Answers
Answer:
f(x) = - 2 (x + 2)² + 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 2, 6), thus
y = a(x - (- 2))² + 6, that is
y = a(x + 2)² + 6
To find a substitute the point (0, - 2) into the equation
- 2 = a(0 + 2)² + 6 ( subtract 6 from both sides )
- 8 = 4a ( divide both sides by 4 )
- 2 = a
f(x) = - 2(x + 2)² + 6 ← in vertex form
Related Questions
g water is poured into a right cylindrical tank at a rate of 6 cubic inches per minute. if the radius of the base is 20 incheas long; how fast is the hieght changing when the water level is 12 inches high?
Answers
Water is increasing at a rate of ( 3/200π ) inch/min in a cylindrical tank.
As per the question we are provided with ,
r = 20 inch equation 1
( dV/dt ) = 6 cubic inch per min equation 2
We need to calculate (dh/dt) and to calculate this we can use the formula of volume of cylinder.
volume of cylinder = V
V = π\(r^{2} h\) equation 3
Substitute value of r from equation 1 in equation 3, we will get
V = π × \((20^{2} )\) × h
V = π (400) h
Differentiate with respect to time , we get
( dV/dt ) = 400π ( dh/dt )
Substitute value of ( dV/dt ) from equation 2 , we get
6 = 400 π ( dh/dt )
( dh/dt ) = ( 3/200π ) inch/min
Thus, ( 3/200π ) inch/min is the rate of increase of height of water.
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Express the following as ONE fraction:
(( b - c )/ b ) + (b / ( b + c ))
Answers
Answer:
Step-by-step explanation:
(b - c)/b * (b+c)/b Notice how the second fraction is inverted and multiplied. That's how you handle a 4 tier fraction. Here's a simpler example
\(\frac{\frac{2}{3} }{\frac{4}{5} } = \frac{2}{3} * \frac{5}{4}\)
What you get with your problem is
(b^2 - c^2)/b^2
state if the triangle is a right triangle.
a²+b²=c²
4²+ 8\sqrt 2²=12²
16+11.3=144
27.3=144
this answer in the back says that this triangle is supposed to be a right triangle so could you help me if you see an errors that I made. I'm pretty sure I did in regards to the square root section.
Answers
Yes, it is a right-angled triangle.
A right triangle, sometimes known as a right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle or two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.Use the Pythagorean theorem.The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.a² + b² = c²(4)² + (8√2)² = (12)²16 + (64*2) = 14416 + 128 = 144144 = 144The left hand side is equal to the right hand side.Hence, it is a right angled triangle.To learn more about the Pythagorean theorem, visit :
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SOMEONE PLEASE ANSWER THIS
Answers
Answer:
The answers are option b and option e
What is the minimum score necessary to be in top 60% of the distribution for a normal distribution with mean=70 and standard deviation=10?I got the explanation but why there is need to subtract from 1. I didnt understand fully.
Answers
Substituting the values mean = 70 and standard deviation = 10, we can find the minimum score necessary to be in the top 60% of the distribution.
In a normal distribution, the area under the curve represents the probability. To find the minimum score necessary to be in the top 60% of the distribution, we need to find the score that corresponds to the 60th percentile.
Since the normal distribution is symmetric, we can find the cutoff point by subtracting the area below the 60th percentile from 1. By doing so, we are essentially finding the area to the right of the cutoff point.
In this case, we want to find the z-score (standardized score) that corresponds to the 60th percentile. We can use a standard normal distribution table or a calculator to find this z-score.
Once we have the z-score, we can use the formula:
X = mean + (z-score * standard deviation)
Substituting the values mean = 70 and standard deviation = 10, we can find the minimum score necessary to be in the top 60% of the distribution.
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Use the Limit Comparison Test to determine whether the infinite series is convergent. [infinity] sigma n = 3 for (2n + 2)/(n(n − 1)(n − 2)) Identify bn in the following limit. lim n→[infinity] (an/bn) = lim n→[infinity] (2n + 2)/(n(n − 1)(n − 2)) = L Then determine weather the series converges or diverges
Answers
The required answer is lim(n→∞) (a_n/b_n) = lim (n→∞) ((2n + 2)/(n(n-1)(n-2))) / (1/n^2)
To use the Limit Comparison Test, we need to identify a series with known convergence properties that is similar to the given series. We can do this by finding bn in the following limit:
lim n→[infinity] (an/bn) = lim n→[infinity] (2n + 2)/(n(n − 1)(n − 2)) = L
To find bn, we need to look for a dominant term in the denominator that behaves similarly to n(n − 1)(n − 2). One such term is n^3, since it is the highest order term in the denominator. Therefore, we can set bn = n^3 and simplify the limit:
lim n→[infinity] (2n + 2)/(n(n − 1)(n − 2)) * (n^3)/(1) = lim n→[infinity] (2n + 2)/(n^4 - 3n^3 + 2n^2)
This limit can be evaluated using L'Hopital's Rule, which gives:
lim n→[infinity] (2n + 2)/(4n^3 - 9n^2 + 4n) = lim n→[infinity] (1/n^2)
Since the limit is a nonzero finite value, L = 1. By the Limit Comparison Test, the given series converges if and only if the series with general term bn = n^3 converges.
We know that the series with general term bn = n^3 is a p-series with p = 3, which converges since p > 1. Therefore, by the Limit Comparison Test, the given series also converges.
In summary, the given series is convergent.
To use the Limit Comparison Test, we first need to identify a simpler series b_n that we can compare the given series to. We are given the series an = (2n + 2)/(n(n-1)(n-2)). We can choose b_n = 1/n^2 since the highest degree in the numerator and denominator are the same.
Next, we'll calculate the limit L as n approaches infinity of the ratio a_n/b_n:
lim(n→∞) (a_n/b_n) = lim(n→∞) ((2n + 2)/(n(n-1)(n-2))) / (1/n^2)
To simplify the expression, we can multiply the numerator and denominator by n^2:
A divergent series is an infinite series that is not convergent, which means that the infinite sequence of the series partial sums has no finite limit.
lim (n→∞) ((2n + 2)n^2) / (n(n-1)(n-2))
Now, we'll divide each term by n^2 to simplify the limit expression:
lim (n→∞) (2 + 2/n) / ((1)(1-1/n)(1-2/n))
As n approaches infinity, the terms with n in the denominator approach 0:
lim (n→∞) (2) / (1) = 2
Since L = 2 is a finite positive number, the Limit Comparison Test tells us that the original series a_n converges or diverges based on the behavior of the series b_n. We know that the series b_n = 1/n^2 is a convergent p-series with p = 2, which is greater than 1. Therefore, the series b_n converges.
A series said to be convergent when the limits of the series converges to the finite possible value for the series.
Since bn converges and L is a finite positive number, we can conclude that the original series a_n also converges according to the Limit Comparison Test.
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What is the slope of the line that is parallel to the line whose equation is 4x + y2 = 0?
Answers
We know the slope formula
m=-a/bm=-4/2m=-2Parallel lines have equal slope so it has m=-2
Using the following weights:.3, 2, .5 find the forecast for the next period. Month 1 – 381, Month 2-366, Month 3 - 348. O a. 143 O b. 241 O c. 360 O d. 421
Answers
The forecast for the next period using the following weights: 0.3, 2, 0.5 is Option d. 421.
To compute the forecast for the next period, we'll use the weighted moving average (WMA) formula.WMA formula:
WMA = W1Yt-1 + W2Yt-2 + ... + WnYt-n
Where, WMA is the weighted moving average
W1, W2, ..., Wn are the weights (must sum to 1)
Yt-n is the demand in the n-th period before the current period
As we know Month 1 – 381, Month 2-366, and Month 3 - 348.
Weights: 0.3, 2, 0.5
We'll compute the forecast for the next period (month 4) using the data:
WMA = W1Yt-1 + W2Yt-2 + W3Yt-3WMA
= 0.3(381) + 2(366) + 0.5(348)WMA
= 114.3 + 732 + 174WMA
= 1020.3
Therefore, the forecast for the next period is 1020.3, which rounds to 421. Hence, option d is correct.
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express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 3 π , 5 π ]
Answers
The given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].
To express the limit as a definite integral, we can rewrite the sum as a Riemann sum and take the limit as n approaches infinity.
The given sum can be written as:
lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi],
where Δxi = (b - a) / n is the width of each subinterval, xi is a sample point in the i-th subinterval, and [a, b] is the interval [3π, 5π].
To express the limit as a definite integral, we can rewrite the sum using the definite integral notation:
lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi] = ∫[3π, 5π] cos(x) dx,
where dx represents an infinitesimally small change in x. By taking the limit as n approaches infinity, the sum converges to the definite integral.
Therefore, the given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].
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Question is depicted below:
Answers
Solution:
Solve the system of equations to find the value of y.
10x + 10y = 405x + 3y = 8
10x + 10y = 402(5x + 3y = 8)
10x + 10y = 4010x + 6y = 16
4y = 24y = 6Substitute the value of y into any equation to find the value of x.
10x + 10y = 40=> 10x + 10(6) = 40=> 10x + 60 = 40=> 10x = -20=> x = -2Putting them in (x,y) form.
(x,y) ⇒ (x = -2,y = 6) ⇒ (-2,6)The expression 8x3y2z is a
A. Monomial
B. Binomial
C. Trinomial
Answers
Greta uses 3 ounces of pasta to make 3/4 of a serving of pasta.
How many ounces of pasta are there per serving?
Answers
Answer:
3 oz / 3/4
3*4/3=12/3=4
4 oz/1
4oz per serving
find the volume of the solid that lies under the plane 4x 10y − 2z 15 = 0 and above the rectangle r = {(x, y) | −1 ≤ x ≤ 4, −1 ≤ y ≤ 1}.
Answers
The volume of the solid is 55 cubic units.
To find the volume of the solid that lies under the plane 4x - 10y - 2z + 15 = 0 and above the rectangle r = {(x, y) | −1 ≤ x ≤ 4, −1 ≤ y ≤ 1}, we need to first determine the bounds for z.
We can rearrange the equation of the plane to solve for z:
z = 2x - 5y + (15/2)
Now we can substitute the bounds for x and y from the rectangle r to find the bounds for z:
-1 ≤ x ≤ 4
-1 ≤ y ≤ 1
-2 ≤ 2x - 5y ≤ 9
-2 ≤ z ≤ 9/2
Therefore, the volume of the solid can be found by integrating the constant function 1 over the region R = {(x, y, z) | −1 ≤ x ≤ 4, −1 ≤ y ≤ 1, -2 ≤ z ≤ 9/2}:
V = ∭R dV = ∫_{-1}^{4} ∫_{-1}^{1} ∫_{-2}^{9/2} dz dy dx
V = ∫_{-1}^{4} ∫_{-1}^{1} (9/2 + 2) dy dx
V = ∫_{-1}^{4} 11 dy dx
V = 11 ∫_{-1}^{4} dy
V = 11(5)
V = 55
Therefore, the volume of the solid is 55 cubic units.
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the hamster walked x feet. the guinea pig walked 1/4 more than that.
Answers
Answer:
2x+\(\frac{1}{4}\)
Step-by-step explanation:
hamster=x
guinea pig = x+ 1/4
x+x=2x
then just add the 1/4
In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.
{15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5}
Which of the following stem-and-leaf plots correctly graphs the data set?
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5 5 5
2 0 0 0 0 3 6
3 0 1 4 9 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5 5 5
2 0 0 0 0 3 6
3 1 4 9 9
Key 1|1 = 11
Answers
The stem-and-leaf plot that correctly graphs the data set {15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5} is given as follows:
0| 0 5
1| 1 5 5 5
2| 0 0 0 0 3 6
3| 1 4 9 9
Key 1|1 = 11
What is shown by a stem-and-leaf plot?A stem and leaf plot is a type of data visualization that displays numerical data in a way that shows the distribution of the data while also preserving the individual data points. It is particularly useful for small to medium-sized data sets.
In a stem and leaf plot, the digits in each data point are split into two parts: the stem and the leaf. The stem is usually the leftmost digits of the number, while the leaf is the rightmost digit. The stems are listed in a column from top to bottom, and each leaf is listed next to its corresponding stem. The resulting plot looks like a table with two columns, where the first column shows the stems and the second column shows the leaves.
For example, as the team scored 20 points four times, we have the following observation:
2| 0 0 0 0
(one leaf of zero for each time, with the stem of 2).
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Solve each. Show all necessary work.
8. Write the equation of the line in slope-intercept form that passes through (10.21) and (15.36)
Answers
Answer:
y = 3x - 9
Step-by-step explanation:
First, find the slope using y2 - y1 / x2 - x1
36 - 21 = 15
15 - 10 = 5
15/5 = 3, so the slope (m) is 3.
Now, plug into point-slope form: y - y1 = m (x - x1)
y - 21 = 3 (x - 10)
Simplify
y - 21 = 3x - 30
y = 3x - 9
I hope this helps!!
Someone help and plz make sure it’s right
Answers
Answer:
a=40° hope I helped:)....
The graph shows the amount of money Miguel earns after working x hours.
What is the rate of change of the amount earned with
respect to hours worked for this function?
1/13 hours per dollar
2/5hours per dollar
3 dollars per hour
13 dollars per hour
Answers
Answer:
13 dollars per hour ! ^^
Step-by-step explanation:
According to the proportional relationship shown by the graph, the rate of change is of 13 dollars per hour.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality, which is also the rate of change.
Considering the graph, the rate of change, in dollars per hour, is given by:
k = 65/5 = 26/2 = 13.
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what are all the possible factors of the quadratic term for x2 10x − 24?
Answers
Answer:
The factors are,
x + 12 and x - 2
Step-by-step explanation:
x^2 + 10x - 24,
Here, we note that,
12 - 2 = 10,
and (12)(-2) = 24,
so, we can re-write 10x as 10x = 12x - 2x
so,
\(x^2 + 12x - 2x - 24 = 0\)
Taking x common from the 1st two terms (x^2 and 12x),
and taking -2 common from the last two tems (-2x and -24), we get,
\(x^2 + 12x - 2x - 24 \\x(x+12)-2(x+12)\\taking \ (x+12) \ common,we \ get,\\(x+12)(x-2)\)
So, The factors are,
x + 12 and x - 2
What is the rate of change for y= 0.75-2?
Answers
Answer:
The slope is 0.75.
The equation is y=0.75x-2
Step-by-step explanation:
An amusement park charges $8 for admission and $2 for each ride. Use the graph to find the slope and the y-intercept. Then write an equation for the function that relates the total cost to the number of rides.
show your work.
Answers
Answer:
y=2x+8
Step-by-step explanation:
y=mx+b
M: cost for each ride, $2
B: Flat admission rate, $8
You have a mortagege of $275,000
after down payment with an interest
rate of 3% for 30 years.
What does P, r,n, and t are equal to?
Answers
Answer:
Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this
Step-by-step explanation:
Which describes the correlation shown in the scatterplot?
On a graph, points are grouped together and decrease.
A. There is a positive correlation in the data set.
B. There is a negative correlation in the data set.
C. There is no correlation in the data set.
D. More points are needed to determine the correlation.
Answers
It can be said that the "there is a negative correlation in the data set". Option B is correct.
The graph shows points that are grouped together and are decreasing.
The gathered data shows that there is a possibility to get correlation between them.
The group of data is decreasing. So, the correlation of the data will be negative in nature.
Therefore, it can be said that the "there is a negative correlation in the data set". Option B is correct.
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Answer:
The answer B
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Have a blessed day guys and gals
a spinner is divided into 8 identical sectors and labeled 1 through 8 how many spins are expected for a multiple of 3 to be spun 15 times
Answers
24 spins are expected for a multiple of 3 to be spun 6 times.
What is a sector?The area of a sector is the space inside the circle formed by two radii and an arc. It is a fraction of the total area of the circle. A significant sector has a central angle that is greater than 180° 180° 180° 180°.A circular sector (symbol: ) is the piece of a disk (a closed region circumscribed by a circle) enclosed by two radii and an arc, where the smaller area is known as the minor sector and the bigger as the major sector.To find how many spins are expected for a multiple of 3 to be spun 6 times:
If there are 8 sections, there is a 1 in 8 chance of getting each section. Consider multiples of 3 ⇒ 3, 6.And to spin that multiple 6 times, you need to multiply the number of sections by the number of multiples.The number of sections(nos) is 8, and the number of multiples(nom) is 3.So,
nos × nom = 8 × 3 = 24Therefore, 24 spins are expected for a multiple of 3 to be spun 6 times.
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The correct question is given below:
A spinner is divided into 8 identical sectors and labeled 1 through 8.
How many spins are expected for a multiple of 3 to be spun 6 times?
Select from the drop-down menu to correctly complete the sentence.
The spinner is expected to have to spin approximately (12,16,24,28)
times for a multiple of 3 to be spun 6 times.
Which of the following is not included in the cost of merchandise inventory? O Purchase discounts. O Purchase returns and allowances. O Purchase price of the inventory. O Freight costs paid by the seller. O Freight costs paid by the buyer. 4 pts 0 Question 2 Sunshine Cleaning purchased $3,500 worth of merchandise. The seller offered a 2% cash discount. Transportation costs for the buyer were an additional $310. The company returned $240 worth of merchandise and then paid the invoice within the discount period. The total cost of this merchandise is: O $3.570.00. O $3,500.00 O $3,332.00 O $3,430.00. $3,504.80 Question 5 A company has not sales of $759.300 and cost of goods sold of $548.300. Its not income is $10.280. The company's gross margin and operating expenses, respectively, are: O $211.000 and $230,750 $739.550 and $191,720 O $529,020 and $230.750 O $211.000 and $191,720 $230,750 and $529,020 4 pts D D Question 5 A company has not sales of $750,300 and cost of goods sold of $548,300. Its not income is $10.280 The company's groas margin and operating expenses, respectively, arm O $211,000 and $230,750 O $739,550 and $191,720 $529,020 and $230,750 O $211.000 and $191,720 O $230.750 and $529,020 Question 6 Sales less sales discounts, less sales returns and allowances equals: Cost of Goods Sold Net Income O Net Sales O Gross Profit 4 pts 4 pts Goods in transit are included in a purchaser's inventory: O At any time during transit. O After the half-way point between the buyer and seller, When the supplier is responsible for freight charges. When the goods are shipped FOB shipping point. OIf the goods are shipped FOB destination. Question 11 The inventory costing method that smooths out erratic changes in costs is: O LCM. O FIFO. OLIFO. O Specific Identification. O Weighted average. 4 t ne 0 Question 12 Krusty Krab has the following products in its ending inventory Compute lower of cost or market for inventory. applied separately to each product Inventory by Product Product Quantity Cost per Unit 500 $ 500 $ 30 600 Scuba Masks Scuba Sults O $265,000 O $290,000. O $250,000 $268,000 O $275,000. Question 13 Market per Unit $ 550 $ 25 If equity is $368,000 and liabilities are $186,000, then assets equal: O $554,000. $922,000. $368,000. $186,000. O $182,000. 2 pts
Answers
Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."
2: The total cost of the merchandise is $3,332.00.
5: The company's gross margin and operating expenses, are $211,000 and $191,720.
What is the cost of merchandise inventory?Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.
Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.
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On the graph below where the following areas are the x - axis, the y - axis,quadrant 1,quadrant 2, quadrant 3 and quadrant 4
Answers
HELP!!!! PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: red hot= $4
gummies=$9
Step-by-step explanation:
3r+1g=21
-(3r+3g=39)
3r+1g=21
-3r-3g=-39
-2g=-18
g=9
3r+1(9)=21
3r=12
r=4
63 precent done ✅ help
Answers
children should develop strategies for remembering the facts before they engage in drill and practice to develop fluency
Answers
Developing strategies for remembering facts is essential for children before they engage in drill and practice activities to develop fluency. By establishing these strategies, children can effectively learn, retain, and recall information, ultimately enhancing their performance during practice sessions.
Yes, it is important for children to develop strategies for remembering facts before engaging in drills and practice to develop fluency. By doing so, children can enhance their ability to recall information more quickly and accurately, making it easier for them to perform well on tests and assignments. Strategies such as visualizing, chunking, and using mnemonic devices can help children remember information more effectively. Once these strategies are established, drill and practice can then be used to further reinforce their understanding and speed up their recall time. This approach can ultimately lead to improved academic performance and a stronger foundation for learning.
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Ms. Lauren Alexander, supply chain manager of ACR, Inc., is negotiating a contract to buy 25,000 units of a common component from a global supplier. Ms. Alexander conducted a thorough cost analysis on manufacturing the part in-house and determined that she would need $450,000 in capital equipment and incur a variable cost of $19.00 per unit to manufacture the part in-house. There is no fixed cost in purchasing the component from the supplier. What is the maximum purchase price per unit of component that Ms. Alexander should negotiate with her supplier?
Answers
The maximum purchase price per unit of the component that Ms. Alexander should negotiate with her supplier is $19.00, which is equal to the variable cost per unit to manufacture the part in-house.
In this scenario, Ms. Alexander needs to determine the maximum price per unit that she should be willing to pay the supplier for the component. She conducted a cost analysis and found that manufacturing the part in-house would require $450,000 in capital equipment and have a variable cost of $19.00 per unit.
Since there is no fixed cost associated with purchasing the component from the supplier, the maximum purchase price per unit should not exceed the variable cost per unit of manufacturing in-house. This ensures that the company does not incur additional costs by outsourcing the component.
Therefore, Ms. Alexander should negotiate a price with the supplier that is equal to or lower than the variable cost per unit, which is $19.00. By doing so, the company can avoid the initial capital investment and ongoing variable costs associated with in-house production, making it more cost-effective to purchase the component from the supplier.
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