Answer:
Number of ways to select 3 cars and 4 trucks = 18,480
Step-by-step explanation:
Let x be the number of ways to select 3 cars and 4 truck.
Given:
Total number of cars = 8
Total number of Trucks = 11
We need to find out how many ways can the inspector select 3 cars and 4 truck.
Solution:
Using combination formula.
[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
Where, n = Total number of object.
m = Number of selected object.
We need to find out how many ways can the inspector select 3 cars and 4 truck from 8 cars and 11 trucks.
So, we write the the combination as given below.
[tex]8C_{3}\times 11C_{4} = Number\ of\ ways\ to\ selection[/tex]
[tex]\frac{8!}{3!(8-3)!} \times \frac{11!}{4!(11-4)!}= x[/tex]
[tex]x = \frac{8\times 7\times 6\times 5!}{3!\times 5!} \times \frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}[/tex]
Factorial 5 and 7 is cancelled.
[tex]x = \frac{8\times 7\times 6}{6} \times \frac{11\times 10\times 9\times 8}{24}[/tex] ([tex]3! = 6\ and\ 4! = 24[/tex])
[tex]x = (8\times 7) \times (11\times 10\times 3)[/tex] ([tex]\frac{9\times 8}{24}=\frac{72}{24}=3[/tex])
[tex]x=56\times 330[/tex]
x = 18480
Therefore, the Inspector can select 3 cars and 4 trucks in 18,480 ways,
To determine how many ways the state inspector can select 3 cars from 8 and 4 trucks from 11, we need to calculate the combinations separately for each type of vehicle and then multiply them together to find the total number of ways to make both selections simultaneously.
### Selection of Cars:
The number of ways to choose 3 cars from 8 is a combination problem, because the order in which we select the cars does not matter. The formula for combinations, denoted as C(n, k), where n is the total number of items to choose from, and k is the number of items to be chosen, is given by:
C(n, k) = n! / (k! * (n - k)!)
Let's apply this formula to select 3 cars from 8:
C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!) = (8 × 7 × 6) / (3 × 2 × 1)
Simplify the factorials by canceling out common terms:
C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = (8/2) × (7/1) × (6/3) = 4 × 7 × 2 = 56
So, there are 56 ways to choose 3 cars out of 8.
### Selection of Trucks:
Similarly, to choose 4 trucks out of 11 we use the combination formula again:
C(11, 4) = 11! / (4! * (11 - 4)!) = 11! / (4! * 7!) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1)
Simplify the factorials:
C(11, 4) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1) = (11/1) × (10/2) × (9/3) × (8/4) = 11 × 5 × 3 × 2 = 330
So, there are 330 ways to choose 4 trucks out of 11.
### Total Ways:
To find the total number of ways to select both the cars and trucks for inspection, we multiply the number of ways to choose the cars by the number of ways to choose the trucks:
Total number of ways = number of ways to choose cars × number of ways to choose trucks
Total number of ways = 56 (from choosing cars) × 330 (from choosing trucks)
Total number of ways = 56 × 330 = 18480
Therefore, the state inspector can select 3 cars out of 8 and 4 trucks out of 11 in 18,480 different ways.
At what points on the graph of f(x)=2x^3-6x^2-27x is the slope of the tangent line -9?
Answer:
(-1, 19) and (3, -81)
Step-by-step explanation:
f(x) = 2x³ − 6x² − 27x
f'(x) = 6x² − 12x − 27
-9 = 6x² − 12x − 27
0 = 6x² − 12x − 18
0 = x² − 2x − 3
0 = (x + 1) (x − 3)
x = -1 or 3
f(-1) = 19
f(3) = -81
The points are (-1, 19) and (3, -81).
Dominic pays 7% interest on his $15,000 college loan and 12% interest on his 11,000 car loan. What average interest rate does he pay on the total $26,000 he owes?
The requried, Dominic pays an average interest rate of approximately 9.115% on the total $26,000 he owes.
To find the average interest rate Dominic pays on the total $26,000 he owes, we can use a weighted average approach based on the interest rates and amounts of each loan.
Given:
College loan amount: $15,000
College loan interest rate: 7%
Car loan amount: $11,000
Car loan interest rate: 12%
Let's calculate the weighted average interest rate:
Calculate the total interest paid for each loan:
Interest paid on the college loan = 0.07 * $15,000
Interest paid on the car loan = 0.12 * $11,000
Calculate the total interest paid for both loans:
Total interest = Interest on college loan + Interest on car loan
Calculate the weighted average interest rate based on the total interest paid and the total amount owed:
Weighted average interest rate = (Total interest / Total amount owed) * 100
Let's do the calculations:
Interest on college loan: 0.07 * $15,000 = $1,050
Interest on car loan: 0.12 * $11,000 = $1,320
Total interest: $1,050 + $1,320 = $2,370
Total amount owed: $15,000 + $11,000 = $26,000
Weighted average interest rate: ($2,370 / $26,000) * 100 ≈ 9.115%
So, Dominic pays an average interest rate of approximately 9.115% on the total $26,000 he owes.
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Dominic pays a total interest of $2,370 on his college and car loans, which sums up to $26,000. Therefore, the average interest rate he pays on the total loan amount is calculated to be 9.12%.
Explanation:Dominic's interest for his college loan is calculated by multiplying the total loan amount of $15,000 by 7% which equals $1,050. The interest on his car loan is calculated by multiplying $11,000 by 12%, equalling $1,320. His total interest paid for both loans is $1,050 + $1,320 = $2,370. To find the average interest rate that Dominic pays on the total amount of $26,000, you would divide his total interest paid ($2,370) by the total loan amount ($26,000) and then multiply by 100%. That's $2,370 / $26,000 * 100% = 9.12%. Therefore, on average Dominic is paying an interest rate of 9.12% on his total owed amount.
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A forest ranger is on a 90-foot fire watch tower. He spots a fire at an angle of depression to the fire that is 7 degrees. What is the horizontal distance between the tower and the fire
Answer: the horizontal distance between the tower and the fire is 732.89 feet
Step-by-step explanation:
Considering the situation, a right angle triangle is formed. The height of the fire watch tower represents the opposite side of the right angle triangle.
The horizontal distance, h between the tower and the fire represents the adjacent side of the right angle triangle.
If the angle of depression to the fire that is 7°, the angle of elevation from of the tower watcher from the fire is also 7° because they are alternate angles.
To determine h, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 7 = 90/h
h = 90/tan7 = 90/0.1228
h = 732.89 feet
A trader bought x mangoes at the rate of 4 mangoes for 10 naira five of the mangoes were bad so he sold the remaining at the rate of 5 mangoes for 20 naira and he made a gain of 10 naira how many mangoes did he buy ?
Answer:
20 mangoes.
Step-by-step explanation:
Given:
Total number of mangoes, a trader bought = [tex]x[/tex]
A trader bought at the rate of 4 mangoes for 10 naira.
Five of the mangoes were bad.
He sold the remaining at the rate of 5 mangoes for 20 naira.
He made a gain of 10 naira
Question asked:
Total number of mangoes, a trader bought = [tex]x[/tex] = ?
Solution:
Unitary method
Cost price of 4 mangoes = 10 naira.
Cost price of 1 mango = [tex]\frac{10}{4}[/tex]
Cost price of [tex]x[/tex] mango = [tex]\frac{10}{4}\times x= \frac{5}{2} x[/tex]
As 5 of the mangoes were bad and he sold the remaining mangoes, then Total number of mangoes sold = [tex]x-5[/tex]
Sale price of 5 mangoes = 20 naira
Sale price of 1 mango = [tex]\frac{20}{5}[/tex]
Sale price [tex]x-5[/tex] of mango = [tex]\frac{20}{5}\times(x-5)=4(x-5)=4x-20[/tex]
Now, as we know,
[tex]Gain = Sale price - cost price[/tex]
[tex]10 = 4x-20 -\frac{5}{2} x\\ 10=4x-\frac{5}{2} x-20\\10=\frac{8x-5x}{2} -20[/tex]
[tex]10 =\frac{3x}{2} -20[/tex]
Adding both sides by 20
[tex]30=\frac{3x}{2}[/tex]
Multiplying both sides by 2
[tex]60 = 3x[/tex]
Dividing both sides by 3
[tex]x=20[/tex]
Therefore, total number of mangoes, a trader bought is 20.
A maple syrup company is making a new label for its barrels of syrup. If the barrels are 5 feet tall and have a radius of 2 feet, what is the area of the label the company needs? (Use 3.14 for .) A. 62.8 sq ft B. 314 sq ft C. 10 sq ft D. 219.8 sq ft
Answer:
(A)62.8 square feet
Step-by-step explanation:
Height of the barrels = 5 feet
Radius of the barrels= 2 feet
[tex]\pi[/tex]=3.14
The barrel is in the shape of a cylinder and the area of the label the company needs is that of the round sides(curved surface area) of the cylinder.
Curved Surface Area of a Cylinder=[tex]2\pi rh[/tex]
=2X3.14X2X5
=62.8 square feet
The company need 62.8 square feet of label.
10 POINTS AND BRAINLIEST!
Calculate the area of the trapezoid, which is not drawn to scale.
Answer:
A = (5+4) divided by 1/2 x 11 (h) = 49.5 in
Answer:38 inches
Step-by-step explanation:A=1/2 (base 1 + base 2) x height = area
Base 1 = 11 in
Base 2 = 8 in
Height = 4 inches
Area if trapezoid = 1/2 x 11 + 8 x 4 =!19 sum of bases
19x4(H) = 76
76/2=38 inches
Area of trapezoid = 38 inches
It was predicted that a country will have an elderly population (65 and older) of 8 comma 176 comma 000 in the year 2050 and that this will be 22.1% of the population. What is the total predicted population of this country in 2050?
Answer:
36,995,475
Step-by-step explanation:
In the year 2050, a country's elderly population is predicted to be 8,176,000
This is 22.1% of the tota population
If x=total population in the year 2050
and 22.1% of x = 8,176,000
Then:
22.1% of x = 8,176,000
[tex]\frac{22.1}{100}x= 8176000[/tex]
On Cross multiplication
22,1x = 817,600,000
x=[tex]\frac{817600000}{22.1}[/tex] =36995475.11
We jettison fractional values because we are dealing with population.
Therefore, In the year 2050, the total population of the country will be 36,995,475
PLLLLZ HELP Find the seventh partial sum of 13, 22, 31, 40, ...
9
67
106
280
Just got the test and answered 67...was absolutely sure it is correct answer...Most likely the answer is 9 ....Since to get every next sum is +9.. Well, at least 67 is a wrong answer..:(
The seventh partial sum is 280
Option D is the correct answer.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
The sequence has a common difference of 9, so it is an arithmetic sequence.
The first term is 13.
To find the seventh partial sum, we need to add up the first seven terms of the sequence:
= 13 + 22 + 31 + 40 + 49 + 58 + 67
= 280
Therefore,
The seventh partial sum is 280
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A tailor cuts a piece of thread One-half of an inch long from a piece Nine-sixteenths of an inch long. What is the length of the remaining piece of thread?
Answer:
The length of the remaining piece of thread is [tex]\frac{1}{16}.[/tex]
Step-by-step explanation:
Given:
A tailor cuts a piece of thread One-half of an inch long from a piece Nine-sixteenths of an inch long.
Now, to find the length of the remaining piece of thread.
Total thread = [tex]\frac{9}{16} \ inch.[/tex]
Tailor cuts a piece of thread = [tex]\frac{1}{2}\ inch.[/tex]
Now, to get the length of the remaining piece of thread by subtracting tailor cuts a piece of thread from the total thread:
[tex]\frac{9}{16} -\frac{1}{2} \\\\=\frac{9-8}{16} \\\\=\frac{1}{16}[/tex]
Therefore, the length of the remaining piece of thread is [tex]\frac{1}{16}.[/tex]
Answer lovely
Step-by-step explanation:
Consider the statement that the product of two of the numbers 651000 − 82001 + 3177, 791212 − 92399 + 22001, and 244493 − 58192 + 71777 is nonnegative (for the purpose of this agreement, we will think of 0 as carrying a positive sign).Identify the correct proof of the given statement.(You must provide an answer before moving to the next part.)NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the statement that the product of two of the numbers 651000 - 82001 - 3177791212-92399 22001, and 244493_58192+71777 is nonnegative (for the purpose of this agreement, we will think of O as carrying a positive sign). Identify the correct proof of the given statement. (You must provide an answer before moving to the next part.) A) Of these three numbers, at least two numbers must be negative, since there are only two signs. The product of these two numbers is nonnegative. B) Of these three numbers, at least two must be positive. The product of these two numbers is nonnegative. C) Of these three numbers, all three must have the same sign. Thus, the product of any two numbers is nonnegative. D) Of these three numbers, at least two must have the same sign, since there are only two signs. The product of two with the same sign is nonnegative. E) Of these three numbers, at least two must have the same sign. The product of one of these numbers and the third number is nonnegative.
Answer:
a c
Step-by-step explanation:
Final answer:
All three calculated numbers are positive, and therefore, the product of any two of them will also be positive. Option B is correct, which states that at least two numbers must be positive, making the resulting product nonnegative.
Explanation:
The statement that the product of two of the numbers 651000 - 82001 + 3177, 791212 - 92399 + 22001, and 244493 - 58192 + 71777 is nonnegative relies on the principles of arithmetic involving the addition and multiplication of numbers with different signs. Calculating the given numbers:
651000 - 82001 + 3177 = 573176 (positive)
791212 - 92399 + 22001 = 710814 (positive)
244493 - 58192 + 71777 = 255078 (positive)
All three numbers are positive, so the product of any two would also be positive, according to the multiplication rules that state the product of two positive numbers is always positive.
Therefore, the correct answer to the statement is:
B) Of these three numbers, at least two must be positive. The product of these two numbers is nonnegative.
A defunct website listed the "average" annual income for Florida as $35,031. What is the role of the term average in statistics? Should another term be used in place of average?
Answer:
For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]
And the average is calculated with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
Where n represent the sample size
N represent the population size, and X the observations for this case the annual income.
This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]
After calculate the average they got:
[tex] \bar X= 35031[/tex]
And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data
Step-by-step explanation:
For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]
And the average is calculated with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
Where n represent the sample size
N represent the population size, and X the observations for this case the annual income.
This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]
After calculate the average they got:
[tex] \bar X= 35031[/tex]
And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data
If it takes Daniel 9 hours to clean an office building and it takes Mark 6 hours, how long would it take the two of them, working together, to clean the building?
It would be 3 hours. This is 3 hours because the problem says that daniel takes 9 hours to clean and office building and mark takes 6 hours so if you subtract 9hours from 6 hours it would be 3 hours total. Now this can be 2 answers it can also be 15 hours if you were to add 9 hours to 6 hours.
Answer: it will take 3.6 hours
Step-by-step explanation:
If it takes Daniel 9 hours to clean an office building, it means that the rate at which he cleans the office building per hour is 1/9
If it takes Mark 6 hours to clean the office building, it means that the rate at which Mark cleans the office building per hour is 1/6
If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be
1/9 + 1/6 = (6 + 9)/54 = 15/54
Assuming it takes t hours for both of them to clean the office working together, the working rate per hour would be 1/t. Therefore,
15/54 = 1/t
t = 54/15 = 3.6 hours
Asna works on a shipping dock at a tire manufacturing plant. She load a pallet with 4 Mudslinger tires and 6 Roadripper tires. The tires on the pallet weigh 212 pounds. She loads a secong pallet with 7 Mudslinger tires and 2 Roadripper tires. The tires on the secong pallet weigh 184 pounds. How much does each Mudslinger and each Roadripper tire weigh? (9th Grade CP Math)
Answer:
A Mudslinger tire weighs 20.71 pounds and a Roadripper tire weighs 19.52 pounds
Step-by-step explanation:
Let the weight of a Mudslinger tire=m
Let the weight of a Roadripper tire=r
4 Mudslinger tires and 6 Roadripper tires weigh 200 pounds
4m+6r=200.....(i)
7 Mudslinger tires and 2 Roadripper tires weigh 184 pounds
7m+2r=184....(ii)
To find the values of m and r, we solve the two derived equations simultaneously.
4m+6r=200.....(i)
7m+2r=184....(ii)
Multiply (ii) by 3 to get (iii)
21m+6r=552....(iii)
4m+6r=200.....(i)
SUbtract (i) from (iii)
17m=352
m=352/17=20.71 pounds
Substitute m=20.71 in (i)
4(20.71)+6r=200
6r=200-82.84=117.16
r=117.16/6=19.52 pounds
Explain how to use the figure below and a sequence of similarity transformations from Circle A to Circle C to prove that all circles are similar.
transformation: Translating then diilating
first you go from A to C
then you shrink it down to size n
Priya rewrites the expression 8y - 24 as 8(y - 3). Han rewrites 8y - 24 as 2 (4y - 12). Are Priya's and Han's expressions each equivalent to 8y - 24? Explain your reasoning
Answer:
They are equivalent
Step-by-step explanation:
Priya rewrites the expression 8y - 24 as 8(y - 3).
Han rewrites 8y - 24 as 2(4y - 12)
The two expressions are equivalent. This is reached by taking note of the fact that if the factorized form is expanded, they both give the same result.
In Priya's Version,
8(y - 3)=(8 X y)-(8 X 3)=8y-24
Likewise In Han's Version
2(4y - 12)=(2 X 4y) - (2 X 12) =8y-24
We can see from the bolded that our results are the same. Priya's Version is a fully factorized form while Han's Version can still be factorized further to get Priya's version.
i.e. 2(4y - 12)=2 X 4(y-3)=8(y-3)
Both Priya's expression (8(y - 3)) and Han's expression (2(4y - 12)) are equivalent to the original expression 8y - 24. By distributing the multiplicative factors, both expressions simplify to the original expression, proving their equivalence.
Explanation:Yes, both Priya's and Han's expressions are equivalent to 8y - 24. To confirm that Priya's and Han's expressions represent the same value as the original expression, we can simplify their expressions through the distributive property, which states that multiplying a sum by a number gives us the same result as multiplying each addend by the number separately and then adding the products.
For Priya's expression, 8(y - 3), we distribute the 8:
8 × y = 8y8 × (-3) = -24Thus, Priya's expression simplifies to 8y - 24, which is the original expression.
For Han's expression, 2(4y - 12), we also distribute:
2 × 4y = 8y2 × (-12) = -24So, Han's expression simplifies to 8y - 24, which is again the original expression.
Therefore, we can conclude that both methods provide equivalent expressions to 8y - 24, showcasing that math provides multiple paths to reach the same answer.
Show that the curve y = 4 x 3 + 7 x − 5 y=4x3+7x-5 has no tangent line with slope 2 2. y = 4 x 3 + 7 x − 5 ⇒ m = y ' = y=4x3+7x-5⇒m=y′= Preview , but x 2 x2 0 0 for all x x, so m ≥ m≥ for all x x.
Answer: The statement is true (see Step-by-step explanation).
Step-by-step explanation:
The slope of the tangent line for all point of the curve is determine by derive the expression abovementioned in the statement:
[tex]y' = 12 \cdot x^{2} + 7[/tex]
The previous expression represents a parabola, whose output will be positive for all [tex]x[/tex] due to the symmetry of [tex]x^{2}[/tex] and the positive coefficients of the polynomial. If the function is evaluated at [tex]x = 0[/tex], where the minimum occurs, it is evident that the smallest value is [tex]y' = 7[/tex] . Therefore, the inexistence of any tangent line with slope 2 associated with that curve is true.
Last week 23,847 tickets were sold At the Atlantic school. The principal rounded the number of tickets. To the nearest thousand.He rounded the number of tickets sold for the music festival to the nearest thousand as well. They both rounded to the same number. How many tickets were sold for the music festival?
Answer: 24,000 tickets
Step-by-step explanation: The idea is just to round up the original ticket sold to the nearest thousand. That is 23,847 tickets to the nearest thousand is 24,000 since the next number after 3 is 8 which is greater or equal to five so you take it as 1 and add it to 3 making the total number of tickets sold as 24,000.
Find the value of the given function's derivative at x=3
f(x)=k(g(x))
g(x)=2x-x^2
k'(-3)=2
f'(3)=[]
According to the chain rule, if we have a function:
[tex]f(x)=k(g(x))[/tex]
The derivative at a point [tex]a[/tex] will be:
[tex]f'(a)=k'(g(a))g'(a)[/tex]
We know that:
[tex]f'(3)=k'(g(3))g'(3)\\ \\ \\ a=3 \\ \\ \\ Then: \\ \\ g(3)=2(3)-3^2 \\ \\ g(3)=6-9 \\ \\ g(3)=-3 \\ \\ \\ k'(g(3))=k'(-3)=2 \\ \\ \\ g'(x)=2-2x \\ \\ g'(3)=2-2(3)=-4 \\ \\ \\ Finally: \\ \\ f'(3)=2(-4) \\ \\ \boxed{f'(3)=-8}[/tex]
David waits by the crosswalk sign on his way to school. The angle outlined on the sign turns through 50 one-degree angles. Find the measure of the angle.
the measure of the angle outlined on the sign is 50∘.
To find the measure of the angle outlined on the sign, we simply multiply the number of one-degree angles by the measure of one degree.
Given that the angle turns through 50 one-degree angles, we can calculate the measure of the angle as follows:
Measure of the angle = Number of one-degree angles × Measure of one degree
Measure of the angle=50 * 1
Measure of the angle=50
So, the measure of the angle outlined on the sign is 50∘.
The probable question maybe:
David waits by the crosswalk sign on his way to school. The angle outlined on the sign turns through 50 one-degree angles. What is the measure of the angle outlined on the crosswalk sign?
A student uses the ratio of 4 oranges to 6 fluid ounces to find the number of oranges needed to make 24 fluid ounces of juice. The student writes this proportion: StartFraction 4 over 6 EndFraction = StartFraction 24 over 16 EndFraction Explain the error in the student's work.
The student made a mistake in setting their proportion, which resulted in the wrong calculation. The correct proportion should have been 4/6 = x/24, where x is the number of oranges needed. Solving this proportion gives us 16 oranges needed for 24 fluid ounces of juice.
Explanation:The error in the student's work lies in the improper establishment of the proportion. The initial ratio provided was 4 oranges to 6 fluid ounces.
The proportion, therefore, should have been StartFraction 4 over 6 EndFraction = StartFraction x over 24 EndFraction, where 'x' is the number of oranges required for 24 ounces of juice. The student incorrectly used '24' as the numerator rather than the denominator, causing an error in calculation.
To correct this, we can cross-multiply to get 4 * 24 = 6 * x, leading to x = 16 oranges. Therefore, 16 oranges are needed for 24 fluid ounces of juice, which is the correct solution.
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Sample response: The second ratio in the proportion is set up as ounces over oranges. The units should be in the same place in the proportion as the first ratio
Step-by-step explanation:
NEED HELP ASAP!! can someone please explain this to me!
Answer:
BG = 3; GE = 6
Step-by-step explanation:
The centroid of a triangle divides the median into two parts in the ratio 1 : 2. That is, the short segment is 1/3 the length of the median, and the long segment is 2/3 the length of the median.
BG = 1/3·BE = 9/3 = 3
GE = 2/3·BE = 2/3·9 = 18/3 = 6
If using the method of completing the square to solve the quadratic equation x^2+17x+12=0x 2 +17x+12=0, which number would have to be added to "complete the square"?
Answer:
289/4
Step-by-step explanation:
x² + 17x + 12 = 0
x² + 17x = -12
Take half of the second coefficient, square it, then add the result to both sides.
(17/2)² = 289/4
x² + 17x + 289/4 = -12 + 289/4
(x + 17/2)² = 241/4
The answer is 289/4.
Solve the equationBy using quadratic equation formula a[tex]x^{2}[/tex] + bx + c = 0, we get:
⇒ [tex]x^{2}[/tex] + 17x + 12 = 0
⇒ [tex]x^{2}[/tex] + 17x = -12
Take half of the second coefficient, square it, then add the result to both sides.
⇒ (17/2)² = 289/4
⇒ [tex]x^{2}[/tex] + 17x + 289/4 = -12 + 289/4
⇒ (x + 17/2)² = 241/4
What are quadratic equations?Quadratic equations are second-degree algebraic expressions and are of the form a[tex]x^{2}[/tex] + bx + c = 0.
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find the relative minimum of
y = 3x^3 + 14x^2 - 11x - 46
(___, ___)
Answer:
(0.353, -48)
Step-by-step explanation:
dy/dx = 9x² + 28x - 11 = 0
Using the quadratic formula:
x = -3.46 and 0.353
d²y/dx² = 18x + 28
Minima when d²y/dx² is positive
x = 0.35284 or (-14+sqrt(295))/9
y = 3x³ + 14x² - 11x - 46
y = -48.00651351
The relative minimum of a function is (1/2, -65/4), derive the function, set it to zero, solve for x, and find the corresponding y-value.
To find the relative minimum of the function y = 3x^3 + 14x^2 - 11x - 46, we need to first take the derivative of the function, set it equal to zero, and then solve for the critical point.
This will give us the x-coordinate of the minimum. Next, plug this x-value back into the original function to find the corresponding y-coordinate.
The relative minimum of the function y = 3x^3 + 14x^2 - 11x - 46 is at the point (1/2, -65/4).
Ronnie and Angela went to the pizza shop and each bought a medium pizza. Angela cut her pizza into four pieces and ate three of them. Ronnie cut his pizza as show below
Answer: there is nothing shown below
Step-by-step explanation:
Y=11x+6 determine the intercepts of the line
Final answer:
The y-intercept of the line y = 11x + 6 is (0, 6), and the x-intercept is (-6/11, 0). To find these, you set x to 0 to find the y-intercept and set y to 0 to solve for the x-intercept.
Explanation:
To determine the intercepts of the line given by the equation y = 11x + 6, we need to find where the line crosses the x-axis and the y-axis. The y-intercept is found when x = 0; substituting x = 0 into the equation gives us y = 6. Therefore, the y-intercept is at the point (0, 6). To find the x-intercept, we set y = 0 and solve for x; setting y = 0 in our equation results in 0 = 11x + 6. Solving for x gives us x = -6/11. The x-intercept is at the point (-6/11, 0).
Find the arc length of AB. Round your answer to the nearest hundredth.
!no absurd answers please! : )
The arc length of AB is 8 m (app.)
Explanation:
Given that the radius of the circle is 8 m.
The central angle is 60°
We need to determine the arc length of AB
The arc length of AB can be determined using the formula,
[tex]arc \ length=\frac{central \ angle}{360^{\circ}} \times circumference[/tex]
Substituting central angle = 60° and circumference = 2πr in the above formula, we get,
[tex]arc \ length=\frac{60^{\circ}}{360^{\circ}} \times 2 \pi(8)[/tex]
Simplifying the terms, we get,
[tex]arc \ length=\frac{8 \pi }{3}[/tex]
Dividing, we get,
[tex]arc \ length=8.37758041[/tex]
[tex]arc \ length=8(app.)[/tex]
Hence, the arc length is approximately equal to 8.
Therefore, the arc length of AB is 8 m
Becky and luke bought the same kind of pencils and erasers . Becky spent $1.45 for 2 pencils and 3 erasers . Luke spent $2.65 for 5 pencils and 1 eraser what is the Cost of 1 eraser ?
Answer: the cost of each pencil is $0.5
the cost of each eraser is $0.15
Step-by-step explanation:
Let x represent the cost of one pencil.
Let y represent the cost of one eraser.
Becky spent $1.45 for 2 pencils and 3 erasers. This means that
2x + 3y = 1.45- - - - - - - - - -1
Luke spent $2.65 for 5 pencils and 1 eraser. This means that
5x + y = 2.65- - - - - - - - - -2
Multiplying equation 1 by 1 and equation 2 by 3, it becomes
2x + 3y = 1.45
15x + 3y = 7.95
Subtracting, it becomes
- 13x = - 6.5
x = - 6.5/- 13
x = 0.5
Substituting x = 0.5 into equation 2, it becomes
5 × 0.5 + y = 2.65
2.5 + y = 2.65
y = 2.65 - 2.5
y = 0.15
The cost of one eraser is [tex]\(\$0.15\).[/tex]
Let's denote the cost of one pencil as p dollars and the cost of one eraser as e dollars.
According to the given information:
1. Becky spent $1.45 for 2 pencils and 3 erasers, so her total cost can be expressed as:
[tex]\[ 2p + 3e = 1.45 \][/tex]
2. Luke spent $2.65 for 5 pencils and 1 eraser, so his total cost can be expressed as:
[tex]\[ 5p + 1e = 2.65 \][/tex]
We can now solve this system of equations to find the cost of one eraser (e ).
From equation 1, we can express p in terms of e :
[tex]\[ 2p = 1.45 - 3e \]\[ p = \frac{1.45 - 3e}{2} \][/tex]
Substitute this expression for p into equation 2:
[tex]\[ 5\left(\frac{1.45 - 3e}{2}\right) + e = 2.65 \][/tex]
Multiply both sides by 2 to eliminate the fraction:
[tex]\[ 5(1.45 - 3e) + 2e = 5.3 \]\[ 7.25 - 15e + 2e = 5.3 \][/tex]
Combine like terms:
[tex]\[ 7.25 - 13e = 5.3 \][/tex]
Subtract 7.25 from both sides:
[tex]\[ -13e = 5.3 - 7.25 \]\[ -13e = -1.95 \][/tex]
Divide both sides by -13:
[tex]\[ e = \frac{-1.95}{-13} \]\[ e = 0.15 \][/tex]
Therefore, the cost of one eraser is [tex]\(\$0.15\).[/tex]
Prior to ________ many school systems attempted to circumvent the racial desegregation process by using standardized tests and testing procedures to place minority children into segregated programs within public schools
Answer:
Hobson v. Hansen (1967)
Step-by-step explanation:
Hobson v. Hansen (1967) was a federal court case filed by civil rights activist Julius W. Hobson against Superintendent Carl F. Hansen and the District of Columbia's Board of Education on the charge that the current educational system underprivileged blacks and the poor of their right to equal educational opportunities relative to their white and affluent peers, on account of race and socioeconomic status.
Before the landmark 1954 Brown v. Board of Education decision, school systems used standardized tests to maintain segregated programs in public schools. This was in violation of federal laws and highlighted by the Coleman Report, which sparked a debate about desegregation and testing bias.
Explanation:Prior to the Brown v. Board of Education ruling in 1954, many school systems employed a variety of tactics to circumvent the racial desegregation process. Standardized tests and testing procedures were frequently used to place minority children into segregated programs within public schools, reinforcing educational segregation. This practice was a violation of Title VI of the Civil Rights Act of 1964 and other federal legislations aimed at ensuring equal opportunity in education.
After the Coleman Report in 1966, the debate around desegregation, busing, and cultural bias in standardized testing intensified. New policies like mandated busing were implemented to correct the discriminatory practices and to achieve the goals of desegregation. Despite these efforts, many districts faced challenges in successfully integrating schools, resulting in a variety of voluntary and court-ordered methods to promote equal education.
Lin read for x minutes, and Elena read for more than that. Write an expression for the number of minutes Elena read. Only use decimals in your expression
In this exercise, we know some facts:
Lin read for x minutes.Elena read for more than that.The problem tells us nothing about the number of minutes Elena read more than Lin. However, let's say Elena read one-third more than the number of minutes Lin read. Therefore:
For Lin:
[tex]Number \ of \ minutes \ Lin \ read=x[/tex]
For Elena:
[tex]Number \ of \ minutes \ Elena \ read=x+\frac{1}{3}x \\ \\ Number \ of \ minutes \ Elena \ read=\frac{3x+x}{3} \\ \\ Number \ of \ minutes \ Elena \ read=\frac{4x}{3} \\ \\ Number \ of \ minutes \ Elena \ read=\frac{4x}{3} \\ \\ \\ By \ using \ decimals: \\ \\ Number \ of \ minutes \ Elena \ read \approx 1.33x[/tex]
Final answer:
The expression for the number of minutes Elena read is x + 1.
Explanation:
To write an expression for the number of minutes Elena read, we can use the variable x to represent the number of minutes Lin read. Since Elena read for more than Lin, we can use the expression x + 1 to represent the number of minutes Elena read. This expression indicates that Elena read for one minute more than Lin.
Ruth needs 2 1/4cups of flour for one cake recipe and 2 3/4cups of flour for another cake recipe if she makes broths cakes how much flour will ruth use together
Answer:
5 cups
Step-by-step explanation:
2 1/4 + 2 3/4= 5 cups of flour
Answer:
The answer is 5
Step-by-step explanation:
A trick you can use here is by understanding what the fraction is indicating, the number 4 indicates a full cup reached and the first 1/4 is 1 part out of 4 parts to be reached. the second fraction is 3 out of 4 and if you add the one on the other fraction then you get 3+1==4 which majes a full cup
and once you ad the other 4 cups you get 5