Answers
Answer: C.
Step-by-step explanation:
The function graphed is a piece-wise function.
A piece-wise function is a function where more than one formula is used to define the output over different pieces of the domain.
First lets look at the graph an identify the parts of this function:
We see that the first part of the function is a parabola, and from left to right, it starts from infinity and ends with a hole at (2, 8).
A hole is a single point where the graph is not defined and is indicated by an open circle.
The next part of the function starts with a closed circle at (2,2) and decreases at a rate of -1 (-1/1) to negative infinity.
With the graph broken down. lets identify which function in the answer choices is the graphed one.
From the given answer choices we see that all the functions have x^2 + 4 and -x + 4.
How ever each answer choice has different restrictions which can be further known as limits (calculus).
A limit is the value that a function approaches as the input approaches some value.
Lets look at each answer choices restrictions and compare it to the graph:
For answer choice A, x^2 + 4, it has a restriction where x must be less than or equal to two. In comparison to the graph we see that that function doesn't include two, hence its open circle (hole) at (2, 8). Meaning that x must be only less than two, as that part of the function is approaching two but never equaling two. This makes A. incorrect. For answer choice B, x^2 + 4, it has a restriction where x must be greater than or equal to two. This is completely incorrect when compared to the graph, as that part of the function is not greater than two nor does it equal two. This makes B. incorrect.For answer choice C, x^2 + 4, it has a restriction where x must be less than two. This is true with the given graph as that part of the function contains values that are all less than two and doesn't equal two. To make sure it is fully correct, we must check the second part of the function, -x + 4. That part of the function has a restriction where c must be greater than or equal to two. This is true with the given graph as that part of the function starts on a close circle at (2, 2), showing that two is included, and the x values continue to increase as the function goes to negative infinity.For answer choice D, x^2 + 4, it has a restriction where x must be greater than two. This incorrect as that part of the function is not greater than two. This makes D. incorrect.Related Questions
What is the mode of this data set?
A 8.3 centimeters
B 9 centimeters
C 9.1 centimeters
D 10 centimeters
Answers
During the summer you have made the decision to attend summer school, which
precludes you from working at your usual summer job in which you normally earn
$3,000 for the summer. Your tuition cost is $1,000. The opportunity cost of
attending summer school is
$3,000
$1,000
$2,000
$4,000
Answers
Answer:
The opportunity cost of attending summer school in this scenario is $4,000. Opportunity cost is the value of the next best alternative that must be given up in order to pursue a certain action. In this case, by choosing to attend summer school, you are giving up the opportunity to earn $3,000 from your usual summer job. Additionally, you have to pay $1,000 for tuition, bringing the total opportunity cost to $3,000 + $1,000 = $4,000.
Step-by-step explanation:
The opportunity cost of attending summer school in this scenario is $4,000, which includes both the foregone earnings from the summer job and the cost of tuition.
Explanation:The potential earnings from a job that you choose not to do are considered an opportunity cost in economics. In this situation, the opportunity cost of attending summer school is both the $3,000 you lose from not working your summer job and the tuition fee of $1,000 you pay for the school. Economic theory suggests that we consider both of these costs because both are expenses that are a direct result of your decision to attend summer school. Therefore, the total opportunity cost in this scenario is $4,000 ($3,000 + $1,000).
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bottles of cola cost £1.59 each work out the total cost of 21 bottles
Answers
The total cost of 21 bottles of cola at £1.59 each is £33.39.
1. Determine the cost per bottle: Each bottle of cola costs £1.59.
2. Multiply the cost per bottle by the number of bottles: £1.59 x 21 = £33.39.
3. Therefore, the total cost of 21 bottles of cola is £33.39.
In the given scenario, each bottle of cola is priced at £1.59. To calculate the total cost of 21 bottles, we need to multiply the cost per bottle by the number of bottles. By multiplying £1.59 by 21, we get £33.39 as the final answer.
Certainly! Here's an expanded explanation in 100 additional words:
To calculate the total cost of 21 bottles of cola, we need to multiply the cost per bottle by the number of bottles. In this case, each bottle costs £1.59. By multiplying £1.59 by 21, we can determine the total cost.
To perform the calculation, we can use the distributive property of multiplication. We multiply the cost per bottle (£1.59) by the number of bottles (21) individually, and then sum up the results.
First, we multiply the ones place: 9 multiplied by 21, which equals 189. Since 9 multiplied by 1 equals 9, we write down the 9 in the ones place and carry over the 18 to the tens place.
Next, we multiply the tens place: 5 multiplied by 21, which equals 105. Adding the carried-over 18, we get 123. We write down the 3 in the tens place and carry over the 12 to the hundreds place.
Finally, we multiply the hundreds place: 1 multiplied by 21, which equals 21. Adding the carried-over 12, we get 33.
Combining the results, we have £33.39 as the total cost of 21 bottles of cola.
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Let f left parenthesis x right parenthesis equals x cubed minus x squared minus 1 and x subscript 0 equals 1 . To the nearest three decimal places, find x subscript 5 using Newton's method of approximation.
Answers
The value of [tex]x_5[/tex], rounded to the nearest decimal place using Newton's method of approximation is 1.466.
The correct answer is option B.
To find the value of [tex]x_5[/tex]using Newton's method of approximation, we need to iterate the following formula:
[tex]x_(_n_+_1_) = x_n - f(x_n) / f'(x_n)[/tex]
where f'(x) represents the derivative of the function f(x). Let's calculate the values step by step.
Given function: f(x) = [tex]x^3 - x^2 - 1[/tex]
Step 1: Find the derivative of f(x)
f'(x) = [tex]3x^2 - 2x[/tex]
Step 2: Initialize the starting value
[tex]x_0[/tex]= 1
Step 3: Calculate [tex]x_1[/tex]
[tex]f(x_0) = f(1) = (1^3) - (1^2) - 1 = 1 - 1 - 1 = -1[/tex]
[tex]f'(x_0) = f'(1) = (3(1^2)) - (2(1)) = 3 - 2 = 1[/tex]
[tex]x_1 = x_0 - f(x_0) / f'(x_0)[/tex]
= 1 - (-1) / 1
= 2
Step 4: Calculate [tex]x_2[/tex]
[tex]f(x_1) = f(2) = (2^3) - (2^2) - 1 = 8 - 4 - 1 = 3[/tex]
[tex]f'(x_1) = f'(2) = (3(2^2)) - (2(2)) = 12 - 4 = 8[/tex]
[tex]x_2 = x_1 - f(x_1) / f'(x_1)[/tex]
= 2 - 3 / 8
= 1.625
Step 5: Repeat the process until we reach [tex]x_5[/tex]
Performing the calculations for [tex]x_3, x_4, andx_5[/tex], we find:
[tex]x_3[/tex] ≈ 1.465
[tex]x_4[/tex] ≈ 1.466
[tex]x_5[/tex]≈ 1.466
After applying Newton's method of approximation to the function f(x) = [tex]x^3 - x^2 - 1,[/tex]starting with,[tex]x_0 = 1,[/tex] we iteratively calculated the values of [tex]x_1, x_2, x_3, x_4, and x_5[/tex]. The final approximation, [tex]x_5[/tex], is approximately 1.466 when rounded to the nearest decimal place. This aligns with option B as the correct answer.
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Find the polar form and rectangular form of (2cis60°)(5cis30°)
Answers
The polar form of (2cis60°)(5cis30°) is √(75 - 15√3) cis(π/4). The rectangular form of (2cis60°)(5cis30°) is (-5 + 5√3)/2 + (15√3 + 5)i/2.
Polar form:
(2cis60°) and (5cis30°) can be expressed in polar form as follows:
2cis60° = 2(cos60° + isin60°) = 2(1/2 + i√3/2) = 1 + i√3
5cis30° = 5(cos30° + isin30°) = 5(√3/2 + i/2) = (5√3)/2 + (5i)/2
Thus, (2cis60°)(5cis30°) = (1 + i√3)((5√3)/2 + (5i)/2)
To multiply these complex numbers, we can use FOIL method as we do with algebraic expressions to find:
= [(1)(5√3)/2 + (1)(5i)/2 + (i√3)(5√3)/2 + (i√3)(5i)/2]
= [(5√3)/2 + (5i)/2 + (5i√3)/2 − (15/2)]
= [(5√3)/2 − (15/2) + (5i)/2 + (5i√3)/2]
Now, let's determine the magnitude and argument of this complex number:
Magnitude:
|z| = √[(5√3)/2 − (15/2)]² + [(5/2)√3]²
= √[75/4 - 15√3 + 75/4]
= √(75 - 15√3)
Argument:
θ = tan^⁻1((5/2)√3 / [(5√3)/2 − (15/2)])
= tan^⁻1(1)
= π/4
Rectangular form:
To find the rectangular form, we can use the magnitude and argument we just found, and the following formula:
z = r(cosθ + isinθ)
So, we have:
(2cis60°)(5cis30°) = √(75 - 15√3) cis(π/4)
= √(75 - 15√3)(cos(π/4) + isin(π/4))
= (√(75 - 15√3)/2)(1 + i) + (√(75 - 15√3)/2)(√3 - i)
= ([(5√3)/2 − (15/2)] + [(5/2)√3]) + ([(5√3)/2 − (15/2)]√3 + (5/2))
= (-5 + 5√3) + (15√3 + 5)i/2
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Step-by-step explanation:
The rectangular form of a cis equation is
[tex]a + bi[/tex]
Given that we have
[tex]2cis60 \times 5cis30[/tex]
We can just multioly the magnitudes
[tex]2 \times 5 = 10[/tex]
And add the angles
[tex]60 + 30 = 90[/tex]
And that gives us our new equestion
[tex]10cis(90)[/tex]
Remember that
cis is basically
[tex] \cos( \alpha ) + i \sin( \alpha ) [/tex]
So our answer in polar form is
[tex]10( \cos(90) + i \sin(90) )[/tex]
To convert to rectangular form, distribute the 10
[tex]10 \cos(90) = a[/tex]
[tex]10i \sin(90) = bi[/tex]
So
[tex]a = 0[/tex]
[tex]b = 10[/tex]
So, our equation in rectangular form is
[tex]10i[/tex]
helppppp pleaseee!!! will give brainliest
Answers
Answer:
:) ok let's see
i'll do my best.
pls dont sue me.
the graph is going down from what I can see, so I guess it would have a negative correlation.
If we wish to label the strength of the association, for absolute values of r, 0-0.19 is regarded as very weak, 0.2-0.39 as weak, 0.40-0.59 as moderate, 0.6-0.79 as strong and 0.8-1 as very strong correlation, but these are rather arbitrary limits, and the context of the results should be considered.
But, judging from the image, I would say it would have a weak correlation, because the coordinated are not that very well together.
So ultimately, we'll go for answer D.
let me know it u think it's something else.
and don't forget to mark me brainliest!
Michael score 24 28 21 79 84 93 on 6 math test which measure of central tendency would be best used to describe his scores
Answers
The mean score is = 53.16.the average of the two middle values: 53.5. there is no repeated value, so there is no mode.
To describe Michael's scores on the math tests, we can consider different measures of central tendency, namely the mean, median, and mode. Each measure provides a different perspective on the typical or representative value of the data.
The mean is calculated by summing up all the scores and dividing by the number of scores. It is affected by extreme values and can be skewed if there are outliers. In this case, Michael's scores are 24, 28, 21, 79, 84, and 93. The mean score is (24 + 28 + 21 + 79 + 84 + 93) / 6 = 53.16.
The median is the middle value when the scores are arranged in ascending or descending order. It is less affected by extreme values or outliers compared to the mean. To find the median, we sort the scores: 21, 24, 28, 79, 84, 93. Since there is an even number of scores, we take the average of the two middle values: (28 + 79) / 2 = 53.5.
The mode represents the most frequently occurring value in the data set. In this case, there is no repeated value, so there is no mode.
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Which of the following relations are a function? Select all that apply.
Answers
The relations that are functions in this problem are given as follows:
a, d, e.
When does a graphed relation represents a function?A relation represents a function when each input value is mapped to a single output value.
On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.
Hence the relations that are not functions in this problem are listed as follows:
b: input of 6 mapped to multiple outputs.c: input of -1 mapped to multiple outputs.f: vertically aligned points.More can be learned about relations and functions at brainly.com/question/10283950
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Alvarado has 6 different plants. He wants to put 3 of them on the new display stand.
How many different arrangements of plants could he create?
Answers
Alvarado can create 20 different arrangements of plants on the new display stand.
To determine the number of different arrangements of plants that Alvarado can create, we can use the concept of combinations.
When selecting 3 plants out of 6, the order of the plants doesn't matter, since all that matters is which plants are chosen. Therefore, we need to calculate the number of combinations.
The formula for calculating combinations is:
C(n, r) = n! / (r!(n - r)!)
Where:
n is the total number of items (in this case, the total number of plants)
r is the number of items chosen (in this case, the number of plants to be placed on the display stand)
! represents factorial, which is the product of all positive integers up to a given number
Using the values from the problem:
n = 6 (total number of plants)
r = 3 (number of plants to be placed on the display stand)
C(6, 3) = 6! / (3!(6 - 3)!)
C(6, 3) = 6! / (3! × 3!)
C(6, 3) = (6 × 5 × 4) / (3 × 2 × 1)
C(6, 3) = 20
Therefore, Alvarado can create 20 different arrangements of plants on the new display stand.
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identify the terms, coeffeciants, and constants in the expression 7x - 12
Answers
In the expression 7x - 12, the terms, coefficients, and constants can be identified as follows:
Terms:
7x: This is a term consisting of the variable x multiplied by the coefficient 7.
-12: This is a term without a variable, and it is a constant term.
Coefficients:
The coefficient of the term 7x is 7.
It represents the factor by which the variable x is multiplied.
Constants:
The constant in the expression is -12.
It is a term without a variable, representing a fixed value.
or the term 7x.
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1. among the angle 36°,50°,30°,45° one angle cannot be an exterior of a regular polygon. the angle is ? .2if the complement of angle is one -fourth of its supplementary angle .then find the measure of the angle.? 3 what is the volume of rhombus whose diagonal measure 4√3 cm?
Answers
1.) The angle that cannot be an exterior angle of a regular polygon among 36°, 50°, 30°, and 45° is 30°. The sum of the other three angles is less than 360°.
2.) The angle is -60° as its complement is one-fourth of its supplementary angle based on the given condition.
3.) A rhombus has no volume as it is a 2D shape. However, its area is 24 square cm with a diagonal measure of 4√3 cm.
1.) Among the angles 36°, 50°, 30°, and 45°, the angle that cannot be an exterior angle of a regular polygon is 30°. This is because the sum of the exterior angles of any polygon is always 360°, and the sum of the other three angles (36° + 50° + 45°) equals 131°, which is less than 360°. Therefore, 30° is the angle that cannot be an exterior angle of a regular polygon.
2.) Let's assume the measure of the angle is 'x' degrees. The complement of the angle would be (90 - x) degrees, and the supplementary angle would be (180 - x) degrees. According to the given condition, the complement is one-fourth of the supplementary angle:
90 - x = (1/4)(180 - x)
Multiplying both sides by 4 to eliminate the fraction:
360 - 4x = 180 - x
Simplifying the equation:
3x = 180 - 360
3x = -180
Dividing both sides by 3:
x = -60
Therefore, the measure of the angle is -60 degrees.
3.) A rhombus does not have a volume since it is a two-dimensional shape. Volume is a measure of space, and rhombi are flat shapes with no thickness. However, we can calculate the area of a rhombus.
The formula to calculate the area of a rhombus is given by:
Area = (diagonal 1 * diagonal 2) / 2
In this case, the diagonal measure is 4√3 cm:
Area = (4√3 * 4√3) / 2
Area = (16 * 3) / 2
Area = 48 / 2
Area = 24 square cm
Therefore, the area of the rhombus is 24 square cm.
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bn, HD,
30, calons102 929d
47. What is the value of when x = -10?
WIH
Answers
The calculated value of y when x = -10 is -30
Calculating the value of y when x = -10?from the question, we have the following parameters that can be used in our computation:
y varies directly with x
This means that
y = kx
Where
k = constant of variation
So, we have
24 = 8k
k = 3
This also means that
y = 3x
When x = -10, we have
y = 3 * -10
Evaluate
y = -30
Hence, the value is -30
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Question
Suppose y varies directly with x and y=24 when x=8.
What is the value of y when x = -10?
At a baseball game, a vender sold a combined total of 191 sodas and hot dogs. The number of hot dogs sold was 47 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answers
The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.
Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.
According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:
x + y = 191 ...(1)
The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:
y = x - 47 ...(2)
To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:
x + (x - 47) = 191
Simplifying the equation:
2x - 47 = 191
2x = 191 + 47
2x = 238
Dividing both sides by 2:
x = 238/2
x = 119
Substituting the value of x back into equation (2):
y = 119 - 47
y = 72
As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.
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5. The acronym CPCTC stands for "corresponding parts of congruent _______ are congruent.”
A. triangles
B. tables
C. transversals
D. theorems
Answers
Answer:
The correct answer is A. triangles.
Step-by-step explanation:
Answer:
A)triangles
Step-by-step explanation:
CPCTC is a theorem that states that if two triangles are congruent, then their corresponding parts are also congruent. This means that if you have two triangles that are identical in shape and size, you can conclude that their corresponding angles and sides are equal.
Please help me. I really need help. Please.
Answers
The value of x for measure of the angle m∠CED subtended by the arc CD at the circumference is equal to 0.4 to the nearest tenth.
What is angle subtended by an arcThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
arc CD = 2(m∠CED)
Also arc CD = 84°
84° = 2(12x + 37)°
12x + 37 = 84/2 {divide through by 2}
12x + 37 = 42
12x = 42 - 37 {collect like terms}
12x = 5
x = 5/12 {divide through by 12}
x = 0.4167
Therefore, the value of x for measure of the angle m∠CED subtended by the arc CD at the circumference is equal to 0.4 to the nearest tenth.
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What is the mode of this data set?
The line graph is titled Amount of Rainfall. The Y axis is labeled inches. The X axis is labeled weeks. Week 1 has a dot at 2 inches. Week 2 has a dot at 3 inches. Week 3 has a dot at 1 inch. Week 4 has a dot at 3 inches. Week 5 has a dot at 5 inches. Week 6 has a dot at 4 inches. The dots are connected one to the next by a line to show a change in the amount of rainfall. (D Is wrong)
A 2
B 3
C 4
Answers
Answer:
Step-by-step explanation:
It sounds like you are describing a line graph that shows the amount of rainfall over a period of six weeks. The Y axis is labeled in inches, and the X axis is labeled in weeks. Each week is represented by a dot on the graph, with the amount of rainfall for that week indicated by the height of the dot on the Y axis. The dots are connected by a line to show the change in rainfall over time. Based on the information you provided, it looks like the correct answer is B, with week 2 having a dot at 3 inches of rainfall.
The graphic design industry has an annual growth rate of 9% per year. In
2012 there were 23,900 designs in the industry. How many graphic
designers are predicted to be employed in 2023.
Answers
The predicted number of employed graphic designers in 2023 can be calculated by applying the annual growth rate of 9% to the number of designers in 2012. Based on this calculation, it is estimated that there will be approximately 35,889 graphic designers employed in 2023.
1. Determine the initial number of graphic designers in 2012: The question states that there were 23,900 designs in the industry in 2012.
2. Calculate the annual growth rate: The question mentions that the graphic design industry has an annual growth rate of 9%. This growth rate represents an increase of 9% each year.
3. Calculate the growth in the number of graphic designers from 2012 to 2023: To find the growth in the number of graphic designers, multiply the initial number of designers (23,900) by the growth rate (9%) for each year. Repeat this process for each year from 2012 to 2023.
4. Add the growth in the number of designers to the initial number of designers: Sum up the growth in the number of designers for each year and add it to the initial number of designers in 2012.
5. Calculate the predicted number of employed graphic designers in 2023: The sum obtained in step 4 represents the estimated number of graphic designers employed in 2023.
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Domain:
O-85x<0 or 0
O-85x50or 0≤x≤2
O 1
O 2
Answers
The domain and the range of the piecewise function in this problem are given as follows:
Domain: -6 ≤ x < 0 or 0 < x ≤ 2.Range: 0 ≤ y < 1 or 1 < y ≤ 6.How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.The function in this problem is defined for all values of x between -6 and 2, except x = 0, and assumes all values of y between 0 and 6, except y = 1, hence the domain and range are given as follows:
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The equation y = 10x represents a proportional relationship. What is the constant of proportionality
Answers
The equation y = 10x represents a proportional relationship. The constant of proportionality is 10.
A proportional relationship means for every change in x, y also changes proportionately. Let us consider an example
If y = 20
then proportionality constant say k = 10
then x will be 2.
if y = 30
then proportionality constant remains the same ie 10
x will be 3
Here it is evident that as you increase x, y also increase. As you decrease x, y also decreases in a proportionate manner.
k here links x and y variables in a proportionate relationship. Therefore k= 10 is the ratio between y and x.
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True or False?
All polygons are quadrilaterals.
Answers
Answer:
FALSE
Step-by-step explanation:
Types of Polygons
Triangle (3sides)
Quadrilateral (4sides)
Pentagon (5sides)
Hexagon (6 sides)
Heptagon (7sides)
Octagon (8 sides)
Nonagon (9sides)
Decagon (10 sides)
'All polygons are quadrilaterals' is a false statement.
A closed shape with four sides, four vertices, and four angles is known as a quadrilateral. It is formed by adjoining four non-collinear points. The sum of all the inner angles of a quadrilateral is always 360°.
A polygon is a two-dimensional object made up of straight lines and can have greater than four sides. Similarly, polygons with different numbers of sides are given distinct names, such as hexagons, heptagons, and octagons for 6, 7, and 8 sides, respectively.
All polygons with greater than or less than four angles and sides are not quadrilaterals. A triangle, for example, has three sides, whereas a quadrilateral has four sides.
Therefore, not all polygons are quadrilaterals, but all quadrilaterals are polygons.
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1) 2;5;5;2;3: ______________ 2) 5;5;5;5;6: ______________
Mean = ____________ Mean = ____________
Median = ____________ Median = ____________
Mode = ____________ Mode = ____________
Range = ____________ Range = ____________
3) 4;4;5;5;9;3: ______________ 4) 9;8;7;4;10;2: ______________
Mean = ____________ Mean = ____________
Median = ____________ Median = ____________
Mode = ____________ Mode = ____________
Range = ____________ Range = ____________
5) 2;5;3;6;2;8;3: ______________ 6) 4;8;2;3;7;10;5;6: ______________
Mean = ____________ Mean = ____________
Median = ____________ Median = ____________
Mode = ____________ Mode = ____________
Range = ____________ Range = ____________
pls help me
Answers
1) 2;5;5;2;3:
Mean = 3.4
Median = 3
Mode = 2 and 5
Range = 3
2) 5;5;5;5;6:
Mean = 5.2
Median = 5
Mode = 5
Range = 6 - 5 = 1
3) 4;4;5;5;9;3:
Mean = 5
Median = 4.5
Mode = 4 and 5
Range = 9 - 3 = 6
4) 9;8;7;4;10;2:
Mean = 6.7
Median = 7.5
Mode = No mode
Range = 8
5) 2;5;3;6;2;8;3:
Mean = 4.1
Median = 3
Mode = 2 and 3
Range = 6
6) 4;8;2;3;7;10;5;6:
Mean = 5.6
Median = 5.5
Mode = No mode
Range = 8
How to find mean, median, mode and range?Mean is the average of a data set. To calculate the mean, you add up all the values in the data set and then divide by the number of values.
Median is the middle value in a data set when the values are ordered from least to greatest.
Mode is the value that appears most often in a data set.
Range is the difference between the biggest number and smallest number in a data set.
1) 2;5;5;2;3:
Mean = (2 + 5 + 5 + 2 + 3)/5
Mean = 17/5
Mean = 3.4
Arrange in order
2, 2, 3, 5, 5
Median = 3
Mode = 2 and 5 (they both appear most i.e. two times)
Range = 5 - 2 = 3
2) 5;5;5;5;6:
Mean = (5 + 5 + 5 + 5 + 6)/5
Mean = 26/5
Mean = 5.2
5, 5, 5, 5, 6
Median = 5
Mode = 5
Range = 6 - 5 = 1
3) 4;4;5;5;9;3:
Mean = (4 + 4 + 5 + 5 + 9 + 3)/6
Mean = 30/6
Mean = 5
Arrange in order
3, 4, 4, 5, 5, 9
Median = (4+5)/2
Median = 9/2
Median = 4.5
Mode = 4 and 5 (they both appear most i.e. two times)
Range = 9 - 3 = 6
4) 9;8;7;4;10;2:
Mean = (9 + 8 + 7 + 4 + 10 + 2)/6
Mean = 40/6
Mean = 6.7
Arrange in order
2, 4, 7, 8, 9, 10
Median = (7+8)/2
Median = 15/2
Median = 7.5
Mode = No mode
Range = 10 - 2 = 8
5) 2;5;3;6;2;8;3:
Mean = (2 + 5 + 3 + 6 + 2 + 8 + 3)/7
Mean = 29/7
Mean = 4.1
Arrange in order
2, 2, 3, 3, 5, 6, 8
Median = 3
Mode = 2 and 3
Range = 8 - 2 = 6
6) 4;8;2;3;7;10;5;6:
Mean = (4 + 8 + 2 + 3 + 7 + 10 + 5 + 6)/8
Mean = 45/8
Mean = 5.6
Arrange in order
2,3, 4, 5, 6, 7, 8, 10
Median = (5 + 6)/2
Median = 11/2
Median = 5.5
Mode = No mode
Range = 10 - 2 = 8
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Convert the equation r=2/(1-sinθ) to rectangular form
Answers
Answer:
[tex]\displaystyle y=\frac{x^2}{4}-1[/tex]
Step-by-step explanation:
[tex]\displaystyle r=\frac{2}{1-\sin\theta}\\\\r-r\sin\theta=2\\\\\sqrt{x^2+y^2}-y=2\\\\\sqrt{x^2+y^2}=y+2\\\\x^2+y^2=y^2+4y+4\\\\x^2=4y+4\\\\\frac{x^2}{4}=y+1\\\\\frac{x^2}{4}-1=y[/tex]
Note that [tex]r=\sqrt{x^2+y^2}[/tex] and [tex]y=r\sin\theta[/tex]
Hank made payments of $219 per month at the end of each month for 30 years to purchase a piece of property. He promptly sold it for $195,258. What interest rate, compounded monthly, would he need to earn on an ordinary annuity for a comparable rate of return?
Answers
To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.
To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.
First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.
Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.
Using the formula for the present value of an ordinary annuity, we have:
PV = P * (1 - (1+r)[tex]^{(-n)})[/tex]/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.
Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)[tex]{(-360)}[/tex])/r.
Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.
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The diagram shows a regular dodecago. Work out the size of one interior angle
Answers
Step-by-step explanation:
You didn't include a diagram, but a dodecagon is a 12 sided polygon.
The SUM of the interior angles = (n-2) * 180 where n =12
(n-2)* 180
(12-2) * 180 = 1800 <====this is the SUM of the 12 interior angles
so EACH angle is 1800 / 12 = 150 degrees
Which has a greater effect on the volume-changing the radius by a given amount or changing the height by the same amount? Why?
Answers
Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.
a man 6feet tall casts a shadow that is 12 feet long
Answers
Answer: 6 feet
Step-by-step explanation:
The height of the man and the length of his shadow are proportional.
This means that we can use proportions to find the height of the man if we know the length of his shadow.
We can set up a proportion as follows: height of man/length of shadow = (which includes the triangle formed by the man, his shadow, and the man/length constant.
Let's call the constant "k". We don't know the value of "k" yet, but we do know that it will be the same for all similar triangles ground).
Using the measurements given in the problem, we get 6 / 12 = simplifying the left side of the equation gives 1 / 2 = kNow we know that k = 1/2.
We can use this to find the height of the man. Let's call the height "h". We can set up another proportion using the value we just found:h / 12 = 1 / 2
Cross-multiplying gives us: 2h = 12
Simplifying further: h = 6 Therefore, the height of the man is 6 feet.
Which of these functions could have the graph shown below ?
Answers
The function that could have the graph shown above include the following: B. [tex]f(x)=20e^x[/tex].
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.By critically observing the graph of f(x) shown in the image attached above, we can reasonably infer and logically deduce that the initial value or y-intercept is located at (0, 20).
Therefore, the required exponential function for the graph shown above include the following:
[tex]f(x)=20e^x[/tex].
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List the terms of the polynomial. Give the coefficient of the second term. -4y5 + 6x4 +9w³ - 4w - 1 Separate terms using commas. Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c . Make sure your variables match those in the question. Terms Coefficient
Answers
The coefficient of the second term, 6x⁴, is 6.
The terms of the polynomial are:
-4y⁵, 6x⁴, 9w³, -4w, -1
The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.
The coefficient is 6.
Therefore, the list of terms is:
-4y⁵, 6x⁴, 9w³, -4w, -1
Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.
The coefficients indicate the scalar value by which each term is multiplied.
The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.
Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.
There is a 6 coefficient.
As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.
Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.
The scalar value by which each phrase is multiplied is shown by the coefficients.
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Kevin looked at the dates on a random sample of 15 pennies taken from a small jar of pennies. He made the graph shown below to display the data. Kevin will take 1 penny from the jar at random. Based on the data in the graph, what is the probability that the date on the penny will be earlier than 1990?
Answers
The probability that the date on the penny will be earlier than 1990 is A. 7/15
What is probability?Probability is the likelihood of an event.
Since Kevin looked at the dates on a random sample of 15 pennies taken from a small jar of pennies. He made the graph shown below to display the data. Kevin will take 1 penny from the jar at random. Based on the data in the graph, what is the probability that the date on the penny will be earlier than 1990?
To find the probability, we proceed as follows
Let P(<1990) = probability that the date on the penny will be earlier than 1990
Now, P(<1990) = n/N where
n = number of pennies earlier than 1990 and n = total number of penniesFrom the graph
n = 1 + 0 + 4 + 2 = 7N = 15So, substituting these into the equation, we have that
P(<1990) = n/N
P(<1990) = 7/15
So, the probability is A. 7/15
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Factorize :
x^2+8x+15
x^2-2x-15
x^2+9x-36
x^2-12x-45
Answers
Answer:
Factorizing each expression:
x^2 + 8x + 15 = (x+3)(x+5)
x^2 - 2x - 15 = (x-5)(x+3)
x^2 + 9x - 36 = (x+12)(x-3)
x^2 - 12x - 45 = (x-15)(x+3)
So the factorized expressions are:
- x^2 + 8x + 15 = (x+3)(x+5)
- x^2 - 2x - 15 = (x-5)(x+3)
- x^2 + 9x - 36 = (x+12)(x-3)
- x^2 - 12x - 45 = (x-15)(x+3)
