It is not possible to describe the standard deviations of salary, hourly rate, years worked, education, and age without having the data.
Standard deviation is a measure of the spread or dispersion of a set of data. It is calculated as the square root of the variance and is used to give an idea of how far the individual values in a data set are from the mean or average.
In order to describe the standard deviations of salary, hourly rate, years worked, education, and age, we would need to have the actual data for those variables. Without the data, it is not possible to calculate the standard deviations and describe what they tell us about the variables.
It is important to note that the standard deviation can give us information about the distribution of the data and the variability of the values. For example, if the standard deviation is small, this means that the majority of the values are close to the mean, while a larger standard deviation indicates that the values are more spread out. This information can be useful in making inferences about the variables and in making predictions about future values.
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two step equations -16 - 5x = -16
Answer:
-16 - 5x = -16
-5X=-16+16
-5X=0
X=5
Step-by-step explanation:
1. What are some differences between arithmetic and geometric sequences and series? What about finite and infinite sequences and series?
2. What are the explicit and recursive formulas for the nth term of an arithmetic sequence?
3. What are the explicit and recursive formulas for the nth term of a geometric sequence?
4. What is the formula for the sum of a finite arithmetic series?
5. What are the formulas for the sum of a finite and an infinite geometric series?
This refers to a sequence in which each term increases by adding/subtracting some constant k.
What is geometric sequences?
This refers to a sequence where each term increases by dividing/multiplying some constant k.
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If a polynomial equation P(x)= 0 has 3+4i as a solution, what other solution must it have?
Answer: 3 - 4i
Step-by-step explanation:
For the given polynomial p(x) , if 3 +4i is a root then, 3 - 4i is also the root of p(x).
Consider the given polynomial equation p(x) = 0 It is given that the polynomial P(x) has one root 3 + 4i .
According to complex conjugate theorem, if V is a polynomial and x + iy is a root of given polynomial then its conjugate x - iy is also the root of the polynomial.
Thus, for the given polynomial p(x) if 3 +4i is a root then, 3 - 4i is also the root of p(x).
If a polynomial equation P(x) = 0 has (3 + 4i) as a solution, the other solution it must have (3 - 4i).
What is a polynomial?
Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Conjugate complex numbers are those that only differ in the imaginary part's sign.
a + bi and a - bi, where a and b are real numbers, are generally conjugate, as are, for instance, 2 + 3i and 2 - 3i, -5 - 7i and -5 + 7i, and so on.
Due to the fact that their output is always a genuine number.
The general case is -
= (a + bi)(a - bi)
= a² - abi + abi - (b²)(i²)
= a² + b²
The real example is -
= (2 + 3i)(2 - 3i)
= 2² + 3²
= 4 + 9
= 13
Complex roots for a polynomial equation P(x) = 0 with real coefficients are always represented as conjugate pairs.
So, the following equation must contain (3 - 4i) as a second root if the coefficients are real.
Therefore, P(x) has second root (3 - 4i).
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If a taco contains any three distinct items. There are 4 meat items and 8 non-meat items.
1. If a three distinct item taco is made at random, what is the probability that the taco contains only non-meat items? Please show steps, thank you!
The probability of a taco containing only non-meat items is 56/220 = 1/4.
To find the probability of a taco containing only non-meat items, we need to find the number of possible combinations of 3 non-meat items out of the 8 non-meat items available and divide that by the total number of possible combinations of 3 items (either meat or non-meat) out of the 12 total items available.
The number of combinations of 3 non-meat items out of the 8 available is: C(8, 3) = 56
The number of combinations of 3 items out of the 12 total items available is: C(12, 3) = 220
The probability of a taco containing only non-meat items is 56/220 = 1/4.
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describe three techniques for analyzing data. how are they organized and summarized, and what are they used for?
The three types of Data analysis can be : Descriptive Analysis, Diagnostic Analysis nad Predictive Analysis.
What is Data Analysis ?In order to find relevant information, support inferences, and help decision-making, data analysis is the process of analyzing, cleaning, manipulating, and modeling data.
Using both recent and old data, descriptive analytics seeks out patterns and connections. Because it only describes patterns and associations without going any further, it is frequently referred to as the most basic kind of data analysis.
A type of advanced analytics called diagnostic analytics looks at data or information to determine "why it happened." Techniques like drill-down, data discovery, data mining, and correlations are used to describe it.
Using data, statistical algorithms, and machine learning approaches, predictive analytics determines the likelihood of future events based on previous data. The objective is to provide the most accurate prediction of what will happen in the future in addition to understanding what has already occurred.
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Four aerial photographers will need 6 batteries to operate their drone. Each found a different website that sells rechargeable batteries.
A first quadrant coordinate plane titled Website A is shown. The horizontal axis is labeled batteries. The vertical axis is labeled cost in dollars. A dotted line is graphed through the points zero comma forty, one comma forty-two, and continues through six comma fifty-two. An advertisement is titled Website B. Zapper. Rechargeable batteries, two dollars and thirty cents each. Battery charger, thirty-five dollars.
The table is titled Website C and has two columns and six rows. The first column is batteries. The second column is cost in dollars. One battery, thirty-nine dollars and ten cents. Two batteries, forty-one dollars and twenty cents. Three batteries, forty-three dollars and thirty cents. Five batteries, forty-seven dollars and fifty cents. Six batteries, forty-nine dollars and sixty cents. A caption reads, Website D: y equals three and five tenths x plus twenty-eight.
For each website, find the cost of 6 rechargeable batteries and a charger. Which website has the best price?
Answer: The cheapest option is Website B.
Step-by-step explanation:
The cost of 6 rechargeable batteries and a charger from each website is:
Website A: 6 batteries * $52/battery = $312
Website B: 6 batteries * $2.30/battery + $35/charger = $16.80 + $35 = $51.80
Website C: 6 batteries * $49.60/battery = $297.60
Website D: 6 batteries * $3.5 x + $28 = $63 + $28 = $91
The cheapest option is Website B with a cost of $51.80.
consider the formula k = 1/(1-s). what happens to the variable k when s grows in value?
When s grows in value, the value of variable k decreases.
Consider the formula k = 1/(1 - s)
We know that when the value of one quantity 'm' increases with respect to decrease in the value of other 'n' or vice-versa, then we say that the two quantities 'm' and 'n' are inversely proportional to each other.
We write this as,
m∝ 1/n
m = p/n
where p is the constant of proportionality
From the formula k = 1/(1 - s) we can observe that the quantities k and s are inversely proportional to each other.
this means, when the value of variable s increases, there is decrease in value of variable k.
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Find the weighted average of the numbers 1 and 5 with one fourth of the weight on the first number and three fourths on the second number.
The Correct answer for the weighted average of given numbers is 4.
What is Weighted average?
Weighted average is one of the most commonly employed measures in statistical data to find the average of quantities when each quantity has a certain weight.
Formula for weighted average:
x= Σ(Weights × Quantity)/Σ(Weights)
In the given question,
first number is 1, Weight of the one of the number given is [tex]\dfrac{1}{4}[/tex](one fourth of first number (1)), The weight of three fourth of the second number is [tex]\dfrac{3}{4}*5[/tex], second number is 5.
Weighted average,
[tex]\dfrac{(\dfrac{1}{4}*1 + \dfrac{3}{4}*5)}{\dfrac{1}{4}+\dfrac{3}{4}}[/tex]
[tex]= \dfrac{16}{4}\\\\=4[/tex]
The weighted average of the numbers 1 and 5 with given condition is 4.
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Determine if the triangles are similar by side-angle-side similarity
Answer:
Step-by-step explanation:
note that all adjacent triangles will share an angle.
for 13 and 14 this is the case.
for 13 and 14 the adjacent sides are also multiples of each other proportionately. find this by dividing one side by the other for both triangles. if equal they are proportionately larger.
13 and 14 are both similar
for 15 and 16 the same logic can be applied to the side lengths. however, we are not given any information on the angles and cannot determine the angles mathematically.
for 17 and 18 the same logic can be applied again for the sides and given that the angles are confined within each other, the angles are the same.
for 17 and 18 you must add the side lengths for each side together and divide to determine the ratio and compare that to the ratio of the initial triangle
How to convert 80 kg to lbs?
When 80 kg is converted to lbs it will be equal to 176.36980975 pounds (lb).
How to convert kg to lb?The conversion factor of 2.20462 can be used to convert kilograms (kg) to pounds (lbs). To calculate the number of pounds, multiply the number of kilograms by 2.20462.Here in this case,
80kg x 2.20462
= 176.36980975 pounds.
It should be noted that this conversion is for the international standard, and the conversion formula may vary depending on the country.Also, keep in mind that the pound (lb) and kilogram (kg) are weight units and should not be confused with mass, which is measured in ounces (oz) and grams (g). Weight is more commonly used in everyday life to measure things like body weight and food weight, whereas mass is more commonly used in scientific settings.To learn more about unit conversion refer to :
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three computer viruses arrived as an email attachment. virus a damages the system with probability 0.4. independently of it, virus b damages the system with probability 0.5. independently of a and b, virus c damages the system with probability 0.2. what is the probability that the system gets damaged? 0.96 0.24 0.76 0.04
The probability that the system gets damaged is P(AUBUC)=0.76
If the probability of occurrence of an event A is not affected by the occurrence of another event B, then A and B are said to be independent events.
The two events are said to be independent events if the outcome of one event does not affect the outcome of another.
The formula can be defined as:
P(A and B) = P(A)×P(B)P(A and B) = P(A)×P(B)
For independent events U and V we have P(U∩V)=P(U)P(V)
if the viruses are truly independent then the probability that the system gets damaged=
P(AUBUC)=P(A)+P(B)+P(C)-P(AnB)-P(anc)-P(bnc)+P(AnBnC).
0.4+0.5+0.2-0.4*0.5-0.4*0.2-0.5*0.2+0.4*0.5*0.2=1.1-0.2-0.08-0.1+0.04
P(AUBUC)=0.76
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Find the values of x and y that ensure each quadrilateral is a parallelogram.
Top of quadrilaterial is: 3x-4y
Bottom of quadrilaterial is: 18
Right of it is: 7
Left of it is: 5x+y
As the sides of the parallelogram are equal, the values of x and y that ensure each quadrilateral is a parallelogram are 2 and -3.
What is parallelogram?A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a sort of quadrilateral with opposing pairs of sides that are parallel and equal. A parallelogram is a form of quadrilateral in geometry. It has four sides and is two-dimensional. A parallelogram's most significant qualities are that its opposite sides are parallel and congruent, and its opposite angles are equal.
Here,
3x-4y=18
5x+y=7
multiply 2nd equation by 4 and solve,
3x-4y=18
20x+4y=28
23x=46
x=2
5*10+y=7
y=-3
The values of x and y that ensure each quadrilateral is a parallelogram is 2 and -3 as the side of parallelogram are equal.
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Let f be a continuous function such that f changes from increasing to decreasing, and the graph of f changes fro concave up to concave down. Which of the following is true about the midpoint Riemann sum approximation for definite integral from 1 to 3 of f(x^2 + x) using 4 subintervals?a. The midpoint Riemann sum approximation underestimates the definite integral.b. The midpoint Riemann sum approximation overestimates the definite integral.c. The midpoint Riemann sum approximation cannot be determined to be an underestimate or an overestimate.
The true statement is Option B, The midpoint Riemann sum approximation overestimates the definite integral.
Given data,
In this case, since the function f changes from increasing to decreasing and the graph of f changes from concave up to concave down, we can infer that the function has a local maximum point within the interval [1, 3].
The midpoint Riemann sum approximation for the definite integral breaks the interval [1, 3] into four subintervals of equal width, and it uses the midpoint of each subinterval to approximate the value of the function within that subinterval.
Now, when the function is increasing, the midpoint Riemann sum approximation will tend to underestimate the value of the definite integral since it approximates the function using values that are smaller than the actual function values.
However, when the function changes from increasing to decreasing, the midpoint Riemann sum approximation will tend to overestimate the value of the definite integral since it approximates the function using values that are larger than the actual function values.
Hence , the midpoint Riemann sum approximation overestimates the definite integral.
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A typing examination found that susan's typing accuracy was 93%. Which decimal number represents susan's typing accuracy?.
Representing fractional values, if a typing examination found that Susan's typing accuracy was 93%, the decimal number representing Susan's typing accuracy is 0.93.
How the decimal number is determined?The decimal number of Susan's typing accuracy is a direct conversion from percentage to decimal since both are fractional values.
We know that the percentage sign represents over 100. When 93 is divided by 100, the decimal value is 0.93.
93% = 93/100 = 0.93
Thus, as a fractional value, Susan's typing accuracy of 93% is the same as 0.93.
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the mean composite score for seniors who took the sat in 2018 was 1068. if the standard deviation for this same year was 180, what is the raw score for a person with a z score of –0.42?
A person with a Z-score of -0.42 would have a raw score of 992.4 on the SAT taken in 2018.
The standard deviation is a measure of how much the data varies from the mean. A Z-score is a standardized value that represents the number of standard deviations a raw score is from the mean.
To find the raw score given a Z-score, we can use the following formula:
raw score = mean + Z-score * standard deviation
For the mean composite score of 1068 and a standard deviation of 180, we can plug in the values for the Z-score of -0.42:
raw score = 1068 + (-0.42) * 180
raw score = 1068 - 75.6
raw score = 992.4
Note: The Z-score of -0.42 indicates that the raw score is 0.42 standard deviations below the mean.
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Two similar figures have a side ratio of 4:3. If the perimeter of the smaller figure is 15 units, what is perimeter of the larger figure?
Enter fractions as decimals.
The perimeter of the larger figure is: 20 units.
How to Find the Perimeter of Similar Figures?Similar figures have perimeters and side lengths that are related in such a way that, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Therefore, if x represents the perimeter of the larger figure, then:
x/15 = 4/3
Cross multiply to find x:
3x = 60
x = 60/3
x = 20
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determine the magnitude and coordinate direction angles of f3 so that the resultant of the three is 0
The magnitude of f3 is 6.403N and the coordinate direction angle is 247.9°
We can calculate the magnitude and coordinate direction angle of f3 using the vector triangle method.
We assume that the coordinate direction angle of f1 is 0° and the coordinate direction angle of f2 is 90°.
Using the law of cosines, we can determine the magnitude of f3, which is 6.403N:
f3^2 = f1^2 + f2^2 -2f1f2cos180°
f3^2 = 5^2 + 8^2 -2(5)(8)cos180°
f3^2 = 25 + 64 -80
f3^2 = 49
f3 = 6.403N
We can then use the law of sines to determine the coordinate direction angle of f3, which is 247.9°:
sinθ3 = f2sin180°/f3
sinθ3 = (8)(180°)/6.403
sinθ3 = 147.6°
θ3 = 247.9°
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we have an urn with 3 green and 4 yellow balls. we draw 3 balls one by one without replacement. (a) find the probability that the colors we see in order are green, yellow, green. (b) find the probability that our sample of 3 balls contains 2 green balls and one yellow ball.
The probability of getting colors in order green-yellow-green is 24/245 and the probability of getting 2 green and 1 yellow ball is 72/245.
(a) The probability that the first ball drawn is green is 3/7. Given that the first ball is green, the probability that the second ball drawn is yellow is 4/6. Given that the first two balls are green and yellow respectively, the probability that the third ball drawn is green is 2/5. The final answer is (3/7) * (4/6) * (2/5) = 24/245.
(b) There are several ways to order 2 green and 1 yellow ball, such as green-green-yellow or green-yellow-green. The total number of such combinations is C(3,2) * C(4,1) = 3 * 4 = 12. The probability of getting any of these combinations is (3/7) * (2/6) * (4/5), so the total probability is 12 * (3/7) * (2/6) * (4/5) = 72/245.
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The probability of getting colors in order green-yellow-green is 24/245 and the probability of getting 2 green and 1 yellow ball is 72/245.
(a) The probability that the first ball drawn is green is 3/7. Given that the first ball is green, the probability that the second ball drawn is yellow is 4/6. Given that the first two balls are green and yellow respectively, the probability that the third ball drawn is green is 2/5. The final answer is (3/7) * (4/6) * (2/5) = 24/245.
(b) There are several ways to order 2 green and 1 yellow ball, such as green-green-yellow or green-yellow-green. The total number of such combinations is C(3,2) * C(4,1) = 3 * 4 = 12. The probability of getting any of these combinations is (3/7) * (2/6) * (4/5), so the total probability is 12 * (3/7) * (2/6) * (4/5) = 72/245.
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what should be t-value to indicate that curve is not over flattening in smoothening of time series data
When smoothing time series data, it's important to ensure that the curve is not over-flattened, as this can lead to important information being lost.
What should be t-value to indicate that curve is not over flattening?To avoid over-flattening, one approach is to use a threshold value, or "t-value", to determine the maximum amount of smoothing that can be applied.Here are some steps to consider when choosing a t-value:Plot the original time series data and the smoothed curve to visualize the smoothing effect.Compare the slope of the smoothed curve to the slope of the original data.Choose a t-value that preserves the important features of the original data, such as trends, seasonality, and outliers.Ensure that the smoothed curve still accurately represents the underlying pattern in the data, while reducing noise and variability.Re-evaluate the t-value if necessary, based on the visual comparison of the original data and the smoothed curve.The t-value should be chosen such that the smoothed curve captures the underlying pattern in the data, while retaining important features such as trends and seasonality. If the t-value is set too high, the curve may become over-flattened and important information may be lost. On the other hand, if the t-value is set too low, the curve may not effectively reduce noise and variability in the data.To learn more about T-value refer:
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Hey if anybody could please give me a hand and explain this question to me and help me out that would be great
Answer:
Step-by-step explanation:
We can use similar triangles to solve this. The bigger triangle is made up of the water tower as the height and the long horizontal line as its base, and the smaller triangle fitted inside the larger is made up of the tripod of the camera as the height and the distance Brian lies on the ground beyond it as the base for that triangle. We have to add this distance to the distance of the larger triangle's base. Setting it up as a proportion:
[tex]\frac{watertower}{base} =\frac{camera}{base}[/tex]
but since everything is in different measurements, we have to sort that out first. Let's change everything to feet.
The water tower's distance is 100 yards + 2 feet 9 inches:
[tex]100yds*\frac{3ft}{1yd}=300'[/tex] and now we add in 2 feet 9 inches which is 2.75 feet to get a total of 302.75 feet from the base of the water tower to the point of the triangle. Since we have already converted Brian's distance to feet we're ready to set up the proportion:
[tex]\frac{x}{302.75} =\frac{5}{2.75}[/tex] and we cross multiply.
2.75x = 1513.75 and divide to get
x = 550.45 feet tall.
The polygons are similar. The area of one polygon is given find the area of the other. V
The other polygon has a 108 [tex]ft^2[/tex] area.
We are given the area overall (27 [tex]ft^2[/tex]) and the length of one side (3 ft) for the polygon on the left. With this knowledge, we can calculate the other side's length, which is 9 feet. I calculated this by multiplying 27 [tex]ft^2[/tex] by 3 ft, which gave me the answer of 9 ft.
We now need to locate the opposite side of the polygon on the right in order to calculate its area. Given that 3 * 2 = 6, it appears as though there is a scale factor of 2 between the two polygons. Knowing that the bottom side of the polygon on the left is nine, we may calculate the bottom side of the polygon on the right by multiplying nine by two. 9 × 2 = 18.
Now that we know the dimensions of the polygon on the right, we can calculate its area.
The other polygon's area is 107 [tex]ft^2[/tex] since 6*18 = 107.
The complete question is;-
The polygons are similar. The area of one polygon is given find the area of the other.
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What is the volume of the sphere? Use 3.14 for π and round to the nearest whole number. Enter your answer in the box.
The volume of the sphere with radius 5 is 523 units³.
What is Sphere?A sphere is a three dimensional figure which consists of set of all the points which are at an equal distance from a point called the center of the sphere.
Volume of a three dimensional shape is the space occupied by the shape.
Volume of a sphere can be found using the formula,
Volume = [tex]\frac{4}{3}[/tex] π r³, where r is the radius of the circle.
Given the radius of the circle = 5.
And π = 3.14
Substituting the values,
Volume = [tex]\frac{4}{3}[/tex] × 3.14 × (5)³
= 523.33 ≈ 523 units³
Hence the volume of the given sphere is 523 units³.
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a cord is a volume of cut wood equal to a stack 8 ft long, 4 ft wide, and 4 ft high. how many cords are in 1.0 m 3 ?
The number of cords in 1 m^3 are four.
Here , volume of a cuboid is involved. If l, b, h are respectively the length, breadth and the height of the cuboid , then its volume is given by
V = l x b x h cubic units.
Now, here we know that 1 m =3.28 ft.
So, 1 m^3 = (3.28)^3 cubic feet. = 35.288 cubic feet.
So, we have to find the number of cords in 35.288 cubic feet.
Now, volume of a single cord = l x b x h = 8 x 4 x 4 = 128 cubic feet.
So, no. of cord = 128/35.288 = 3.66.
Since, the number of cords is always a whole number , so 3.66 can treated as 4 by rounding it off to unit's place.
Hence, The number of cords in 1 m^3 are four.
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The number of cords in 1 m^3 is four.
Here, the volume of a cuboid is involved. If l, b, h are respectively the length, breadth and height of the cuboid, then its volume is given by
V = l x b x h cubic units.
Now, here we know that 1 m =3.28 ft.
So, 1 m^3 = (3.28)^3 cubic feet. = 35.288 cubic feet.
So, we have to find the number of cords in 35.288 cubic feet.
Now, the volume of a single cord = l x b x h = 8 x 4 x 4 = 128 cubic feet.
So, no. of cord = 128/35.288 = 3.66.
Since the number of cords is always a whole number, 3.66 can be treated as 4 by rounding it off to the unit's place.
Hence, The number of cords in 1 m^3 is four.
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At Silver Gym, membership is $45 per month, and personal training sessions are $30 each. At Fit Factor, membership is $75 per month, and personal training sessions are $20 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
To make the price at the two gyms equal, Sarah would have to purchase three training sessions.
what is unitary method ?The unit is a method of conundrum that entails measuring the value of an individual unit, multiplied that value, and then calculating the required value. To put it plainly, using unit method is employed to derive a minimum unit value from just a specified multiple. One writer costs Four rupees, thus 40 pens would pay 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Mathematics of matrices or operators, discrete mathematics, mathematical analysis, and its adjoint and reciprocal are all equivalent.
given
Let S stand in for the monthly membership fee for Silver Gym.
Let F stand in for the monthly expense of using Fit Factor.
The number of training sessions used during the month will be denoted by T.
S = 45 +25T
F = 75 +15T
In order for the expenses to be equal, we need to find T. S = F, where 45 + 25T
= 75 + 15T,
10T = 30, and deduct 45+15T.
T = 3 is divided by 10 using the following formula:
To make the price at the two gyms equal, Sarah would have to purchase three training sessions.
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question content area top part 1 find the average rate of change of the function over the given intervals. f(x)=11x3 11; a) [6,8], b) [−1,1]
the average rate of change = (f(1) - f(-1))/(1-(-1)). Substituting in the values of f(-1) and f(1), we get (143 - (-143))/2
a) Average rate of change of the function over [6,8] = (f(8) - f(6))/(8-6) = (11(83) - 11(63))/2 = 882/2 = 441
b) Average rate of change of the function over [-1,1] = (f(1) - f(−1))/(1-(−1)) = (11(13) - 11(-13))/2 = 244/2 = 122
a) To find the average rate of change of the function f(x)=11x3 over the interval [6,8], first calculate the value of the function at x=6 and x=8. This gives us f(6) = 11(63) = 729 and f(8) = 11(83) = 1728. Then, the average rate of change = (f(8) - f(6))/(8-6). Substituting in the values of f(6) and f(8), we get (1728 - 729)/2 = 882/2 = 441.
b) To find the average rate of change of the function f(x)=11x3 over the interval [-1,1], first calculate the value of the function at x=-1 and x=1. This gives us f(-1) = 11(-13) = -143 and f(1) = 11(13) = 143. Then, the average rate of change = (f(1) - f(-1))/(1-(-1)). Substituting in the values of f(-1) and f(1), we get (143 - (-143))/2
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Vectors A and B are shown in the figure. Vector C is given by C = B-A. The magnitude of vector A is 16.0 units, and the magnitude of vector B is 7.00 units.
Write vectors A, B, and C in unit vectors notation.
Determine the magnitude and direction (Direction should be given ccw from the positive x-axis) of the vector C?
The magnitude of the given resultant vector is found as :C = 16.19 units. The direction is shown in figure.
Explain the term cosine theory in vectors? A sum of the products of the individual components of a two vectors, multiplied by the total of the magnitude of a two vectors, is the cosine of a angle between the two vectors.The dot product of a vectors divided by all product of its lengths equals the cosine of angle formed by two nonzero vectors. Only when the dot product of two vectors is zero do they become orthogonal.For the stated question:
C = B-Avector A = 16.0 unitsvector B = 7.00 unitsBy using the cosine theory of the vectors:
C² = A² + B² - 2A.B cosФ
C² = 16.0² + 7.00² - 2(16.0)(7.00).B cosФ79°
On solving:
C = 16.19 units
Thus, the magnitude of the given resultant vector is found as :C = 16.19 units. The direction is shown in figure.
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The figure for the question is attached.
Mary is looking to lease a car. Gerald's Auto has a car available with a money factor of 0.00355. Hillspring's Auto has the exact same car available with a money factor of 0.00324. Which of the following statements is true? a. The lower money factor with Gerald's Auto will give Jennifer the lowest monthly payment. b. The lower money factor with Hillspring's Auto will give Jennifer the lowest monthly payment. c. The higher money factor with Gerald's Auto will give Jennifer the lowest monthly payment. d. The higher money factor with Hillspring's Auto will give Jennifer the lowest monthly payment.
The statement that is true in this situation is "the lower money factor with Hillspring's Auto will give Jennifer the lowest monthly payment" (option B).
What is the money factor?This is a term used when you lease a car or a similar product. This term is a synonym for the "lease fee", which means it is a percentage of money that you need to pay for the lease.
What money factor is the most convenient?Based on the previous ideas a lower money factor is better because this means the payment will be lowered and this is offered by Hillspring's Auto (option B).
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M is the midpoint of AB
Answer:
Midpoint=(−12,−2)
As a decimal:
Midpoint=(−0.5,−2)
Step-by-step explanation:
M=(xM,yM)
M=(x1+x22,y1+y22)
M=(3+−42,3+−72)
M=(−12,−42)
M=(−12,−2)
As a decimal:
M=(−0.5,−2)
Distance Solution: Between Endpoints
d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√
d=(−4−3)2+(−7−3)2−−−−−−−−−−−−−−−−−−√
d=(−7)2+(−10)2−−−−−−−−−−−−√
d=49+100−−−−−−−√
d=149−−−√
d=12.206556
Suppose we observe the following rates: 1R1 = .08, 1R2 = .12, and E(2r1) = 14. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2? Hint: Ry[(1+R)+E(277)+4)...Q+E(x7)+Lx)} N-1 O 6.15% O 2.15% O 14.00% O 8.45% O 12.45%
If the liquidity premium theory of the term structure of interest rates holds, 0.498% is the liquidity premium for year 2.
What is liquid premium theory?Any additional compensation that is necessary to attract investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. Because it is more difficult to sell than a short-term bond, a long-term bond, for instance, will have a higher interest rate. According to the principle of the liquidity premium, bond investors favour short-dated assets that are highly liquid and have a short sales cycle over those that are longer-dated. According to another tenet of the theory, fluctuations in interest rates provide investors with compensation for greater pricing and default risks.
Given that,
1 + 1R₂= {(1 + 1R₁)(1 + E(2r₁) + L₂)}1/2
or, 1.12 = (1.8)(1.14 + L₂)1/2
or, (1.12)2/1.18 = 1.14 + L₂
or, 1.898 = 1.14 + L₂
or, L₂ = 0.498%
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if x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth?
If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
Given that,
If x and y each represent a single digit
The number 8.3xy round to 8.3
Then, the nearest tenth value is,
Round to the nearest tenth means to write the given decimal number up to one decimal place. This is done in such a way that after rounding off, there is one digit after the decimal point.
To round to the nearest tenth using a number line, look at the tenth place value closest to the number you are rounding. Round 2.12, 2.28 and 2.44 to the nearest tenth.
We can write,
If x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth,
We have the radius, 8.3, so we have all necessary information to solve this problem.
8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
Therefore,
If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
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If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
Given that,
If x and y each represent a single digit
The number 8.3xy round to 8.3
Then, the nearest tenth value is,
Round to the nearest tenth means to write the given decimal number up to one decimal place. This is done in such a way that after rounding off, there is one digit after the decimal point.
To round to the nearest tenth using a number line, look at the tenth-place value closest to the number you are rounding. Round 2.12, 2.28, and 2.44 to the nearest tenth.
We can write,
If x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth,
We have a radius, of 8.3, so we have all the necessary information to solve this problem.
8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
Therefore,
If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.
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