Answer:
Step-by-step explanation:
bring 5 to the left hand side and the equation will becomes x^2-4x-5=0
then lets see for common factors and -5 and +1 are suitable since when you multiply them you get -5 and if you add them it becomes -4 so
x^2+x-5x-5=0
x(x+1)-5(x+1)=0
take (x+1) common
(x-5)(x+1)=0
x-5=0
x=0+5
x=+5
x+1=0
x=0-1
x=-1
so here are the two solutions
Cliff takes out a $5,000 personal loan with 7
fixed annual interest compounded monthly to pay for his wedding. He repays the loan in 2 year.s
How much total interest does Cliff pay on his loan?
Cliff pays a total interest of approximately $679.90 on his $5,000 loan.
To calculate the total interest paid on the loan, we need to use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
Where:
A is the final amount (loan amount + interest)
P is the principal (loan amount)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:
P = $5,000
r = 7% = 0.07
n = 12 (monthly compounding)
t = 2 years
[tex]A = 5000(1 + 0.07/12)^{(12 \times 2)[/tex]
Calculating this expression:
A ≈ 5000[tex](1.00583)^{(24)[/tex]
A ≈ 5000(1.13598)
A ≈ 5679.90
The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):
Total Interest = A - P
Total Interest = 5679.90 - 5000
Total Interest ≈ $679.90
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)The mean voltage of a battery is 15 and S.D 0.2.Find the probability that four such batteries connected in series will have combined voltage of 60.8 or more volts
The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.
In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.
The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.
The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.
Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.
First, we need to standardize the value of 60.8 using the formula:
Z = (X - μ) / σ
Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, the standardized value is:
Z = (60.8 - 60) / sqrt(0.16)
Z = 0.8 / 0.4
Z = 2
Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.
Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
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The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answer:
Step-by-step explanation:
3.6*
It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2
For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.
We get
36 = s^2
Now, we need to get the square root of both sides, which gives us
s = √36 s = 6 cm
Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.
Therefore, the perimeter of the square is 24 cm.
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The solution of the equation 3x + 4 =1 is a) 1 b) 0 c) -1 d) 2
Hello!
3x + 4 = 1
3x + 4 - 4 = 1 - 4
3x = -3
3x/3 = -3/3
x = -1
The solution of the equation 3x + 4 = 1 is -1.
The answer is:
C) x = -1
Work/explanation:
To solve this equation, I subtract 4 from each side:
[tex]\sf{3x+4=1}[/tex]
Subtract :
[tex]\sf{3x=-3}[/tex]
Divide each side by 3:
[tex]\sf{x=-1}[/tex]
Hence, C is correct.
Find the value of y.
Answer:
y = [tex]\sqrt{55}[/tex]
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(altitude)² = product of parts of hypotenuse
then
y² = 11 × 5 = 55 ( take square root of both sides )
y = [tex]\sqrt{55}[/tex]
Find the volume of the following shape
Answer:
24in^3
Step-by-step explanation:
this is a triangular prism and to find the volume of a right prism (a triangular prism in this case) we'll first find the area of cross-section which is basically the base area ( the triangle)
which is 1/2*4in*3in
this equals 6in^2
to find the volume we multiply it by the height of the prism which is 4 (the one on the top) so we multiply our previous answer with 4 to get 24in^3
11. If AB LCD, mZDCE = (7x + 2) and mZECB= (x + 8), find the measure of ZDCE.
AC B.
Since AB is parallel to CD, we have alternate interior angles forming when transversal CE intersects the parallel lines. Therefore,
mZDCE = mZECB (Alternate Interior Angles)
(7x + 2) = (x + 8) (Substitute in the given angle measures)
Solving for x, we get:
7x + 2 = x + 8
6x = 6
x = 1
Now, we can use x to find the measure of angle ZDCE:
mZDCE = (7x + 2)
= (7*1 + 2)
= 9
Therefore, the measure of angle ZDCE is 9 degrees.
Type the correct answer in each box.
Day Amount
1
$26
2
$23
3
$31
4
$26
5
534
The table shows the amount Bill spent on 5 days last week.
The mean of the amount he spent is $
The mean absolute deviation is $
Reset
Next
The mean absolute deviation is $106.6.
Given the table shows the amount Bill spent on 5 days last week.
DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.
Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,
the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:
Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406
The sum of all absolute deviations is:
10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.
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hello
i need the answer of the problems
1. The solution to the system 0.6x + 0.7y = 2 and 0.4x + 0.3y = 1 is x = 1.2857 and y = 1.4286.
2. The solution to the system 2x + 3y + z = 10, 7x + 2y + z = 20, and x + 5y + 8z = 30 is x = 2.4286, y = 0.0952, and z = 3.7730.
3. The solution to the system 4y + 3z = 8, 2x - z = 2, and 3x + 2y = 5 is x = 1, y = 2.5, and z = 4/3.
4. The solution to the system 10x2 + 4x32x4 = -4, -3x1 - 17x2 + x3 + 2x4 = 2, x1 + x2 + x3 = 6, and 8x134x2 + 16x3 - 10x4 = 4 is x = -8/10, y = 2, z = 4/7, and w can take any value.
Sure, let's solve each linear system using Gaussian elimination and row echelon form.
The augmented matrix for the system is:
| 0.6 0.7 | 2 |
| 0.4 0.3 | 1 |
To perform Gaussian elimination, we'll use row operations to eliminate the x-coefficient in the second equation.
Multiply the first equation by 0.4 and subtract it from the second equation.
| 0.6 0.7 | 2 |
| 0 -0.14 | -0.2 |
Now, divide the second row by -0.14 to get a leading coefficient of 1.
| 0.6 0.7 | 2 |
| 0 1 | 1.4286 |
Next, we'll eliminate the x-coefficient in the first equation by multiplying the second equation by -0.6 and adding it to the first equation.
| 0.6 0 | 0.7714 |
| 0 1 | 1.4286 |
The system is now in row echelon form. To solve for x and y, back-substitution can be applied.
From the second equation, y = 1.4286.
Substituting y into the first equation, 0.6x = 0.7714, which gives x = 1.2857.
Therefore, the solution to the system is x = 1.2857 and y = 1.4286.
The augmented matrix for the system is:
| 2 3 1 | 10 |
| 7 2 1 | 20 |
| 1 5 8 | 30 |
We'll start by eliminating the x-coefficient in the second and third equations.
Multiply the first equation by -3.5 and add it to the second equation.
Multiply the first equation by -0.5 and add it to the third equation.
| 2 3 1 | 10 |
| 0 -10.5 -2.5 | -5 |
| 0 3.5 7.5 | 25 |
Now, divide the second row by -10.5 to get a leading coefficient of 1.
| 2 3 1 | 10 |
| 0 1 0.2381| 0.4762 |
| 0 3.5 7.5 | 25 |
Next, eliminate the x-coefficient in the third equation by multiplying the second equation by -3.5 and adding it to the third equation.
| 2 3 1 | 10 |
| 0 1 0.2381| 0.4762 |
| 0 0 6.1905| 23.3333 |
The system is now in row echelon form. To solve for x, y, and z, back-substitution can be applied.
From the third equation, z = 3.7730.
Substituting z into the second equation, y + 0.2381z = 0.4762, which gives y = 0.0952.
Substituting y and z into the first equation, 2x + 3y + z = 10, we find x = 2.4286.
Therefore, the solution to the system is x = 2.4286, y = 0.0952, and z = 3.7730.
The augmented matrix for the system is:
| 0 4 3 | 8 |
| 2 0 -1| 2 |
| 3 2 0 | 5 |
To eliminate the x-coefficient in the second and third equations, multiply the first equation by 2 and subtract it from the second equation.
Multiply the first equation by 3 and subtract it from the third equation.
| 0 4 3 | 8 |
| 2 0 -1| 2 |
| 3 2 0 | 5 |
The system is already in row echelon form. Let's solve for x, y, and z.
From the third equation, 2y = 5, which gives y = 2.5.
Substituting y into the second equation, 2x - z = 2, we find 2x - z = 2.
Substituting y and z into the first equation, 4 + 3z = 8, we get 3z = 4, which gives z = 4/3.
Therefore, the solution to the system is x = 1, y = 2.5, and z = 4/3.
The augmented matrix for the system is:
| 10 2 32 | -4 |
| -3 -17 1 | 2 |
| 1 1 1 | 6 |
| 8 13 -10| 4 |
We'll use row operations to convert the matrix into row echelon form.
| 10 2 32 | -4 |
| 0 -173 -32 | -2 |
| 0 0 -7 | -4 |
| 0 0 0 | 0 |
The system is now in row echelon form. To solve for x, y, z, and w, back-substitution can be applied.
From the third equation, -7z = -4, which gives z = 4/7.
Substituting z into the second equation, -173y - 32z = -2, we find -173y - 32(4/7) = -2, which gives y = 14/7.
Substituting y and z into the first equation, 10x + 2y + 32z = -4, we get 10x + 2(14/7) + 32(4/7) = -4, which simplifies to 10x = -8.
Therefore, the solution to the system is x = -8/10, y = 2, z = 4/7, and w can take any value.
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I need Help please!!!
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
PLEASE HELP! what direction will these electrostatic forces go?
Step-by-step explanation:
this is physics (not math per se).
the first moves to the left, because the distance to the positive charge on the left is shorter than the distance to the positive charge on the right.
the second moves to the right, because the positive charge is greater there and the distance to the positive charge is shorter too.
the third stays where it is. the -2 charge moves to the left until it hits the first +2 charge. there they neutralize each other, and nothing else is happening. also before -2 and +2 meet, they are neutralizing each other already for an outside observer (like the green ringed +2).
but - it depends how picky your teacher tries to be here.
because when you look at the very fine details, until -2 and the right +2 meet and really neutralize each other, there is a tiny little overhang of positive charges the green ringed +2 charge would "feel". simply because the +2 is a little bit closer than the -2.
and when we consider this, the green ringed +2 would move very little to the left (repelled by the other positive overhanging charge on the right) until -2 and +2 actually meet.
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
how long will it take for population of rabbits to reach 1000 rabbits . I will take years)round to nearest0.01 years)
The time it takes for a population to reach a certain size is given by:t = (ln(N/P₀)) / r Where:t = time in yearsN = target population size (1000 rabbits in this case)P₀ = initial population sizer = growth rate (expressed as a decimal)
To determine how long it will take for the population of rabbits to reach 1000 rabbits, we need to consider the growth rate of the rabbit population.
Let's assume that the rabbit population grows exponentially, meaning the growth rate is proportional to the current population. We can use the following exponential growth formula:
P(t) = P₀ * e^(r * t)
Where:
P(t) is the population at time t,
P₀ is the initial population,
e is the base of the natural logarithm (approximately 2.71828),
r is the growth rate,
t is the time in years.
In this case, we want to find the time it takes for the population to reach 1000 rabbits, so P(t) = 1000. Let's assume we know the initial population P₀ and the growth rate r. We can rearrange the equation and solve for t:
t = ln(1000 / P₀) / r
By plugging in the appropriate values for P₀ and r, you can calculate the time it will take for the rabbit population to reach 1000 rabbits, rounding the result to the nearest 0.01 years.
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Alexei finances her purchase of a $900 television. Her one-year loan has a fixed annual interest rate of 2.5%.
What is Alexei's monthly payment?
Alexei's monthly payment is approximately $18.56.
Alexei finances her purchase of a $900 television with a one-year loan that has a fixed annual interest rate of 2.5%. To find Alexei's monthly payment, we can use the formula for calculating monthly loan payments.
The formula for calculating monthly loan payments is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = monthly payment
P = principal loan amount
r = monthly interest rate (annual interest rate divided by 12)
n =number of monthly payments
In this case, the principal loan amount (P) is $900, the annual interest rate (r) is 2.5% (or 0.025 when expressed as a decimal), and the number of monthly payments (n) is 12 (since it is a one-year loan).
First, we need to calculate the monthly interest rate (r) by dividing the annual interest rate by 12: r = 0.025 / 12 = 0.002083.
Next, we can substitute the values into the formula:
M = (900 * 0.002083 * (1 + 0.002083)^12) / ((1 + 0.002083)^12 - 1)
Simplifying the formula gives us:
M = (900 * 0.002083 * 1.002083^12) / (1.002083^12 - 1)
Calculating the values inside the formula gives us:
M = (900 * 0.002083 * 1.026260) / (1.026260 - 1)
Further simplifying the formula gives us:
M = (900 * 0.002083 * 1.026260) / 0.026260
Finally, calculating the expression gives us:
M ≈ 18.56
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factor and solve if necessary
7x^2-14x+7
Hello!
7x² - 14x + 7
7(x² - 2x + 1)
= 7(x(x - 1) - 1(x - 1))
= 7((x - 1)(x - 1))
= 7(x - 1)²
A certain type of kickboard scooter comes in silver, red, 2
or purple with wheel sizes of 125 millimeters or 180
millimeters. Determine the total number of color-wheel size combinations.
(This is probability and I’m having such a hell of a time figuring it out pls help)
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.
Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:
Total combinations = Number of color options × Number of wheel size options
Total combinations = 4 colors × 2 wheel sizes
Total combinations = 8
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
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Sets Sets M and Fare defined as follows: M = {a,b,c,d} F = {c, d, e, f} Find the intersection of M and F.
The intersection of sets M and F contains the elements "c" and "d".
To find the intersection of sets M and F, we need to identify the elements that are common to both sets.
M = {a, b, c, d}
F = {c, d, e, f}
The intersection of M
and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.
Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".
Therefore, the intersection of M and F can be expressed as:
M ∩ F = {c, d}
So, the intersection of sets M and F contains the elements "c" and "d".
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You are given a choice of taking the simple interest on $100,000 invested for 4 years at a rate of %3 or the interest on $100,000 invested for 4 years at an interest rate of 3% compounded . Which investment earns the greater amount of interest? Give the difference between the amounts of interest earned by the two investments.
The investment with compound interest earns a greater amount of interest by $486.12 compared to the investment with simple interest.
To determine which investment earns a greater amount of interest, we need to calculate the interest earned in both scenarios and compare the results.
1. Simple Interest:
The formula for simple interest is given by: I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.
Using this formula, we can calculate the interest earned with simple interest:
I = 100,000 * 0.03 * 4
I = $12,000
2. Compound Interest:
The formula for compound interest is given by: A = P * (1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period.
In this case, the interest is compounded annually, so n = 1. Let's calculate the amount earned:
A = 100,000 * (1 + 0.03/1)^(1*4)
A = 100,000 * (1.03)^4
A = $112,486.12
The interest earned in the compound interest scenario is A - P = $112,486.12 - $100,000 = $12,486.12.
The difference between the amounts of interest earned by the two investments is:
$12,486.12 - $12,000 = $486.12.
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Janna wants to make s'mores at a backyard campfire. The table below shows the parts of marshmallows to graham crackers to make s'mores.
S'mores Marshmallows Graham Crackers
4 8 12
13
At this rate, how many marshmallows and graham crackers will Janna use to make 13 s'mores?
Janna will use 17 marshmallows and 21 graham crackers to make 13 s'mores.
Janna will use 26 marshmallows and 39 graham crackers to make 13 s'mores.
Janna will use 16 marshmallows and 24 graham crackers to make 13 s'mores.
Janna will use 39 marshmallows and 26 graham crackers to make 13 s'mores.
Answer:
Janna will use 26 marshmallows and 39 graham crackers to make 13
Step-by-step explanation:
S'mores Marshmallows Graham Crackers
4 8 12
13
Look at the first line on the table.
For 4 s'mores, 8 marshmallows are used.
8/4 = 2
2 marshmallows are used per s'more.
For 4 s'mores, 12 graham crackers are used.
12/4 = 3
3 graham crackers are used per s'more.
For 13 s'mores,
13 × 2 = 26
13 × 3 = 39
26 marshmallows and 39 graham crackers are needed.
Complete the table:
S'mores Marshmallows Graham Crackers
4 8 12
13 26 39
Answer:
Janna will use 26 marshmallows and 39 graham crackers to make 13
Sandro would like to retire at age 60 with an income of $1500 per month from his
retirement savings. If he is to receive these payments until he is 90 years old, what
amount would he need in his retirement savings account at age 60, if the account
earns 4.5% compounded monthly?
The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.
How the present value is computed:The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.
End of withdrawal period = 90 years old
Beginning of withdrawal period = 60 years old
The number of years between 60 and 90 = 30 years
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 4.5%
PMT (Periodic Payment) = $-1,500
FV (Future Value) = $0
Results:
Present Value (PV) = $296,041.74
Sum of all periodic payments = $540,000 ($1,500 x 360 months)
Total Interest = $243,958.26
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What is the discriminant of the quadratic equation -x^2+6x-6=0
The discriminant of the quadratic-equation -x^2 + 6x - 6 = 0 is 60.
The discriminant of a quadratic equation of the form ax^2 + bx + c = 0 is given by the expression Δ = b^2 - 4ac.
In the given quadratic equation -x^2 + 6x - 6 = 0, we can identify that a = -1, b = 6, and c = -6.
Substituting these values into the discriminant formula, we have:
Δ = (6)^2 - 4(-1)(-6)
The discriminant plays a crucial role in determining the nature of the solutions of a quadratic equation. If the discriminant is positive (Δ > 0), then the equation has two distinct real solutions. If the discriminant is zero (Δ = 0), then the equation has one real solution (also known as a double root). If the discriminant is negative (Δ < 0), then the equation has no real solutions, but it may have complex solutions involving imaginary numbers.
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Prove that "Every well-ordered set is isomorphic to a unique ordinal number"?
Every well-ordered set can be mapped to a unique ordinal number. This mapping preserves the order structure, and the uniqueness arises from the absence of infinite descending chains.
To prove that every well-ordered set is isomorphic to a unique ordinal number, we need to demonstrate two key aspects: (1) that every well-ordered set can be mapped to an ordinal number, and (2) that this mapping is unique, meaning no two different well-ordered sets can be isomorphic to the same ordinal number.
First, let's consider a well-ordered set. By definition, a well-ordered set is a set with a total order relation that satisfies the properties of well-ordering, which include the absence of infinite descending chains.
Now, we can define a mapping from this well-ordered set to an ordinal number. Ordinal numbers represent a specific order type or structure, and they are themselves well-ordered sets. The mapping can be established by assigning each element in the well-ordered set to its corresponding position in the ordinal number based on the order relation.
The key insight is that this mapping is both an isomorphism and unique. It preserves the order structure, meaning that the well-ordered set and the ordinal number have the same order type. Moreover, it is unique because the absence of infinite descending chains ensures that no two different elements in the well-ordered set will map to the same position in the ordinal number.
To illustrate the uniqueness, suppose there were two different well-ordered sets that were isomorphic to the same ordinal number. This would imply that there are two different order structures with the same order type, violating the uniqueness of ordinal numbers.
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10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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The heights of american adult men are normally distributed with a mean of 69.7 inches and a standard deviation of 2.7 inches what is the standard score for a height of 6 foot 2 inches
Answer:
1.5926
Step-by-step explanation:
-We need to first convert the height in feet to inches: Since there are 12 inches in a foot, that means there are 74 inches in a height of 6 foot 2 inches.
-Since the observed height is 74 inches and the mean height is 69.7 inches, we can find the z score by using the following formula:
z = (x-mean) / standard deviation
-We would fill this out like this:
z = (74-69.7) / 2.7
-This equals = 1.592592593
-Rounded to 4 decimal places, this equals 1.5926
The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answer:
a
Step-by-step explanation:
the perimeter (P) of a square is the sum of the 4 congruent sides.
the area of a square is calculated as
area = s² ( s is the length of a side )
here area is 36 , then
s² = 36 ( take square root of both sides )
s = [tex]\sqrt{36}[/tex] = 6
then
P = 4s = 4 × 6 = 24 cm
Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used.
Complete the table by classifying the polynomials by degree and number of terms.
quadratic
constant
exponential
Polynominal
(picture)
The names of the expressions are;
1) Monomial, quadratic
2) Monomial, constant
3) Binomial, Linear
4) Trinomial, quadratic
What are polynomials and trinomials?
An algebraic expression that has one or more terms, each of which is a variable raised to a non-negative integer exponent and multiplied by a coefficient, is referred to as a polynomial. The terms are mixed by adding or removing. A polynomial may include 0 terms or more.
A particular kind of polynomial known as a trinomial has exactly three terms. Trinomials are made up of three different pieces, which are frequently denoted by the formula "ax2 + bx + c," where "a," "b," and "c" are coefficients.
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please help me ive tried so much an still dont get it .
The volume of the sphere as shown in the diagram is 4186.67.
What is volume?volume is the amount of space in a certain 3D object.
To calculate the volume of the sphere, we use the formula below
Formula:
V = 4πr³/3............. Equation 1Where:
V = Volume of the spherer = Radius of the sphereπ = Contant = PieFrom the diagram,
Given:
r = 10 π = 3.14Substitute these values into equation 1
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graph the line y = - 5x + 3
The line passes through the points (0, 3), (1, -2), and (-1, 8), and it extends infinitely in both directions.
To graph the line y = -5x + 3, we can start by plotting a few points and then connecting them to create the line.
We can choose arbitrary values for x and calculate the corresponding y values using the given equation. Let's choose three values of x and calculate the corresponding y values:
When x = 0:
y = -5(0) + 3 = 3
So, we have the point (0, 3).
When x = 1:
y = -5(1) + 3 = -5 + 3 = -2
So, we have the point (1, -2).
When x = -1:
y = -5(-1) + 3 = 5 + 3 = 8
So, we have the point (-1, 8).
Now, we can plot these points on a coordinate plane:
|
10 +
|
|
5 +
|
|
0----+----+----+----+----+----+----+----+----+----+
-2 -1 0 1 2 3 4 5 6 7
Once we have plotted these points, we can connect them to form a straight line:
|
10 +
|
|
5 + .
| .
| .
0----+----+----+----+----+----+----+----+----+----+
-2 -1 0 1 2 3 4 5 6 7
The line passes through the points (0, 3), (1, -2), and (-1, 8), and it extends infinitely in both directions.
The graph of the line y = -5x + 3 is a straight line with a slope of -5 (indicating that it decreases by 5 units in the y-direction for every 1 unit increase in the x-direction) and a y-intercept of 3 (indicating that the line intersects the y-axis at the point (0, 3)).
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Solve the linear inequality. Express the solution using interval notation.
13 ≤ 4x − 3 ≤ 29
[tex]13 \leqslant 4x - 3 \leqslant 29 \\ 13 + 3 \leqslant 4x \leqslant 29 + 3 \\ 16 \leqslant 4x \leqslant 32 \\ 16 \div 4 \leqslant x \leqslant 32 \div 4 \\ 4 \leqslant x \leqslant 8[/tex]
factor and solve if necessary
y-5y-36
Answer:
Step-by-step explanation:
-4(y+9)