Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are [tex]7 , -28 , 112,-448[/tex].
Geometric sequence is type of sequence in which ratio of two consecutive term is equal.
Let the geometric sequence be [tex]G_{1} , G_{2} , G_{3} , G_{4}[/tex] and common ratio be [tex]r[/tex]
According to the question,
[tex]G_{1} = G_{2} + 35[/tex] (eq 1)
⇒ [tex]G_{1} = rG_{1} +35[/tex] ∵ [tex]G_{2}= rG_{1}[/tex]
⇒ [tex]G_{1} (1-r) = 35[/tex]
⇒ [tex]1-r = \frac{35}{G_{1} }[/tex]
⇒ [tex]r = 1 -\frac{35}{G_{1} }[/tex] (eq 2)
Also according to the question,
[tex]G_{3} = G_{4} + 560[/tex]
⇒ [tex]G_{3} = rG_{3} + 560[/tex]
⇒ [tex]G_{3} (1-r) = 560[/tex]
⇒ [tex]r^{2} G_{1} (\frac{35}{G_{1} } ) = 560[/tex]
⇒ [tex]35r^{2} = 560[/tex]
⇒ [tex]r^{2} = 16[/tex]
⇒ [tex]r=[/tex] ±[tex]4[/tex]
∴ [tex]r = -4[/tex] as we can see that value is decreasing at even term and at even term the power of common ration is odd.
Now putting [tex]r= -4[/tex] in eq 2 we get :
[tex]G_{1} =7[/tex]
Hence , Geometric sequence will be [tex]7 , -28 , 112,-448[/tex].
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Which of the following measurements is the GREATEST in magnitude? Hint: be sure
to convert all the measurements to the same units before comparing them!!!
520 g
52 kg
699 g
O2354 mg
Answer:
52kg
Step-by-step explanation:
Please help me with all I’ll mark you brainly
The two lines have the same slope, therefore they are parallel and there is no solution.
y=-2x+6 y=2x+2 is linear or not?
This is an example of a simple linear function. The line you see on the graph, is an expression of the function rule "y = 2x +6".
2x+y=6 ⇒(1)
2x-y=2⇒(2)
Add equ(1) and (2)
so by adding we get,
2x+y+2x-y=6+2
adding the like terms.
we get,
4x=8
x=8/4=2
put x=2 in equ(1)
we get,
2(2)+y=6
4+y=6
y=6-4=2
so the values of x and y are 2 , 2 .
Therefore, The two lines have the same slope, therefore they are parallel and there is no solution.
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The mean and standard deviation of the sample data collected on continuous variable Y are −0.5 and 0.5, respectively. The following table shows the relative frequencies of the data in the given intervals. Based on the table, is it appropriate to use the normal model to approximate the population distribution?
Yes, the data support the use of a normal mode.with two standard deviations, the quantities have always been 0.95, and according to the empirical rule.
According to the question,
The values that are one standard deviation away are:
= 0.33+0.36
= 0.69
As per the empirical rule, the value will be:
= 0.68
Consequently, with two standard deviations, the quantities have always been 0.95, and according to the empirical rule. So the empirical rule followed by the data.
Thus the above response is correct.
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A random sample of 100 people that would best estimate the proportion of all registered voters in a district who support improvements to the high school football field should be drawn from registered voters in the district at a ___football gamesupermarketschool fund-raiserhigh school band concert
A random sample of 100 people that would best estimate the proportion of all registered voters in a district who support improvements to the high school football field should be drawn from registered voters at a football game.
Here,
Drawing the sample at a football game is more likely to provide a representative sample of the entire population of registered voters in the district.
This is because people attending football games are likely to include a diverse mix of registered voters from various backgrounds and demographics.
It can provide a broad representation of the population, which is crucial for obtaining accurate estimates of the proportion of voters who support improvements to the high school football field.
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Pam takes her truck in for basic service. The service agent says a few extra repairs are also needed, so Pam adds the cost of those repairs in her head, rounding to the nearest $10. The costs are as follows: Wheel alignment: $110 Transmission fluid flush: $75 Cabin air filter: $23 What is her total estimate for the repairs? Note: 4 or less: round down, 5 or more: round up. For example, 14 becomes 10, while 15 becomes 20.
Answer:
$210 when round up
Step-by-step explanation:
To find the total estimate for the repairs, we need to add up the cost of each individual repair.
Wheel alignment: $110
Transmission fluid flush: $75
Cabin air filter: $23
Total estimate = $110 + $75 + $23 = $208
Pam rounded the costs to the nearest $10, so the total estimate may not be exactly $208, but it will be close to it.
The formula for the area of a regular polygon is A = [tex]\frac{1}{2} a[/tex] P where a is the length of the apothem and P is the perimeter.
MULTI-CHOICE. Choose ALL that are correct.
A) The apothem of a regular hexagon is 6.322 cm and the length of a side is 7.3 cm. The area equals 276.9[tex]cm^{2}[/tex]
B) The apothem of a regular pentagon is 4.6797 cm, and the perimeter is 34 cm. The area equals 79.55[tex]cm^{2}[/tex]
C) The apothem of a regular octagon is 6.0355 cm, and the length of a side is 5 cm. The area equals 120.71[tex]cm^{2}[/tex]
Answer:
Your answer is:
B) The apothem of a regular pentagon is 4.6797 cm, and the perimeter is 34 cm. The area equals 79.55
And
C) The apothem of a regular octagon is 6.0355 cm, and the length of a side is 5 cm. The area equals 120.71
Step-by-step explanation:
The apothem of a regular pentagon is 4.6797 cm, and the perimeter is 34 cm. The area equals 79.55 and The apothem of a regular octagon is 6.0355 cm, and the length of a side is 5 cm. The area equals 120.71
What is Polygon?Polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
The formula for the area of a regular polygon is A=1/2aP
Where a is the length of the apothem and P is the perimeter.
The apothem of a regular pentagon is 4.6797 cm, and the perimeter is 34 cm. The area equals 79.55
A=1/2×4.6797×34
We have to get 79.55 to tell the option B is true.
A=79.55
SO option B is correct.
Now let us check for C.
The apothem of a regular octagon is 6.0355 cm, and the length of a side is 5 cm. The area equals 120.71
Perimeter of octagon =8a
a is the side
Perimeter=8×5=40
A=1/2×6.0355×40
A=120.71 square centimeter.
Hence, option B and option C are correct.
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Companies are interested in the demographics of those who listen and call in to the radio programs they sponsor. Suppose that only 20% of listeners phoning into a morning talk show are male.a. If the station takes a random sample of 200 callers, what is the probability that the sample proportion of males will be at least 0.30?b. The station management wonders if adding a male host to the program will increase the proportion of callers who are male. After adding the male host, the station records selects a random sample of 200 callers and finds that 30% are male. Does this provide convincing evidence to suggest that the proportion of male callers has increased from 20%? Explain.
The probability that the sample proportion of males will be at least 0.30 is 0.1043.
It can be calculated by using a binomial probability formula. The formula is P(X ≥ 30) = ΣP(X = k), where k = 30, 31, 32, . . . , 200.
The probability is 0.1043.
b. After adding the male host, the station records select a random sample of 200 callers and finds that 30% are male. This provides convincing evidence to suggest that the proportion of male callers has increased from 20%. This is because the probability of observing a sample proportion of 30% or higher is 0.1043, which is greater than the 0.05 significance level commonly used in hypothesis testing. This means that the probability of the observed sample proportion being due to chance is very low and it is likely that the proportion of male callers has increased.
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Triangles LMN and FGH are shown.
Select the correct button in the table to show whether each statement is true or false.
The answer to the true and false questions are given below:
1. MN/NL=GH/HF=true2. LM+MN+NL=FG+GH+HF=false3. Triangle LMN is similar to triangle FGH.=trueHow to solve:Coordinates of L = (-1, -3)
M= (1, 3)
N = (1, -3)
Coordinates of F = (2, 6)
G= (3, 9)
H= (3, 6)
To find the distance b/w the points:
\sqrt(x2-x1)^2 + (y2 -y1)^2)
MN/NL =3
GH/HF = 3
Hence, it is true.
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elena is proving the pythagorean theorem. she knows the goal is to prove that in a right triangle. so far she has: in a right triangle the altitude that intersects the hypotenuse decomposes the triangle into 2 smaller right triangles. these triangles are similar to the large triangle by the angle-angle triangle similarity theorem since each smaller triangle shares one angle with the larger triangle and has a right angle. similar triangles have proportional side lengths, so and . i can rewrite those equations to get and . therefore . . .
If the court of the length of the most comprehensive side of a triangle is equivalent to the sum of the squares of the additional two sides, then the triangle is good.
What is meant by Pythagorean theorem?
The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem.The perpendicular, base, and hypotenuse of this triangle are its three named sides.Remember that in every right triangle, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the two legs side (the two sides that meet at a right angle).The unknown side of a right-angled triangle can be located using Pythagoras' theorem. The three traditional Pythagorean means are the harmonic mean, geometric mean, and arithmetic mean (HM).That exists, in ΔABC, if c2=a2+b2 then ∠C is a right triangle, ΔPQR living at the right angle.
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if triangles are anions and stars are cations, which of the following situations would lead to the most positive membrane potential?
O Both channel types are open
O only star channels are open
O neither channel type is open
O only triangle channels are open
A positive cation and a negative anion makes ionic compound. So both the ions i.e cation and anions are open.
Membrane potential is a potential gradient that forces ions to passively move in one direction: positive ions are attracted by the 'negative' side of the membrane and negative ions by the 'positive' one. Generally Voltage gated channels- open and close in response to changes in the voltage or membrane potential; involved in generating action potentials. As stars and triangles represents the cations and anions both channel types are open to lead the most positive membrane potential.
Therefore , both the channel types ( triangle and star ) are open to lead the most positive membrane potential.
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Dominic collected data on the location where students of two grades would most like to visit and displayed it on a table.
Aspen, Colorado New York, New York Chicago, Illinois Total
Under age 15 21% 16% 12% 49%
Age 15 and above 17% 24% 10% 51%
Total 38% 40% 22% 100%
Which term best describes the entry of 51%?
Marginal frequency
Marginal relative frequency
Joint frequency
Joint relative frequency
The term that best describes the entry of 51% in this table is "Marginal relative frequency. The correct option is B.
What is Marginal relative frequency.?The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single category of data.
For instance, the number of female students would be one marginal frequency in a table of students classified by sex and area of study, and the number of students enrolled in a particular area of study would be another, regardless of sex.
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Sarah borrows $100. she earns $ 300 per day. Let y represent the number of dollars Sarah has in X days. An equation represent this situation is entered into a graphing calculator
The graphing window that will correctly graph the linear function is given as follows:
-1 <= x <= 15 and -150 <= y <= 3700.
How to define the linear function?The linear function in slope-intercept format for this problem is defined as follows:
y = mx + b.
In which:
m is the slope, representing the daily amount earned.b is the intercept, representing the initial amount borrowed.Hence the function for this problem is defined as follows:
y = 100 + 300x.
Meaning that the amounts of the initial and final days are given as follows:
Day 0: 100.Day 12: 100 + 300 x 12 = 3700.And the graph window is given as follows:
-1 <= x <= 15 and -150 <= y <= 3700.
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Terrance hopes to earn $600 $ 600 in interest in 4.7 4.7 years time from $12,000 $ 12,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be
Answer:
The annual rate of interest would have to be approximately 12.77% for Terrance to earn $600 in interest in 4.7 years from an investment of $12,000.
Step-by-step explanation: This can be calculated by using the formula:
(future value) = (principal) * (1 + (interest rate) )^(number of years)
where future value = $12,600, principal = $12,000, number of years = 4.7
so (12600/12000)^(1/4.7) = 1 + r
r = (12600/12000)^(1/4.7) - 1 ≈ 12.77%
Select the correct answer.
Simplify.
1
Multiply 3×6 which gets you 18
Now you have M18 ÷ M18
Divide it, and you'll get 1
TRUE OR FALSE question 8 collaborating with a social scientist to provide insights into human bias and social contexts is an effective way to avoid bias in your data.
True. Collaborating with a social scientist can help identify and address potential sources of bias in data, allowing for more accurate and meaningful results.
Collaborating with a social scientist to provide insights into human bias and social contexts is an effective way to avoid bias in data. Social scientists can help identify and address potential sources of bias in data, allowing for more accurate and meaningful results. This can be done in several ways. Firstly, they can help identify potential sources of bias, such as demographic variables, cultural norms, and other external factors that may affect the data. Secondly, they can help devise strategies to counter the potential sources of bias. For example, they can suggest methods of incorporating diverse perspectives into the data collection process, or of analyzing data in a way that takes into account the potential effects of bias. Finally, they can provide insights into how social contexts can shape the interpretation of data, and can help ensure that any conclusions drawn from the data take into account the complexity of the social environment. By collaborating with a social scientist, researchers can help ensure that their data is free from bias, allowing for more meaningful and accurate results.
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Evaluate this expression for the given values of x and y 2x^2 - y x=3 y=8 QUICK FAST PLEASE HURRY
Answer:
-6
Step-by-step explanation:
2 * 3^2 - (8 * 3) = 18 - 24 = -6
If me.hernandez turns in a late order for 1 turkey sandwich
Answer:
C.
Step-by-step explanation:
If by "turns in" they mean order, than its not a 3:4 ratio
Explain the Fundamental Theorem of Calculus Part 1 (the antiderivative part) and Part 2 (the evaluation part). Then compare each part and specify when one part would be used over the other. Give a real-world example that involves Part 2 of the Fundamental Theorem of Calculus.
I already have an explanation for each separate part but I need help with examples of comparing the two parts, when each part should be used over the other, and a real-world example.
Thanks!
The Fundamental Theorem of Calculus (FTC) has two parts: Part 1 and Part 2.
What is the parts in calculus?Part 1 (The Antiderivative Part) states that if f is a continuous function on an interval [a, b], then there exists an antiderivative F of f on [a, b], meaning that F'(x) = f(x) for all x in [a, b].
This means that given a function, we can find a new function that when differentiated, returns the original function.
Part 2 (The Evaluation Part) states that if F is an antiderivative of f on [a, b], then the definite integral of f over [a, b] can be calculated as the difference of the values of the antiderivative F evaluated at the endpoints, i.e., ∫_a^bf(x)dx = F(b) - F(a).
This means that we can evaluate the definite integral of a function by finding its antiderivative and evaluating it at the endpoints of the interval.
Part 1 is used to find antiderivatives, while Part 2 is used to evaluate definite integrals. They are complementary and are used in tandem to solve problems involving integration.
A real-world example that involves Part 2 of the FTC is the calculation of the total distance traveled by a moving object. If the velocity of the object is given as a function of time, we can use the FTC to calculate the total distance traveled by finding the definite integral of the velocity function over the time interval and evaluating it at the endpoints. The result is the difference between the final and initial positions of the object.
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please help i cant figure it out
5(2x-6) + 8 - 2x = x + 2(x-11)
Answer:
Step-by-step explanation:
10x - 30 + 8 - 2x = x + 2x - 22
8x - 22 = 3x - 22
-3x -3x
5x-22=-22
22 22
5x=0
/5 /5
x=0?
H=10.00+0.07x after 20 months
The numeric value of the function H(x) = 10 + 0.07x when x = 20 is given as follows:
11.4.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function in this problem is defined as follows:
H(x) = 10 + 0.07x.
When x = 20, the numeric value is found replacing the lone instance of x by 20, hence:
H(20) = 10 + 0.07(20)
H(20) = 10 + 1.4
H(20) = 1.4.
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A company is investigating working conditions throughout its operations and has offered employees the opportunity to complete a questionnaire on this subject.
Select the type of sample that has been formed in each presented situation:
Simple random sample
Stratified random sample
Voluntary response sample
Multistage sample
Correct answer is :- Voluntary response sample
'What is Voluntary response sample?'
A sample made up of people who have voluntarily decided to take part in the sample group is known as a voluntary response sample.
Those who want to participate in a voluntary response sample typically do so because they are passionate about the topic of the survey. This is why voluntary response samples frequently produce results that are considerably biased, as the majority of participants will have strong opinions on the subject. The ease of joining the survey is another factor in people's participation.
An example would be a TV show host asking his audience to visit his website and participate in an online survey.
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Popcorn at a concession stand comes in two different-sized containers. The dimensions of the small container with a diameter of 4 in. are shown below.
A popcorn container shaped like a cylinder is shown. A dashed line across the top of the container is labeled four inches. The height of the container is labeled four and five tenths inches.
The large container of popcorn has the same height as the small container, but its diameter is 1.5 times greater. How do the volumes of the two containers of popcorn compare? Use 3.14 for π.
Select the answers from the drop-down lists to correctly complete each sentence.
The volume of the large container of popcorn is _______ in.^3
OPTIONS FOR BLANK :
A) 56.52 B) 84.78 C)127.17 D) 169.56
This is ______ times the volume of the small container.
OPTIONS FOR THIS BLANK :
A) 2.88 B) 2.25 C) 1.8 D) 1.5
The volume of the large container is given as follows:
508.68 in³.
The ratio of the volumes is of:
B) 2.25
How to obtain the volume of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The parameters for the large container are given as follows:
h = 4.5, r = 0.5 x 8 x 1.5 = 6.
(as the diameter is half the radius).
Hence the volume of the large container is obtained as follows:
V = 3.14 x 6² x 4.5 = 508.68 in³.
The ratio is of 2.25, as the radius is squared.
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One of the top 10 occupations in terms of job growth in the next few years is expected to be registered nurses. The number of people, y, in thousands, employed as registered nurses in a certain country can be estimated by the linear equation
559 x minus 10 y equals negative 27 comma 010
559x−10y=−27,010, where x is the number of years after 2012.
a. Find the slope and the y-intercept of the linear equation.
b. What does the slope mean in this context?
c. What does the y-intercept mean in this context?
Answer: a. To find the slope and y-intercept of the linear equation, we need to write it in slope-intercept form (y = mx + b). To do this, we can add 10y to both sides and divide both sides by 10 to get:
y = -559x/10 - 2701/10
y = -55.9x - 270.1
The slope of the equation is -55.9, and the y-intercept is -270.1
b. The slope of a linear equation is the rate of change of the dependent variable (y) with respect to the independent variable (x). In this context, the slope of -55.9 means that for every year after 2012, the number of people employed as registered nurses is expected to decrease by 55.9 thousand.
c. The y-intercept of a linear equation is the point where the line crosses the y-axis. In this context, the y-intercept of -270.1 means that in 2012, there were expected to be 270.1 thousand people employed as registered nurses.
Step-by-step explanation:
In a certain year, 30% of adults in a certain country viewed a college education as essential for success. For the following ten-year period, this percentage increased by approximately 2.3 each year. The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by ________. The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by
The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by y = 31 + 2.3x
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, In a certain year, 30% of adults in a certain country viewed a college education as essential for success. For the following ten-year period, this percentage increased by approximately 2.3 each year.
Therefore, we have,
Initial percentage = 31%
Average increase of percentage = 2.3% per year
Therefore, it can be represented as:
y = 31 + 2.6x,
Where,
y- percentage after x years, x - number of years after the first year
Hence, the percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by y = 31 + 2.3x
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I have attached a picture of the question but have typed out the option, i know a little bit about the function and what it would look like but im confuzed on what the plane y=?z=sin(xy)Give reasons for your choices. This function is [zero / linear / parabolic / period] in both x and y, and the function is [the same / not the same]when x is interchanged with y, so its graph is [ symmetric / not symmetric] about the plane y =[ ] . In addition, the function is [zero / linear / parabolic / periodic ] along the x- and y-axes. These conditions are satisfied only by [A / B / C / D / E / F ] and [ I / II / III / IV / V / VI ].
The function is periodic in both x and y, and the function is the same when x is interchanged with y, so its graph is symmetric about the plane y = 0. In addition, the function is periodic along the x- and y-axes. These conditions are satisfied only by C and IV.
A: The function plane does not have a zero or linear behavior, so this option is not correct.
B: The function does not have a linear behavior, so this option is not correct.
C: The function is periodic in both x and y, so this option is correct.
D: The function does not have a parabolic behavior, so this option is not correct.
E: The function does not have a periodic behavior, so this option is not correct.
F: The function does not have a linear behavior, so this option is not correct.
I: The function is the same when x is interchanged with y, so this option is correct.
II: The function is not symmetric about the plane y = 1, so this option is not correct.
III: The function is not symmetric about the plane y = 2, so this option is not correct.
IV: The function is symmetric about the plane y = 0, so this option is correct.
V: The function is periodic along the x- and y-axes, so this option is correct.
VI: The function is not linear along the x- and y-axes, so this option is not correct.
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For 3-4, use the table at the right.
3. Emma has $100 to spend at the pet store. She needs
to buy 1 bag of dog food and 2 chew toys. Will
Emma have enough money left over to buy 3 times
as many catnip toys as chew toys? Explain.
No, Emma will not have enough money left over to spend 3 times as many catnip toys as chew toys.
How does math relate to money?For planning our spending, saving, and investing, we need math. In each scenario, having a solid grasp of mathematical ideas will be advantageous to your own finances. We are all effectively "bankers" in our individual lives because the term "banking" relates to handling money.
In this question,
1. Emma needs to spend $35 on 2 chew toys and 1 bag of dog food, which comes out to $20 + $15.
2. She has $65 in leftover funds because she has $100 to spend and $35 to spend it on.
3. She would need to spend $30 on 6 catnip toys, which is three times the amount she would spend on chew toys.
4. Nevertheless, she has just $65 left over, which is insufficient to pay for six catnip toys.
5. Consequently, Emma does not have enough cash on hand to purchase three times as many catnip toys as chew toys.
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What is (12^2*5)/4+9-1?
I am giving 15 points away and will give brainiest to the correct answer and who also show there work,
Answer:
60
Step-by-step explanation:
Calculate the sum or difference
12^2 x 5 / 12
Cancel out the common factor 12
12 x 5
Multiply the numbers
60
Solution:
60
Hope this helps!! <3
ara sells apples at a farmers market she begins the day with 35 1/2 pounds of apples she sells half of the apples in the mornning 4/19 of the apples in the afternoon and 1/4 of the apples in the evening how many pounds of apples dose she have left
5 integers have a
mean = 6
mode = 5
range = 9.
What could the 5 numbers be?
Answer:
5, 5, 3, 12, 5
Step-by-step explanation:
This is because the criteria for the numbers are;
*** It must sum up to 30 to get a mean of 6
*** 5 must occur more than once
*** The difference between the largest and smallest number is 9
if z=1-i then find the argumed of z
The argument of the complex number z = 1 - i is approximately -0.785 radians.
What is the argument in complex numbers?
In complex numbers, the argument (also called the amplitude or angle) of a complex number is the angle that the complex number makes with the positive x-axis in the complex plane. It is usually expressed in radians and is denoted by arg(z).
Given a complex number z = 1 - i, the argument of z can be found using the inverse tangent function (atan). In this case, we want to find the angle θ such that tan(θ) = (imaginary part of z) / (real part of z):
θ = atan((-1) / 1) = -π/4 radians
Hence, the argument of the complex number z = 1 - i is approximately -0.785 radians.
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