The 160 feet range and 70 feet height of the path of Gunter Money which can be described with a quadratic equation, gives;
(a) The path is; y = -1.09375×10²·x² + 1.75·x
(b) The vertex form of the equation is; y = -1.09375·(x - 80)² + 70
(c) The angle at the start is approximately 60.3°
What is quadratic equation?A quadratic equation is a single variable polynomial equation of the second degree.
The points in the path which is a path of a projectile and has a shape of a parabola are;
(0, 0), (80, 70), and (160, 0)
The equations are;
y₁ = a·x₁² + b·x₁ + c
y₂ = a·x₂² + b·x₂ + c
y₃ = a·x₃² + b·x₃ + c
Plugging in the coordinates of the three points in the path gives;
0 = a·0² + b·0 + 1·c70 = a·80² + b·80 + 1·c0 = a·160² + b·160 + 1·cThe matrix becomes;
[tex]A = \begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}[/tex]
[tex]X = \begin{bmatrix}a \\b \\c\end{bmatrix}[/tex]
[tex]Y = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]
We have;
A·X = Y, which gives;
[tex]\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}\cdot \begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]
[tex]X = \dfrac{Y}{A} = A^{-1}\cdot Y[/tex]
Where;
A⁻¹ = The inverse of the matrix A
[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \frac{ \begin{bmatrix}0 \\70 \\0\end{bmatrix}}{\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}} = \begin{bmatrix}\dfrac{1}{12800} & -\dfrac{1}{6400} & \dfrac{1}{12800} \\\\-\dfrac{3}{160} &\dfrac{1}{40} & -\dfrac{1}{160} \\\\1 &0 &0 \\\end{bmatrix}\bullet \begin{bmatrix}0\\ \\70\\ \\0\end{bmatrix}=\begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]
[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]
[tex]a = -\dfrac{7}{640}[/tex]
[tex]b = \dfrac{7}{4}[/tex]
c = 0
The equation for Gunter Money's path is therefore;
[tex]y = -\dfrac{7}{640} \cdot x^2 + 1\dfrac{3}{4} \cdot x + 0 = -1.09375\times 10^2 \cdot x^2 + 1.75\cdot x[/tex]
(b) The vertex of the path is (h, k) = (80, 70)
The vertex form of a quadratic equation is; y = a·(x - h)² + k
The equation of Gunter Money's path in vertex form is therefore;
[tex]y = -\dfrac{7}{640} \cdot \left(x - 80)^2 + 70 = -1.09375\times 10^2\cdot (x - 80)^2+70[/tex]
(c) The angle of the parabolic path of Gunter Money's motion at a point is given by the value of the arctangent of the differentiation of the function for the motion at the point as follows;
[tex]y' = -\dfrac{7\times 2}{640} \cdot x + 1\dfrac{3}{4}[/tex]
At the point Gunter Money takes off, (0, 0), we have;
[tex]tan(\theta) = y' = -\dfrac{7\times 2}{640} \times 0 + 1\dfrac{3}{4} = 1\dfrac{3}{4} = 1.75[/tex]
[tex]\theta = arctan(1.75) \approx 60.3^{\circ}[/tex]
The angle is approximately 60.3°
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Calculate the standard score (z-score) of the given sample mean. Round your answer to two decimal places.
μ=31 and σ=9; n=64; x¯=30
The standard score (z-score) of the given sample mean is equal to 7.11
What is a standard score?A standard score is also referred to as a z-value or z-score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
Mathematically, the standard score of a given sample mean can be calculated by using this formula:
[tex]Z=\frac{\bar{x}\;-\;\mu}{ \frac{\delta}{n} }[/tex]
Where:
Where:
x represents the sample score.u represents the mean point.z represents the standard score.σ represents the standard deviation.n represents the number of samples.Substituting the given parameters into the formula, we have;
Standard score, z = (30 - 31)/(9/64)
Standard score, z = -1/0.140625
Standard score, z = 7.11
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Solve the following using the elimination or substitution method. Show all work.
Jim has 65 coins in his pocket. All of the coins are nickels and dimes. If the total value of his coins is $5.10, how many nickels or dimes does he have?
Step-by-step explanation:
Jim has 65 coins in his pocket. All of the coins are nickels and dimes. If the total value of his coins is $5.10, how many nickels or dimes does he have?
nickels = n
dimes = d
We use:
d + n = 65
0.10d + 0.05n = 5.10
solve for d:
d + n = 65
d + n - n = 65 - n
d = 65 - n
substitute in for the second equation: d = 65 - n
0.10(65 - n) + 0.05n = 5.10
6.5 - 0.10n + 0.05n = 5.10
6.5 - 0.05n = 5.10
6.5 - 0.05n - 6.5 = 5.10 - 6.5
- 0.05n= -1.4
n = 28
so there are 28 nickels
Now, solve for d: when n = 28
d + n = 65
d + 28 = 65
d = 37
so there are 37 dimes
Jim has 28 nickels and 37 dimes in his pocket. which is determined by the substitution method.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
Let the number of nickels would be n
Let the number of dimes would be d
As per the given question,
d + n = 65 ....(i)
0.10d + 0.05n = 5.10 ....(ii)
From equation (i),
d + n = 65
d + n - n = 65 - n
d = 65 - n
Substitute in for the equation(ii): d = 65 - n
0.10(65 - n) + 0.05n = 5.10
6.5 - 0.10n + 0.05n = 5.10
6.5 - 0.05n = 5.10
6.5 - 0.05n - 6.5 = 5.10 - 6.5
- 0.05n = -1.4
n = 28
This means there are 28 nickels
Substitute the value of n = 28 in the equation (i),
d + n = 65
d + 28 = 65
d = 37
So there are 37 dimes
Thus, Jim has 28 nickels and 37 dimes in his pocket.
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Complete the following table: (Round your final answers to the nearest cent.) Units Unit Cost Beg. Inventory Jan. 1 8 $ 6.00 Apr. 11 24 $ 11.00 May 17 30 $ 14.00 Dec. 5 19 $ 16.00 21 units sold Calculate: LIFO FIFO Weighted-Average Cost of Ending Inventory A C E Cost of Goods Sold B D F
1. The completion of the inventory table is as follows:
Inventory Table:Units Unit Cost Total Cost
Jan. 1 Beg. Inventory 8 $6.00 $48
Apr. 11 Purchases 24 $11.00 $264
May 17 Purchases 30 $14.00 $420
Dec. 5 Purchases 19 $16.00 $304
2. The Cost of Ending Inventory and the Cost of Goods Sold under LIFO, FIFO, and Weighted-Average, are as follows:
LIFO FIFO Weighted-Average
Ending inventory $704 $845 $767.40
Cost of goods sold $332 $191 $268.60
How do the inventory methods differ?FIFO (First-in, First-out) is based on the assumption that the physical flow of goods sold depends on the chronological order of acquisition.
LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.
The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.
LIFO:
Ending inventory = $704 ($48 + $264 + 28 x $14)
Cost of goods sold = $332 ($1,036 - $704)
FIFO:
Ending inventory = $845 (11 x $11 + 30 x $14 + 19 x $16)
Cost of goods sold = $191 ($1,036 - $845)
Weighted Average:
Ending inventory = $767.40 (60 x $12.79)
Cost of goods sold = $268.60 (21 x $12.79)
Inventory Table:Units Unit Cost Total Cost
Beg. Inventory Jan. 1 8 $6.00 $48
Apr. 11 Purchases 24 $11.00 $264
May 17 Purchases 30 $14.00 $420
Dec. 5 Purchases 19 $16.00 $304
Total 81 $1,036
Units sold 21
Ending inventory 60
Average cost per unit = $12.79 ($1,036/81)
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My sister has three Maltese puppies. Scout weighs 8 1/3 pounds, Kenadi weighs 3 1/8 pounds, and Major weighs 8 1/5 pounds. What is the order of the puppy’s weights from least to greatest?
A.8 1/3,8 1/5 3 1/8
B.8 1/3,3 1/8, 8 1/5
C.3 1/8,8 1/3,8 1/5
D.3 1/8, 8 1/5,8 1/3
Answer: D because 8 1/5 is smaller than 8 1/3
1. (03.03 MC)
The subtotal for Abdiel's takeout order is $24.30. What will Abdiel's total be if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount? (2 points)
O $26.73
$27.46
$33.02
$33.29
Abdiel's total if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount is $27.46
The correct answer option is option B
What is Abdiel's total?Abdiel's subtotal = $24.30Abdiel's coupon = 12%Tip = 25%Amount of total after discount = 12% × $24.30
= 0.12 ×24.30
= $2.916
Amount of abdiel's tip = 25% × $24.40
= 0.25 × 24.30
= $6.075
Abdiel's total after discount before tip = (Amount of abdiel's tip + Abdiel's subtotal) - Amount of total after discount
= (6.075 + 24.30) - $2.916
= $30.375 - $2.916
= $27.459
Approximately,
$27.46
Therefore, the total amount Abdiel paid after discount before tip is $27.46
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Which is the correct answer ????
A surveyor is determining the area of a triangle piece of land bordered by three stretts. In the coordinate plane,the vertices of the triangle are at 0,0 -100,-300,and 200 -200. One unit in the coordinate plane represents 1m.what is the area of piece of land
The area of the piece of land with coordinates (0, 0), (-100, 300) and (200, -200) is as measured by the surveyor is 4000 square meter
How to calculate the area of the piece of the landThe given coordinates being plotted as
A (0, 0)
B (-100, 300)
C (200, -200)
Area of triangle is solved by 0.5 * base * height
dimensions from attached plot, BC = 316.2, Aa = 253
= 0.5 * BC * Aa
= 0.5 * 253 * 316.2
= 39 999.3 approximately 40 000
The plot gave an area of 40 000 square units on paper converting using the given scale which is: One unit in the coordinate plane represents 1m
1 unit = 1 m
1 square unit = 1 square meter
4000 square units = ?
cross multiplying
? = 4000 square units
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Given triangle ABC with vertices A(16,0), B(9,2) and C(5,-12). Which side of triangle ABC represents the altitude of the triangle with a slope of -2/7?
Side AB
side BC
side AC
Answer:
so now i think you can find the slope of the sides.the product of slopes of two perpendicular lines is - so now you can also find the slopes of the altitude. i will do one side for you and you do the remaining the slope of side BC is (2-0)/(9-0) = 2/9 so the slope of the altitude passing through A will be -9/2
Step-by-step explanation:
so i think it would be side AC
Answer:
Side BC
Step-by-step explanation:
Let's calculate the slopes of the sides of triangle ABC:
Slope of side AB = (2 - 0) / (9 - 16) = 2 / (-7) = -2/7
Slope of side BC = (0 - 2) / (2 - 9) = -2 / (-7) = 2/7
Slope of side CA = (0 - 0) / (2 - 16) = 0 / (-14) = 0
Among the three sides, only side BC has a slope of 2/7, which is the negative reciprocal of the given slope of -2/7.
Therefore, side BC represents the altitude of triangle ABC with a slope of -2/7.
How do I solve this question
The partial fraction form of the given fraction [x+5/(x-7)(x-5)] is
[A/(x-7)+B/(x-5)].
What is decomposition to partial fractions?For a rational fraction to be partially decomposed or expanded in algebra, the fraction must be expressed as the product of a polynomial and one or more fractions with a simpler denominator.Partial fraction decomposition is the process of taking a rational expression and breaking it down into smaller rational expressions that we can combine or divide to recover the original rational expression.So, the fraction is:
x+5/(x-7)(x-5)We know that:
px + q/(x-a)(x-b), a≠b ⇒ A/(x-a) + B/(x-b)Use the same identity to get the partial fraction of the given fraction as follows:
x+5/(x-7)(x-5)A/(x-7) + B/(x-5)Therefore, the partial fraction form of the given fraction [x+5/(x-7)(x-5)] is [A/(x-7) + B/(x-5)].
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Natalie has a budget of $15,000 dollars to spend on tracking devices to study bison. A radio tracker costs $650 and a GPS tracker costs $1400. Natalie wants to buy at least 9 radio trackers and more than 3 GPS trackers. The following system of inequalities represents this situation, where x is the number of radio trackers and y is the number of GPS trackers. x ≥ 9 y > 3 650x + 1400y ≤ 15000
The inequality as per the question is x ≥ 9 and y > 3 and the diagram according to this is attached below.
What is an equality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the given information in the question.,
x ≥ 9 and,
y > 3
The equation is,
650 x + 1400 y ≤ 1
[tex]\frac{x/15000}{650}+\frac{y/15000}{1400} \leq 1[/tex]
x/23.07 + y/10.71 ≤ 1
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After arriving in Australia, Jason exchanged $750 of US currency for $1,041.67 Australian
dollars. Complete the two statements based on this currency exchange. Round to the
nearest hundredth.
9. What is the exchange rate of US dollars per Australian dollar?
What is the exchange rate of Australian dollars per US dollar?
The exchange rate of US dollars per Australian dollar is 0.72
The exchange rate of Australian dollars per US dollar is 1.39
Exchange rate
Exchange rate is the price of a country's money in relation to another country's money and it is “fixed” when countries use gold or another agreed-upon standard, and each currency is worth a specific measure of the metal or other standard.
Given,
After arriving in Australia, Jason exchanged $750 of US currency for $1,041.67 Australian dollars. Complete the two statements based on this currency exchange.
Here we need to find the exchange rate of US dollars per Australian dollar and Australian dollars per US dollar then round it to the nearest hundredth.
According to the given details,
Total amount in US dollars = $750
Converted amount in Australian dollar = $1,041.67
When we divide the US dollar by the Australian dollar then we get the value of one dollar rate,
=> 750/1041.67
=> 0.719
When we round off it to the nearest hundredth then we get the exchange rate of $1 is 0.72
Similarly, now we have to divide the Australian dollar by the US dollar then we get the value of one dollar rate,
=> 1041.67/750
=> 1.388
When we round off it to the nearest hundredth then we get the exchange rate of $1 is 1.39.
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line x is the perpendicular bisector of segment ZY
what does YT equal
Answer:
Step-by-step explanation:
ZT=YT
x+3=3x-11
x-3x=-11-3
-2x=-14
x=-14/-2=7
YT=3×7-11=21-11=10
YT=10
A chemist is mixing a 30% salt solution with a 15% salt solution to make 60 L of a new solution that will contain 20% salt. How much of the 30% solution
should the chemist use?
20 amount of 30% salt solution
How to find the salt solution percentage?
Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.
Let x be the amount of 30% salt solution
Then, 60-x = amount of 15% salt solution
Salt content of the first solution + salt content of second solution = salt content of the mixture
∴ 0.30x + 0.15(60-x) = 0.20*60
0.30x + 9 - 0.15x = 12
0.15x = 3
x = 20
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-5ax6(2ax4 + 7x2)
what might be the answer to this?? (pleasee!! it’s for my semester final.)
The solution of the given expression -5ax⁶(2ax⁴ + 7x²) is equal to -10a²x¹⁰-35ax⁸.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is -5ax⁶(2ax⁴ + 7x²). The solution of the expression will be done as,
E = -5ax⁶(2ax⁴ + 7x²)
E = -10a²x¹⁰-35ax⁸.
Therefore, the solution of the given expression -5ax⁶(2ax⁴ + 7x²) is equal to -10a²x¹⁰-35ax⁸.
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Erik has 2 bags of bird seed. One bag has
10 pounds of seed, and the other bag has
8 pounds of seed. He fills
7 bird feeders
with 2 pounds each. Write and solve
an
equation to find how many
pounds of bird
seed are left.
Answer:
(10 + 8) - (7 * 2) = x, 4 pounds of birdseed left
Step-by-step explanation:
For the first part of our equation, we will find the total amount of pounds of seeds among the bags (addition).
For the next part, we will find out how much of the bird seed is used (subtraction).
Then, it will equal whatever is left.
(10 + 8) - (7 * 2) = x, x = pounds of bird seed left
Now, we will solve.
(10 + 8) - (7 * 2) = x
(18) - (14) = x
x = 4 pounds of birdseed left
Danielle cecils driver rating factor is 1.60 and her car is in age group d and insurance rating group d. She wants 100/300 bodily injury and $50000 property damage coverage a)anual base premium B) anual premmium
a. The annual base premium when Danielle cecils driver rating factor is 1.60 and her car is in age group is $709.
b. The annual premium is $1134.40
What is a premium?It should be noted that the annual premium simply refers to the amount of premium that's paid yearly by the entity. The insurance company has premium payment options for the clients.
The annual base premium will be:
= Liability premium + Collision premium + Comprehensive premium
= $383 + $240 + $86
= $709
The annual premium will be:
= Annual base premium × Driver rating factor
= $709 × 1.60
= $1134.40
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A poll asked adults in a certain country whether immigration was a good thing or a bad thing for the country. Out of 1,095 respondents, 631 said it was a good thing.
c. Find a 95% confidence interval for the proportion who believe immigration is a good thing.
A 95% confidence interval for the proportion who believe immigration is a good thing is; CI = (0.4173, 0.7173)
What is the Confidence Interval of Proportions?The formula for the confidence interval of proportions is;
CI = p ± z√(p(1 - p)/n)
where;
p is sample proportion
z is z-score at confidence level
n is sample size
We are given;
Number of success; x = 631
Sample size; n = 1095
Thus;
sample proportion; p = x/n = 631/1095 = 0.5763
The z-score at 95% confidence level is 1.96. Thus;
CI = 0.5673 ± 1.96√(0.5673(1 - 0.5673)/1095)
CI = 0.5673 ± 0.015
CI = (0.5673 - 0.15), (0.5673 + 0.15)
CI = (0.4173, 0.7173)
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I really need help to this answer ASAP.
(x - 5)²
Step-by-step explanation:
use formula
[tex](x - y) {2} = x {}^{2} - 2xy + y {}^{2} [/tex]
Use the compound interest formula to compute the total amount accumulated and the interest earned.
$3500 for 2 years at %3 compounded quarterly.
The total amount accumlated after 2 years is ____.
(Round to the nearest cent as needed.)
The total amount accumulated after 2 years is $3704. 0
How to determine the compound interestThe formula for calculating compound interest is expressed as;
A = P ( 1 + r/ n) ^nt
Where;
A is the final amountP is the principal amountr is the ratet is the timen is the number of times interest applied per periodNow, let's substitute the values into the formula, we have;
A = $3500 ( 1 + 0. 03 / 0. 25) ^(0.25× 2)
Find the exponent
A = $3500 ( 1 + 0. 03 / 0. 25) ^0.5
A = $3500( 1+ 0. 12)^0. 5
Expand the bracket
A = $3500 (1. 12)^0. 5
A = $3500(1. 05)
multiply the values
A = $3704. 0
Hence, the value is $3704. 0
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4. A Bag of marbles has 4 yellow, 5 red, and 1 purple. Create a situation that would satisfy the following:
a) Something that is IMPOSSIBLE to
happen.
b) Something that is EQUALLY
LIKELY to happen.
c) Something that is LIKELY to
happen.
According to the solving Probability the value are as follows.
a) P(Blue)= 0/10
b) P(Red)= 5/10
c) P(Red or Yellow)= 9/10
What is probability?The definition of probability is "How likely something is to happen."
Probability is indeed a number ranging from 0 to 1 that expresses the likelihood that an event will take place as specified.
First, 0 P(E) 1 (where P(E) specifies the probability of an event E) and second, the sum of the probabilities of any collection of mutually and exclusive exhaustive occurrences equals 1 are the two characteristics that define a probability.
According to the given data:We have a Bag of marbles has 4 yellow, 5 red, and 1 purple.
Total balls in a bag= 4+5+1=10 balls.
Something that is IMPOSSIBLE to happen.
P(Blue)= 0/10
Something that is EQUALLY LIKELY to happen.
P(Red)= 5/10
Something that is LIKELY to happen.
P(Red or Yellow)= 9/10
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Draw and label a set of axes on your graph paper. Plot and label the following points: (1,3) , (4,2) , (0,5) , and (5,1).
We have to label a graph with the following points: (1,3), (4,2), (0,5), and (5,1).
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation. Thus, if a point is on te graph of a function, then it must also satisfy the function.
To plot the graph with the points follow all the steps given below;
Points are (1,3) , (4,2) , (0,5),and (5,1).
Step1 The coordinate of the graph are; (1,3) , (4,2) , (0,5),and (5,1).
Step2 Plot the coordinate 1 on the x-axis and 3 on the y-axis.
Step3 Plot coordinate 4 on the x-axis and 2 on the y-axis.
Step4 Plot the coordinate 0 on the x-axis and 5 on the y-axis.
Step5 Plot the coordinate 5 on the x-axis and 1 on the y-axis.
Step6 Then Draw a line with the help of the scale and meet all the points.
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Bookwork code: K45 not allowed
The number line below shows information about a variable, p.
Select all of the following values that p could take:
-4, 0, -6, 5, -1, -2.5
T
T
р
-5 -4 -3 -2 -1 0 1 2 3 4 5
✓ Scroll down
A number line is a simple graph with numerical increments spaced evenly. The numbers on the line determine how the number on the line can be answered. The number's application is determined by the question to which it corresponds, such as when plotting a point.
What is meant by number line?A number line is a horizontal line with evenly spaced numerical increments. The numbers on the line will determine how to answer the number on the line. The number's use is determined by the question that goes with it, such as plotting a point.
The number line is a straight line with divisions at equal intervals, similar to a scale. You can choose any point as "0," and all positive numbers will be to the right of the "0," and all negative numbers will be to the left of the "0." Q.
Therefore,
The third number line correctly provides the solution to the statement -5 + (-4).Plot 1's solution is (-5) + (-2) because both arrows point 4 units to the left.Plot 2's solution is (5 + 2) because both arrows point 4 units to the right.Plot 3's solution is (5) + (2) because one arrow points 4 units to the left and the other points 4 units to the right.The plot 4 solution is (5 + 2) because one arrow points 4 units to the left and the other points 8 units to the right.As a result, the third number line is the one that shows the solution 5 + (-4).To learn more about number line refer
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The seating capacity y for a banquet hall is represented by y = 8x + 56,
where x is the number of extra tables you need. How many extra tables
do you need to double the original seating capacity?
The number of extra tables that you need to double the original seating capacity will be 7.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The seating capacity y for a banquet hall is represented by y = 8x + 56, where x is the number of extra tables you need.
If the no extra table is there. Then the value of 'y' will be
y = 8 (0) + 56
y = 56
Then the number of extra tables do you need to double the original seating capacity will be
8x + 56 = 2 × 56
8x = 56
x = 7
Then the number of extra tables that you need to double the original seating capacity will be 7.
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What is the explicit form of an arithmetic sequence if the
first term is 5 and the recursive formula is an an-1 + 8?
=
The explicit form of the arithmetic sequence is
5, 13, 21, 29, .....
What is arithmetic sequence?
A sequence of numbers is said to be in arithmetic progression if the difference between the consecutive terms of the series are same
If the first term is a, common difference is d, then nth term of the sequence is given by
[tex]a_n = a + (n-1)d[/tex]
The recursive form of the given arithmetic series is
[tex]a_n = a_{n-1} + 8[/tex]
First term [tex]a_1 = 5[/tex]
[tex]a_2 = a_1 + 8\\a_2 = 5 + 8\\a_2 = 13[/tex]
[tex]a_3 = a_2 + 8\\a_3 = 13 + 8\\a_3 = 21[/tex]
[tex]a_4 = a_3 + 8\\a_4 = 21+8\\a_4 = 29[/tex]
So the explicit form of the arithmetic sequence is
5, 13, 21, 29, .....
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Differentiate the function with respect to x.
Answer:
[tex]16x {}^{3} + 1[/tex]
Step-by-step explanation:
We need to differentiate the following function,
[tex]\longrightarrow f(x) = 4x^4 + x [/tex]
Let ,
[tex]\longrightarrow y = f(x) [/tex]
So that ,
[tex]\longrightarrow y = 4x^4+x [/tex]
Differentiating both sides wrt x ,
[tex]\longrightarrow \dfrac{dy}{dx}= \dfrac{d(4x^4+x)}{dx}\\[/tex]
[tex]\longrightarrow\dfrac{dy}{dx}= \dfrac{d(4x^4)}{dx}+\dfrac{dx}{dx}\\ [/tex]
[tex]\longrightarrow \dfrac{dy}{dx} = 4(4)x^{4-1} + 1 \\ [/tex]
[tex]\longrightarrow \underline{\underline{ \dfrac{dy}{dx}= 16x^3 +1}}[/tex]
Randy is 8 years old. His brother is twice as old as randy. Randys sister is three years younger than randy. Write a expression to represent the age of randys brother
The expression that represents the age of randy's brother is
2x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Randy age = 8 years old
Randy's brother age = 2 x 8 = 16
Randy's sister age = 8 - 3 = 5
The expression that represents the age of randy's brother.
Let the age of Randy = x.
= 2x
= 2x
= 2 x 8
= 16 years old.
Thus,
The expression that represents the age of randy's brother is
2x.
Where x is the age of Randy.
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Find the x- and y-intercepts of the graph of 3x−8y=39. State each answer as an integer or an improper fraction in simplest form.
The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.
Given that,
The equation is 3x-8y=39.
We have to find the x- intercept and y- intercept of the equation.
We know that,
x/a + y/b = 1 is the intercept form of the line's equation. One of the key types of line equations is this one. In this equation, the sign of the intercepts also enables us to determine where the line is in relation to the coordinate axes.
To find the x- intercept of the equation.
We have to take y as 0.
3x-8(0)=39
3x=39
x=39/3
x=13
To find the y- intercept of the equation.
We have to take x as 0.
3(0)-8y=39
-8y=39
x=-39/8
Therefore, The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.
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Can I pleaseeeee get some help solving these problems I’m really struggling
Answer:
2. $19,547.04
3. $10,276.54
4. $16,758.38
Step-by-step explanation:
You have three problems in compound interest with different initial payments, interest rates, and compounding intervals. You want the relationship between the initial payment and the future value.
Future value multiplierThe multiplier of a single payment earning annual interest rate r compounded n times per year for t years is ...
k = (1 +r/n)^(nt)
2.For this problem, r=0.09, n=1, t=9. The multiplier of the payment is ...
k = (1 +0.09/1)^(1·9) = 1.09^9 = 2.17189328
Then the future value of $9000 will be ...
FV = $9000 × 2.17189328 ≈ $19,547.04
3.For this problem, r=0.10, n=12, t=4. The multiplier of the payment is ...
k = (1 +0.10/12)^(12·4) = 1.08333...^48 = 1.48935410
Then the future value of $6900 will be ...
FV = $6900 × 1.48935410 ≈ $10,276.54
4.For this problem, r=0.13, n=12, t=13. The multiplier of the payment is ...
k = (1 +0.13/12)^(12·13) = 1.0108333...^156 = 5.3704484
Then the payment that gives a future value of $90,000 will be ...
P = $90,000/5.3704484 = $16,758.38
__
Additional comment
For the spreadsheet calculation, we used the "Goal Seek" capability to adjust the value of cell F4 to 90000 by changing the value in cell B4.
We could have calculated the multiplier as above, then used it different ways for the different problems. Instead, we used one FV( ) function for all of the problems.
Zoe wants to buy 6 tins of beans for the cheapest possible price. Shop A and Shop B both have a special offer. Shop A 5% off the normal price of 48p each Shop B 65p each Buy 2 get 1 free Which shop should Zoe buy the beans from? You must show how you get your answer.
A plant manufactures parts whose links are normally distributed with a mean of 16.3 cm and a standard deviation of 2.5 cm if one part is randomly selected find the probability that the part is between 10.8 and 12.8 cm
The probability that the part is between 10.8 and 12.8 cm is 0.0669.
What is a normal distribution?
Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is symmetric around the mean.
Here, we have
Mean = 16.3cm
Standard deviation = 2.5cm
We have to find the probability that the part is between 10.8 and 12.8 cm
Now,
we know that z = (x−μ)/σ
putting values in the normal distribution formula, we get
P( 10.8 < x < 12.8) = P( (10.8 - 16.3)/2.5 < z < (12.8 - 16.3)/2.5)
= P ( -2.2 < z < -1.4)
P( 10.8 < x < 12.8) = 0.0669, by normal distribution table
Hence, the probability that the part is between 10.8 and 12.8 cm is 0.0669.
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