The dot plot allows us to know the exact data we are graphing.
What does a dot plot show us that a box and whisker doesn't?In a dot plot, we have the different possible values on the horizontal axis, and dots above each of these values that count how many times that value has appeared in an experiment.
Instead, in a whisker plot or a box plot we have a representation in a kinda of "rectangle with whiskers".
This type of plot is usefull to find the quartiles of the data set, but not to know exactly how many of each data points we have, like in the dot plot.
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The sum of the first 3 terms of a geometric sequence
is 30 1/2. The sum of the 4th, 5th and 6th term is 3 15/16.
Determine the value of r.
The value of r is approximately 0.62.
The sum of the first 3 terms of a geometric sequence is 30 1/2 and the sum of the 4th, 5th, and 6th term is 3 15/16. To determine the value of r, we can use the formula for the sum of a geometric sequence:
S_n = a_1 (1 - r^n) / (1 - r)
Where S_n is the sum of the first n terms, a_1 is the first term, and r is the common ratio.
For the first 3 terms, we have:
30 1/2 = a_1 (1 - r^3) / (1 - r)
For the 4th, 5th, and 6th terms, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 r^(n-1)
So the 4th term is a_1 r^3, the 5th term is a_1 r^4, and the 6th term is a_1 r^5. The sum of these terms is:
3 15/16 = a_1 r^3 + a_1 r^4 + a_1 r^5
We can factor out a_1 r^3 to get:
3 15/16 = a_1 r^3 (1 + r + r^2)
Now we can substitute the expression for a_1 r^3 from the first equation into the second equation:
3 15/16 = (30 1/2) (1 - r) (1 + r + r^2)
Simplifying and rearranging terms, we get:
r^5 - 8r^4 + 15r^3 - 8r^2 + r = 0
This is a quintic equation, which cannot be solved algebraically. However, we can use numerical methods to find an approximate value of r. Using a graphing calculator, we find that r ≈ 0.62.
Therefore, the value of r is approximately 0.62.
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on a certain object, the acceleration of the object is 5 /ms2. If the force is changed to 14 N, what will be the acceleration of the object?
The acceleration of the object when a force of 14 N acts on it will be 7 m/s².
We can use the proportionality relationship between force and acceleration to solve this problem. The relationship can be expressed as:
F = k a
where F is the force, a is the acceleration, and k is a constant of proportionality.
We are given that the force and acceleration are directly proportional, so we can set up a proportion using the given information:
10 N / 5 m/s² = 14 N / a
Solving for a, we can cross-multiply and simplify:
10 N * a = 5 m/s² * 14 N
a = (5 m/s² * 14 N) / 10 N
a = 7 m/s²
Therefore, the acceleration of the object when a force of 14 N acts on it will be 7 m/s².
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The scale factor of two similar hexagons is 3:7.
The area of the smaller hexagon is 18 m2.
What is the volume of the larger hexagon
Possible answers
98 m2
324 m2
42 m2
36 m2
5832 m2
Answer:
Since the hexagon is a 2D shape, it does not have volume. We can find the area of a hexagon but not its volume.
Step-by-step explanation:
The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths. In this case, since the figures are hexagons, we can use the ratio of their corresponding side lengths to find the ratio of their areas.
Since the scale factor of the hexagons is 3:7, we know that the ratio of their side lengths is also 3:7. Therefore, the ratio of their areas is:
(3/7)^2 = 9/49
We are given that the area of the smaller hexagon is 18 m^2, so we can use this to find the area of the larger hexagon:
(area of larger hexagon) = (area of smaller hexagon) x (ratio of areas)
(area of larger hexagon) = 18 x (9/49)
(area of larger hexagon) = 3.28 m^2 (rounded to two decimal places)
Since the hexagon is a 2D shape, it does not have volume. We can find the area of a hexagon but not its volume.
A dog's body temperature (t), in degrees Fahrenheit (°F), is considered normal when the value of the expression below is no more than 0.75.
|t - 101.75|
A dog's body temperature is 101.2°F. Based on the expression, which statement about the dog's body temperature is true?
A. Since normal body temperature is from 100.25°F to 103.25°F, the dog's body temperature is considered normal.
B. Since normal body temperature is from 100.25°F to 103.25°F, the dog's body temperature is not considered normal.
C. Since normal body temperature is from 101°F to 102.5°F, the dog's body temperature is considered normal.
D. Since normal body temperature is from 101°F to 102.5°F, the dog's body temperature is not considered normal.
C. The dog's body temperature is regarded normal because the range for a healthy adult is 101°F to 102.5°F.
What exactly is value?
Value is the appraised, monetary, or material worth of a good, service, or asset. Several ideas are associated with the word "value," including shareholder value, company value, fair value, and selling price.
The phrase to assess whether a dog's body temperature is acceptable or not is:
|t - 101.75| ≤ 0.75
When we replace the specified value for the dog's body temperature, we obtain:
|101.2 - 101.75| = |-0.55| = 0.55
The body temperature of the dog is regarded as normal because 0.55 is less than 0.75.
Option C, however, is the one that accurately depicts the dog's core body temperature:
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Can someone please help me with these and a tip on how to solve em step by step please
Applying the definition of complementary angles, the measures are:
7. m<DBE = 64°; m<CBE = 26°
8. m<WVZ = 84°; m<XVW = 96°
9. m<RTS = 63°; m<PTQ = 27°
10. m<EFG = 139°
m<IFH = 49°
What are Complementary Angles?Complementary angles are two angles whose sum is equal to 90 degrees. In other words, when two angles are placed side by side, forming a right angle, they are said to be complementary.
7. Angles DBE and CBE are complementary angles, therefore:
17x + 13 + 32 - 2x = 90
15x + 45 = 90
15x = 90 - 45
15x = 45
x = 3
m<DBE = 17x + 13 = 17(3) + 13 = 64°
m<CBE = 32 - 2x = 32 - 2(3) = 26°
8. 5x + 29 = 9x - 15 [vertical angles are equal]
5x - 9x = -29 - 15
-4x = -44
x = 11
m<WVZ = 9x - 15 = 9(11) - 15 = 84°
m<XVW = 180 - 84 = 96° [linear pair]
9. 8x - 17 = 5x + 13 [vertical angles]
8x - 5x = 17 + 13
3x = 30
x = 10
m<RTS = 5x + 13 = 5(10) + 13 = 63°
m<PTQ = 180 - 90 - 63 = 27°
10. (2x + 3) + (6x + 25) = 180 [linear pair]
8x + 28 = 180
8x = 180 - 28
8x = 152
x = 19
m<EFG = 6x + 25 = 6(19) + 25 = 139°
m<IFH = 90 - (2x + 3) = 90 - (2(19) + 3)
m<IFH = 49°
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Which of the equation choices could represent the circle shown on the graph?
The equation that represents the circle shown in the graph is:[tex](x - 2)^2 + (y + 1)^2 = 9.[/tex]
What is circle ?
A circle is a shape in geometry that is defined as a closed curve that is formed by a set of points that are equidistant from a single fixed point called the center. The distance between any point on the circle and the center is called the radius of the circle.
The center of the circle appears to be at the point (2, -1) and the radius seems to be approximately 3 units.
Using the values of the center and radius, we can plug them into the general equation of a circle to obtain the equation that represents the circle:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Substituting h = 2, k = -1, and r = 3, we get:
[tex](x - 2)^2 + (y + 1)^2 = 9[/tex]
Therefore, the equation that represents the circle shown in the graph is:[tex](x - 2)^2 + (y + 1)^2 = 9.[/tex]
Option D is the equation that represents the circle, which is[tex](x - 2)^2 + (y + 1)^2 = 9.[/tex]
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13. Daniel bought some oranges and x apples. He bought twice as many oranges as apples. Each apple
cost $0. 35 and each orange cost $0. 50. Daniel paid $5. 40 in total for oranges and apples. How many
apples did he buy? Write an equation and solve it.
Daniel bought 8 apples and 16 oranges. The equation we will use to solve the problem is 0.35x + 0.5(2x) = 5.4.
We know that Daniel bought twice as many oranges as apples, so let's call the number of apples he bought "x". Therefore, the number of oranges he bought would be "2x".
We also know that each apple cost $0.35 and each orange cost $0.50, so we can write the equation:
0.35x + 0.5(2x) = 5.4
Simplifying the equation, we get:
0.35x + x = 5.4 ÷ 0.5
0.35x + x = 10.8
1.35x = 10.8
x = 8
So, Daniel bought 8 apples, which means he also bought 2x = 16 oranges.
However, we need to check if this solution makes sense hence the cost of the apples would be:
0.35 × 8 = 2.8
And the cost of the oranges would be:
0.5 × 16 = 8
Adding those together, we get:
2.8 + 8 = 10.8
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Casio Company produces four-season drinks by mixing juices of four fruits in season. The standard costs and input for a 50-liter batch of the juice are as follows:
Fruits "Standard input
Quantity in Liters" "Standard Cost
Per Liter" Total Standard Costs
Apple 20 P10.00 P200.00
Mango 10 P21.25 P212.50
Pineapple 25 P7.50 P187.50
Peach 5 P15.00 P75.00
60 P675.00
The quantities purchased and used during the current month are shown below. A total of 14 batches were produced during the month
Fruits Quantity purchased Purchase Price Quantity used
(liters) (liters)
Apple 300 P9.50 290
Mango 150 P22.00 130
Pineapple 350 P7.20 350
Peach 80 P15.40 75
1,450 How much is the total materials cost variance
The materials yield variance is(provide amount only)
The materials purchase usage variance is
provide amount only
The total materials purchase usage variance is -P122.50.
The total materials cost variance is calculated by subtracting the total standard cost from the total actual cost. The total standard cost is P675.00 per batch and there were 14 batches produced during the month, so the total standard cost is P675.00 x 14 = P9,450.00. The total actual cost is calculated by multiplying the quantity purchased by the purchase price for each fruit and then adding them all together. The total actual cost is (300 x P9.50) + (150 x P22.00) + (350 x P7.20) + (80 x P15.40) = P2,850.00 + P3,300.00 + P2,520.00 + P1,232.00 = P9,902.00. The total materials cost variance is P9,902.00 - P9,450.00 = P452.00.
The materials yield variance is calculated by subtracting the standard quantity of materials from the actual quantity of materials used and then multiplying by the standard cost per liter. The standard quantity of materials is 60 liters per batch and there were 14 batches produced during the month, so the standard quantity of materials is 60 x 14 = 840 liters. The actual quantity of materials used is 290 + 130 + 350 + 75 = 845 liters. The materials yield variance is (840 - 845) x P10.00 = -P50.00.
The materials purchase usage variance is calculated by subtracting the standard cost per liter from the actual cost per liter and then multiplying by the actual quantity of materials used. The materials purchase usage variance for each fruit is (P9.50 - P10.00) x 290 + (P22.00 - P21.25) x 130 + (P7.20 - P7.50) x 350 + (P15.40 - P15.00) x 75 = -P145.00 + P97.50 - P105.00 + P30.00 = -P122.50. The total materials purchase usage variance is -P122.50.
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The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 80.2° is added to the data, how does the range change?
The range stays 47°.
The range decreases to 47°.
The range stays 48°.
The range increases to 50°.
Answer:
The range stays 48°
Step-by-step explanation:
The range is the difference between the highest and lowest values in the data set. Before adding 80.2°, the highest temperature is 105° and the lowest temperature is 57°, so the range is 105° - 57° = 48°.
After adding 80.2°, the highest temperature becomes 105° + 80.2° = 185.2° and the lowest temperature becomes 57° + 80.2° = 137.2°. So the new range is 185.2° - 137.2° = 48°.
Therefore, the range stays the same at 48°. The answer is: The range stays 48°.
Answer:
The range stays 48°
Step-by-step explanation:
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The measure of arc ED is 78.7°
How to find the measure of an arc?An arc of a circle is a portion of the circumference of a circle. It is defined by two endpoints and the arc itself.
The measure of an arc is given in degrees or radians, and it is determined by the angle that it subtends at the center of the circle.
Since FC is the diameter and arc FB is equivalent to arc BC. We can say:
arc FB + arc BC = 180°
arc FB = arc FB = 90°
Also, arc ED is twice the measure of arc CD. We can write:
arc ED = 2 * arc CD
arc CD = (arc ED)/2
Since the sum arc FB and arc BC is 180°. We can say:
arc FE + arc ED + 0.5(arc ED) = 180°
62° + arc ED + 0.5(arc ED) = 180°
62° + 1.5(arc ED) = 180°
1.5(arc ED) = 180 - 62
1.5(arc ED) = 118
arc ED = 118/3
arc ED =78.7°
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In the diagram below line MN is parallel to line JK. If KN=12, MN=25, and JK=40 find the length of line LN
The length of line LN is 25.
What is Similarity of Triangles?
Two triangles are similar if they have the same shape but possibly different sizes. This means that their corresponding angles are congruent and their corresponding sides are proportional.
Since line MN is parallel to line JK, we can use the property that corresponding angles are congruent to set up the following proportion:
LN/KJ = NM/JK
Substituting the given values, we have:
LN/40 = 25/40
Multiplying both sides by 40, we get:
LN = 25
Therefore, the length of line LN is 25.
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A rectangular box with a volume of 60x^(6)y^(6)z^(10) width of 2x^(2)y^(3)z^(4) length of 10x^(3)y^(4)z^(5) units and a height, 2x^(2)y^(3)z^(4) units. Write an expression for its height
The expression for the height of the box is 3x^(1)y^(-1)z^(1) units.
The volume of a rectangular box is given by the formula V = lwh, where l is the length, w is the width, and h is the height. We are given the volume, width, and length of the box and we are asked to find the expression for its height.
Volume = 60x^(6)y^(6)z^(10)
Width = 2x^(2)y^(3)z^(4)
Length = 10x^(3)y^(4)z^(5)
Substituting the given values into the formula for volume, we get:
[tex]60x^{(6)}y^{(6)}z^{(10)} = (2x^{(2)}y^{(3)}z^{(4))}(10x^{(3)}y^{(4)}z^{(5))(h)[/tex]
Simplifying the right side of the equation, we get:
60x^(6)y^(6)z^(10) = 20x^(5)y^(7)z^(9)(h)
Dividing both sides of the equation by 20x^(5)y^(7)z^(9), we get:
h = (60x^(6)y^(6)z^(10))/(20x^(5)y^(7)z^(9))
Simplifying the fraction, we get:
h = 3x^(1)y^(-1)z^(1)
Therefore, the expression for the height of the box is 3x^(1)y^(-1)z^(1) units.
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The value of stocks in a certain new startup company is being modeled by the function S(t)S(t), where tt is in years since the company going public in 2015. How would you best interpret the following information about the value of the company's stocks?
S′(5)=0S′(5)=0 and S′′(t)>0S″(t)>0 for 5 ≤ t ≤ 65 ≤ t ≤6.
The best interpretation of the given information about the value of the company's stocks is that the value of the company's stocks has reached a local minimum at t=5 and is increasing at an increasing rate for 5 ≤ t ≤ 6.
The value of stocks in a certain new startup company is being modeled by the function S(t), where t is in years since the company going public in 2015. The given information about the value of the company's stocks is S′(5)=0 and S′′(t)>0 for 5 ≤ t ≤ 6.
The derivative S′(t) represents the rate of change of the value of the company's stocks with respect to time. Therefore, S′(5)=0 means that the rate of change of the value of the company's stocks at t=5 is zero, or in other words, the value of the company's stocks is not changing at t=5. This indicates that the value of the company's stocks has reached a local maximum or minimum at t=5.
The second derivative S′′(t) represents the rate of change of the first derivative S′(t) with respect to time. Therefore, S′′(t)>0 for 5 ≤ t ≤ 6 means that the rate of change of the first derivative S′(t) is positive for 5 ≤ t ≤ 6, or in other words, the first derivative S′(t) is increasing for 5 ≤ t ≤ 6. This indicates that the value of the company's stocks is increasing at an increasing rate for 5 ≤ t ≤ 6.
the best interpretation of the given information about the value of the company's stocks is that the value of the company's stocks has reached a local minimum at t=5 and is increasing at an increasing rate for 5 ≤ t ≤ 6.
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In a ratio of 3:4:5, three entrepreneurs invested in a project an amount of $875,000 altogether. Calculate the second largest share of the three. Round off to the nearest 100th.
The second largest share of the three entrepreneurs is $291,666.68.
To calculate the second largest share of the three entrepreneurs, we need to first find the total ratio by adding the three individual ratios: 3 + 4 + 5 = 12.
Next, we can find the value of one part of the ratio by dividing the total amount invested by the total ratio: $875,000 ÷ 12 = $72,916.67.
Finally, we can calculate the second largest share by multiplying the value of one part of the ratio by the second largest individual ratio, which is 4: $72,916.67 × 4 = $291,666.68.
Therefore, the amount of the second largest share is $291,666.68.
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The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals:
a. 13
b. 24
c. 576
d. 28,461
The standard deviation of the sample is 24. Therefore the correct option is, option b. 24.
The variance of a sample is the square of the standard deviation. In other words, the standard deviation is the square root of the variance. Therefore, to find the standard deviation of the sample, we need to take the square root of the variance:
√576 = 24
Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
Like the variance, if the data points are close to the mean, there is a small variation whereas the data points are highly spread out from the mean, then it has a high variance.
So, the standard deviation of the sample of 169 observations and variance 576 equals 24. The correct option is b.
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write and solve a proportion to find the perimeter of a square when its side length is 12
Therefore, the perimeter of the square when its side length is 12 is 48 units.
What, for example, is a perimeter?The perimeter of an object is the space surrounding it. For instance, the yard around your house is fenced in. The perimeter of the barrier is its length. If the yard is 50 by 50 feet, your fence is 200 feet long.
Since a square has all equal sides, the perimeter of a square is just four times the length of one side. Therefore, the perimeter of the square when its side length is 12 is:
Perimeter = 4 x 12 = 48
To write a proportion to solve for the perimeter of a square when its side length is x, we can set up the following ratio:
12/x = 48/p
where p represents the perimeter of the square. We can cross-multiply to get:
12p = 48x
p = 4x
Now we can substitute 12 for x to find the perimeter when the side length is 12:
p = 4(12) = 48
Therefore, the perimeter of the square when its side length is 12 is 48 units.
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6. Given a right triangle with leg lengths 19 inches and 17 inches, find the length of the
hypotenuse. Round to the nearest tenths.
The hypotenuse of the right triangle is 25.5 inches.
How to find the hypotenuse of a right triangle?A right triangle is a triangle that has one angle as 90 degrees. The sum of angles in a triangle is 180 degrees.
The right right triangle has the legs as 19 inches and 17 inches. Let's find the hypotenuse.
Using Pythagoras's theorem,
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
c² = 19² + 17²
c² = 361 + 289
c = √650
c = 25.495097568
c = 25.5 inches
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i need help with this questchin
The triangle in this problem is classified as follows:
Scalene obtude triangle.
How to classify the triangle?According to the largest angle measure, the triangle is classified as follows:
Less than 90º: acute.90º: straight = right.Greater than 90º: obtuse.The largest angle measure in this problem is of 102º > 90º, hence the triangle is an obtuse triangle.
The triangle is also classified as scalene, isosceles or equilateral as follows:
Scalene: 3 different angle measures.Isosceles: 2 equal and 1 different angle measure.Equilateral: 3 equal angle measures.The three angle measures for this problem are different, hence the triangle is scalene.
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helppppppp
Find the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly.
The final amount for the investment of $5,000 is $ 6,749.29.
Compound interest:Compound interest is a type of interest calculation in which the interest earned on an initial principal amount is added to the principal, and the new total amount earns interest in subsequent periods.
This means that the interest earned in each period is based on the total amount, which includes both the principal and the accumulated interest from previous periods.
The formula used for compound interest:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]Where:
P = Initial investment
r = Rate of interest (as a decimal)
n = Number of compounds
t = Time period in years
Here we have
P = $5,000,
r = 6% = 0.06,
n = 4 (since the interest is compounded quarterly), and
t = 5 years.
Using the above formula
[tex]A = 5000(1 + 0.06/4)^{(4*5)[/tex]
[tex]A = 5000(1.015)^{20[/tex]
[tex]A = 5000(1.34985711)[/tex]
[tex]A =\$6,749.29[/tex]
Therefore,
The final amount for the investment of $5,000 is $ 6,749.29.
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price money of R4000 must be shared among the first three winners in the ratio 5:3:2, calculate how much each winner will receive?
Answer: Explanation below
Step-by-step explanation:
R4000 is the money to be split
5:3:2 is the ratio
We can add the ratios together.
5+3+2=10
The first winner = 5/10 x 4000
= R2000
The second winner = 3/10 x 4000
= R1200
The third winner = 2/10 x 4000
= R800
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Describe the translation that maps figure ABCD onto figure EFGH
The translation that maps figure ABCD onto figure EFGH is described as follows: Translate figure ABCD 7 units right to form figure EFGH..
What is a translation?Translation transformation is a type of geometric transformation that moves every point of an object or shape in a straight line without changing its orientation or size.
A translation happens when either a figure or a function are moved horizontally or vertically.
How to determine the translation ruleIf we look at the corresponding vertices on each figure, we have that:
7 was added to the x-coordinate of each vertex.The y-coordinate of each vertex remains constant.Hence: Translate figure ABCD 7 units right to form figure EFGH.
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All Il of the following are reasons that you might receive a 1099 statement EXCEPT....
Working as an independent contractor
b. Receiving unemployment benefits
c. Earning interest or dividends
d. Working as a post office clerk
Answer:
File Form 1099-MISC for each person to whom you have paid during the year:
At least $10 in royalties or broker payments in lieu of dividends or tax-exempt interest.
At least $600 in:
Rents.
Prizes and awards.
Other income payments.
Medical and health care payments.
Crop insurance proceeds.
Cash payments for fish (or other aquatic life) you purchase from anyone engaged in the trade or business of catching fish.
Generally, the cash paid from a notional principal contract to an individual, partnership, or estate.
Payments to an attorney.
Any fishing boat proceeds.
Step-by-step explanation:
In addition, use Form 1099-MISC to report that you made direct sales of at least $5,000 of consumer products to a buyer for resale anywhere other than a permanent retail establishment.
Halla el valor de la cofunción de sec(y−π ). Recuerda que p = 180° y π/2
= 90°
Answer:
La cofunción del seno de un ángulo es igual al coseno de su complemento. Similarmente, la cofunción del coseno de un ángulo es igual al seno de su complemento.
Entonces, para encontrar la cofunción de sec(y-π), primero encontramos el complemento de (y-π), que es (π/2 - (y-π)) = (π/2 - y + π) = (3π/2 - y).
Por lo tanto, la cofunción de sec(y-π) es igual al coseno de su complemento, que es el coseno de (3π/2 - y):
cos(3π/2 - y) = -sin(y)
Entonces, la cofunción de sec(y-π) es igual a -sin(y).
Determine if the vectors ([1],[-2],[3]),([2],[-2],[0]) and ([0],[1],[7]) are a linearly independent set.
The vectors [tex]([1],[-2],[3]),([2],[-2],[0])[/tex] and [tex]([0],[1],[7])[/tex] are a linearly independent set.
To determine if the vectors are a linearly independent set, we can use the determinant method. The determinant of a 3x3 matrix is given by:
[tex]\begin{bmatrix}a_1 & a_2 &a_3 \\ b_1& b_2 &b_3 \\ c_1&c_2 &c_3 \end{bmatrix}[/tex]
We can create a 3x3 matrix using the given vectors as the columns of the matrix:
[tex]\begin{bmatrix}1 & 2 &0 \\ -2& -2 &1 \\ 3&0 &7 \end{bmatrix}[/tex]
Now, we can find the determinant of this matrix using the formula:
[tex]det(\begin{bmatrix}1 & 2 &0 \\ -2& -2 &1 \\ 3&0 &7 \end{bmatrix})[/tex]
[tex]= 1(-2*7 - 1*0) - 2(-2*7 - 1*3) + 0(-2*0 - 1*-2)[/tex]
[tex]= -14 - 0 - 4(-14) - 6 + 0[/tex]
[tex]= -14 + 56 - 6[/tex]
[tex]= 36[/tex]
Since the determinant is not equal to zero, the vectors are linearly independent.
Therefore, the vectors[tex]([1],[-2],[3]),([2],[-2],[0])[/tex] and [tex]([0],[1],[7])[/tex] are a linearly independent set.
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Hi! Question is attached ty!
The rate of interest per annum when he invested £6,500 and got £6,838 will be 5.2%.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
The amount after one year is £6838 if he invested £6,500. Then the rate of interest is given as,
£6,838 = £6,500 × (1 + r)¹
1 + r = 1.052
r = 0.052 or 5.2%
The rate of interest per annum when he invested £6,500 and got £6,838 will be 5.2%.
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Factor the polynomial using Pascal's Triangle and the properties of binomial cubes. 8x^(3)+12x^(2)+6x+1
The polynomial 8x^(3) + 12x^(2) + 6x + 1 can be factored as (2x + 1)^(3) using Pascal's Triangle and the properties of binomial cubes.
To factor the given polynomial using Pascal's Triangle and the properties of binomial cubes, we need to first identify the coefficients of the polynomial and then use the pattern of Pascal's Triangle to find the factors. Here are the steps:
Step 1: Identify the coefficients of the polynomial. The coefficients are 8, 12, 6, and 1.
Step 2: Use the pattern of Pascal's Triangle to find the factors. The third row of Pascal's Triangle is 1, 3, 3, 1. We can use this pattern to factor the polynomial as follows:
8x^(3) + 12x^(2) + 6x + 1 = (2x + 1)^(3)
Step 3: Use the properties of binomial cubes to simplify the factors. The formula for the cube of a binomial is (a + b)^(3) = a^(3) + 3a^(2)b + 3ab^(2) + b^(3). We can use this formula to simplify the factors as follows:
(2x + 1)^(3) = (2x)^(3) + 3(2x)^(2)(1) + 3(2x)(1)^(2) + (1)^(3) = 8x^(3) + 12x^(2) + 6x + 1
Therefore, the factors of the polynomial are (2x + 1)^(3).
The polynomial 8x^(3) + 12x^(2) + 6x + 1 can be factored as (2x + 1)^(3) using Pascal's Triangle and the properties of binomial cubes.
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there are 3242 candies in a jar. 7 candies are kept in each pack what fraction of candies is left behind
The fraction of candies left behind is 3/7.
To find the fraction of candies left behind, we need to divide the total number of candies by the number of candies in each pack and find the remainder. This remainder will be the numerator of the fraction and the number of candies in each pack will be the denominator.
Step 1: Divide the total number of candies by the number of candies in each pack: 3242 ÷ 7 = 463 with a remainder of 3
Step 2: The remainder, 3, is the numerator of the fraction and the number of candies in each pack, 7, is the denominator. So the fraction of candies left behind is 3/7.
The fraction of candies left behind is 3/7.
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At an ice cream shop, the cost of 4 milkshakes and 2 ice cream sundaes is $23.50. The cost of 8 milkshakes and 6 ice cream sundaes is $56.50.
A milkshake costs $3.50 and an ice cream sundae costs $4.75.
What is a system of linear equations?
A system of linear equations is a set of two or more linear equations that contain the same variables. A linear equation is an equation of a straight line and has the form ax + by = c, where a, b, and c are constants and x and y are variables.
The goal of a system of linear equations is to find the values of the variables that satisfy all the equations in the system simultaneously. This can be done by different methods, such as substitution, elimination, or matrix methods.
Systems of linear equations are widely used in mathematics, science, engineering, and economics to model and solve real-world problems involving multiple unknowns. They are a fundamental concept in algebra and linear algebra.
Using this information, we can set up a system of equations to find the cost of a milkshake and the cost of an ice cream sundae. Let's use x to represent the cost of a milkshake and y to represent the cost of an ice cream sundae.
From the first sentence, we can write the equation:
[tex]4x + 2y = 23.5[/tex]
From the second sentence, we can write the equation:
[tex]8x + 6y = 56.5[/tex]
Now we can solve for x and y using any method of solving systems of equations, such as substitution or elimination.
Let's use elimination. Multiplying the first equation by -3 and adding it to the second equation, we get:
[tex]-12x - 6y = -70.5[/tex]
[tex]8x + 6y = 56.5[/tex]
[tex]-4x = -14[/tex]
Dividing both sides by -4, we get:
[tex]x = 3.5[/tex]
Now we can substitute x = 3.5 into one of the original equations to solve for y. Let's use the first equation:
[tex]4x + 2y = 23.5[/tex]
[tex]4(3.5) + 2y = 23.5[/tex]
[tex]14 + 2y = 23.5[/tex]
[tex]2y = 9.5[/tex]
[tex]y = 4.75[/tex]
Therefore, a milkshake costs $3.50 and an ice cream sundae costs $4.75.
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HELP pls I beg u I need this answer
Answer:
The slope of the given line on the graph is 1/3.
Answer:
1/3
Step-by-step explanation:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Let's start at 0 with x = 0 and y = 0 or (0,0)
You see the graph crosses coordinate (3,1)
so y goes from 0 to 1 => rise = 1
x goes from 0 to 3 => run = 3
then rise/run = 1/3
Please can someone help me
Answer:
Matt is a lawyer who used to charge his clients $330 per hour. Matt recently reconsidered his rates and ultimately decided to charge $231 per hour. What was the percent of decrease in the billing rate?
Step-by-step explanation:
c is the ansswer