277.
The exponential is the inverse of the ln, hence:
Fuel Efficiency = e^3.277
Fuel Efficiency = 26.50 mpg.
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At the book store, you purchased some $5 clearance mystery books and $12 regular-priced science fiction books. How many of each did you buy if you spent a total of $126?
Answer: View answer in explanation below.
Step-by-step explanation: Let's use variables to represent the unknown quantities.
Let x be the number of $5 clearance mystery books purchased.
Let y be the number of $12 regular-priced science fiction books purchased.
We can set up a system of equations based on the given information:
5x + 12y = 126 (total amount spent)
x + y = total number of books purchased
We need to solve for x and y.
Let's use the second equation to solve for one variable in terms of the other:
y = total number of books purchased - x
Now we can substitute this expression for y into the first equation:
5x + 12(total number of books purchased - x) = 126
Simplifying and solving for x:
5x + 12total number of books purchased - 12x = 126
-7x + 12total number of books purchased = 126
-7x = -12total number of books purchased + 126
x = (12total number of books purchased - 126)/7
Since x must be a whole number (you can't buy a fraction of a book), we need to find a value of total number of books purchased that makes x a whole number. We can start by trying different values of total number of books purchased:
If total number of books purchased is 10:
x = (12(10) - 126)/7 = -6/7 (not a whole number)
If total number of books purchased is 11:
x = (12(11) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 12:
x = (12(12) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 13:
x = (12(13) - 126)/7 = 12/7 (not a whole number)
If total number of books purchased is 14:
x = (12(14) - 126)/7 = 18/7 (not a whole number)
If total number of books purchased is 15:
x = (12(15) - 126)/7 = 24/7 (not a whole number)
If total number of books purchased is 16:
x = (12(16) - 126)/7 = 30/7 (not a whole number)
If total number of books purchased is 17:
x = (12(17) - 126)/7 = 36/7 (not a whole number)
If total number of books purchased is 18:
x = (12(18) - 126)/7 = 42/7 = 6 (a whole number)
So, you bought 6 $5 clearance mystery books and 12 - 6 = 6 $12 regular-priced science fiction books.
The spinner above is used in a game. What is the theoretical probability of the given event with one spin?
P (5)
Answer:
B
Step-by-step explanation
so there is 8 numbers so when you spin you have a 1/8 chance of spinning the numberThe cost price of 20 articles is the same as sellling price of 16 articles find the gain percent
If the cost price of 20 articles is the same as selling price of 16 articles, then the gain percentage is 25%
To find the gain percent, we first need to calculate the profit earned on the sale of the 16 articles.
Let the cost price of each article be "C" and the selling price of each article be "S".
Given that the cost price of 20 articles is the same as the selling price of 16 articles, we can write:
20C = 16S
We can simplify this equation to:
S = (20/16)C = (5/4)C
Now, let's calculate the profit earned on the sale of 16 articles:
Profit = Total Selling Price - Total Cost Price
Profit = 16S - 20C
Profit = 16(5/4)C - 20C
Profit = 5C/2
The profit earned is 5C/2. The profit percent can be calculated as:
Profit Percent = (Profit / Cost Price) x 100
Profit Percent = (5C/2) / (20C) x 100
Profit Percent = 25%
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Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. )
P = $1300, r = 8. 5%, t = 11 years
n A
1 $
2 $
4 $
12 $
365 $
Continuous $
The complete table for the amount balance, A when P dollars is invested at rate r for t years and compounded n times per year is present in above figure 2.
The compound interest formula is written as A = P( 1 + r/n)ⁿᵗ
where, A--> total Amount of money after t years
P --> Principal
r --> Annual rate of interest (as a decimal)
t --> Number of years:
n--> number of times interest is compounded per year
Here, principle, P = $1300, rate of interest, r = 8.5% = 0.085 , time periods, t = 11 years. We have to complete the above table for compound interest.
Case 1: n = 1
Substitute the known values in above formula, A = 1300( 1 + 0.085/1)¹¹
= 1300( 1.085)¹¹
= 3,189.12
Case 2: n = 2
A = 1300( 1 + 0.085/2)²²
= 1300( 2.085/2)²²
= 1300( 1.0425)²²
= 3,248.01
I'll let you work out the cases where n = 4, 12 and 365 since all you need to do is place those in for n as done in the 1st 2 cases. For the Compounded continuously case, the formula becomes,
[tex] A = Pe^{rt}[/tex]
Where: A-> Total amount of money after t years
P --> Principal Amount
e --> Natural log constant:
r = Annual rate of interest (as a decimal)
Case: Continuous: e = 2.71828 (approx), r = 0.085
A = 1300( 2.71828)⁰·⁰⁸⁵⁽¹¹⁾
= 1300(e)⁰·⁹³⁵ = 3,311.34
Hence, required value is $3,311.3775.
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Complete question :
The above table completes the question.
Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. ) P = $1300, r = 8. 5%, t
= 11 years
In the diagram below what is the measure in angel x
Answer:
143°
When solving angle problems, make sure to label the other angles (even the ones that are not asked) and use them to relate to each other to find the answer.
Please simplify the following expression while performing the given operation.
(-3+i)+(-4-i)
Hence, the abbreviated formula is -7 + 0i, or just -7.
What is the simplifying rule?The terms in the parentheses can be immediately simplified. So, we can carry out the operations indicated by the brackets in the following order: multiplication, addition, subtraction, division. Note: The brackets should be shortened in the following order: (),, []. Simplify: 14 + (8 - 2 3) for Example 2.
We must combine like terms in order to make the phrase simpler.
First, we can individually merge the real and made-up parts:
The genuine parts add out to -3 - 4 = -7.
i - i = 0 is the imaginary part's total.
Hence, the abbreviated formula is -7 + 0i, or just -7.
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Complete question:
Please simplify the following expression while performing the given operation. (-3+i)+(-4-i)
Enter the correct answer for the box.
Making r the subject of formula in this equation A = V²/r gives r = V²/A.
How to calculate centripetal acceleration?In Mathematics and Science, the centripetal acceleration of a physical object (body) can be calculated by using the following mathematical expression:
A = V²/r
Where:
A represent the centripetal acceleration.r represent the distance (radius) from a circular track.V represent the velocity of a physical object (body).In this exercise, you are required to make radius (r) the subject of formula. Therefore, by making radius (r) the subject of formula, we have the following:
Radius, r = V²/A
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Scientists determined that the cause of death in many prawns off the coast of Chile was a nutrient deficiency. So, they set out to determine if the distribution of plants in the ocean near the coast was out of proportion when compared to the ideal environment: 40% Kelp, 25% Phytoplankton, 25% Coral and 10% Other (mostly nutrient-low seaweed). In randomly chosen areas along the coast, they sampled 240 plants.
KELP PHYTOPLANKTON CORAL OTHER
84 67 57 32
In an ideal environment how many of the 240 plants would you expect to be Kelp?
If a goodness of fit test is conducted, what is the null Hypothesis?
If a goodness of fit test is conducted, what is the alternative Hypothesis?
What is the probability of getting the observed values or values as extreme from the ideal?
Is there enough evidence to conclude that the environment for prawns is not ideal? Base this conclusion on p-value and a level of significance of 0.05 or 5%.
Answer:
Step-by-step explanation:
Further Mathematics Assignment 1) A bowl contains 7 cooked and 5 uncooked In how many ways can: a) 2 cooked or 3 uncooked eggs be selected. b) 2 cooked and 3 uncooked eggs be selected.
Please this is my school homework!
Please HELP!!!
15 MRKS
Therefore, the total number of ways to select 2 cooked and 3 uncooked eggs is 210 ways.
What is combination?In mathematics, a combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In other words, a combination is a selection of items from a larger set, without regard to the order in which they are chosen. The number of combinations of size r that can be chosen from a set of n elements is denoted by the symbol C(n, r), and is given by the formula:
C(n, r) = n! / (r! * (n-r)!)
where n! (pronounced "n factorial") is the product of all positive integers up to n, and r! is the product of all positive integers up to r.
Here,
a) To find the number of ways to select 2 cooked or 3 uncooked eggs, we need to use the combination formula, which is:
ⁿCₓ= n! / r!(n-r)!
where n is the total number of eggs, r is the number of eggs we want to select, and ! represents factorial.
For 2 cooked eggs, we can select them in:
⁷C₂ = 7! / 2!(7-2)! = 21 ways
For 3 uncooked eggs, we can select them in:
⁵C₃ = 5! / 3!(5-3)! = 10 ways
Therefore, the total number of ways to select 2 cooked or 3 uncooked eggs is:
21 + 10 = 31 ways
b) To find the number of ways to select 2 cooked and 3 uncooked eggs, we need to use the product rule of counting. That is, we need to multiply the number of ways to select 2 cooked eggs and 3 uncooked eggs.
The number of ways to select 2 cooked eggs is:
⁷C₂ = 21 ways
The number of ways to select 3 uncooked eggs is:⁵C₃ = 10 ways
Therefore, the total number of ways to select 2 cooked and 3 uncooked eggs is:
21 x 10 = 210 ways
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answer quickly please
Answer:
m = -3/4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0, -2) (-3,2)
We see the y increase by 4 and the x decrease by 3, so the slope is
m = -3/4
Please help me with my math
Answer:
[tex]\textsf{$\boxed{\checkmark}\;\;y$-value\;of\;vertex\;is\;$-1$}[/tex]
[tex]\textsf{$\boxed{\checkmark}$\;\;Minimum\;value\;occurs\;at\;$y = -1$}[/tex]
Step-by-step explanation:
Given equation:
[tex]y=x^2+8x+15[/tex]
As the given equation is quadratic with a positive leading coefficient, it is a parabola that opens upwards. Therefore, its vertex is its minimum point. This means that the minimum value of the range is the y-value of the vertex.
The x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a. Therefore, the x-value of the vertex of the given equation is:
[tex]\implies x=\dfrac{-8}{2(1)}=-4[/tex]
To find the y-value of the vertex, substitute x = -4 into the equation:
[tex]\begin{aligned}\implies y&=(-4)^2+8(-4)+15\\&=16-32+15\\&=-16+15\\&=-1\end{aligned}[/tex]
Therefore, the minimum y-value of the function is y = -1, so the range is y ≥ -1.
Therefore, the following are true statement about the given equation:
y-value of vertex is -1Minimum value occurs at y = -1Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.W = {[\begin{array}{ccc}a\\b\\c\\\d\end{array}\right] : 3a+b=c, a+b+2c=2d}
An appropriate theorem to show that the given set, W, is a vector space. A specific example can be
[tex]\left[\begin{array}{ccc}p\\q\\r\end{array}\right][/tex] , -p- -3q = s and 3p = -2s - 3r
Sets represent values that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.
The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.
The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.
The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.
Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is
S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties
u +v =y+ u and (u + v)+w=u + (v +W).
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A friend is building a garden with two side lengths 16 ft and exactly one right angle. What geometric figures could describe how the garden might look?
SELECT ALL THAT APPLY:
A. Kite.
B. Isosceles right triangle
C. Quadrilateral
D. Parallelogram
(Remember it is multiple choice)
Answer:
B. Isosceles right triangle
C. Quadrilateral
D. Parallelogram
Step-by-step explanation:
Answer:
The geometric figures that could describe how the garden might look are B. Isosceles right triangle and C. Quadrilateral.
