Write the equation of the piece wise function that is represented by the graph.
Looking at the function, there are two sections of the graph, one on the interval [-1, 1) and the other on the interval [1, ∞). On the first interval, the function corresponds to a quadratic function. The endpoints are (-1, 1) and (1, 1), so the function should be:
\(x^2,-1\leq x<1\)On the other hand, the second section of the graph is a horizontal parabola, so the function corresponds to a square root function. It passes through the points (1, 1), (4, 2), and (9, 3), so the function should be:
\(\sqrt[]{x},1\leq x\)Then, the piecewise function is:
\(f(x)=\begin{cases}x^2,\text{ if }-1\leq x<1 \\ \sqrt[]{x},\text{ if }x\ge1\end{cases}\)i will give brainleist if you answer all of them (or explain how to do it) <3
Answer: look at explanation
Step-by-step explanation: add the amount it will take for each value to transform into what you want these values to add are online
wo neighboring homeowners, , 2, simultaneously choose how many hours to spend maintaining a beautiful lawn. The average benefit per hour is
To calculate the average benefit of hours we must add all the values then divide by the number of values that we have.
What is the average?Average is a term that refers to a value that represents the mean of a group of values. For example, if my friends and I have a race to run from point A to point B and our times are:
69 seconds.58 seconds.45 seconds.120 seconds.76 seconds.The average time of my group of friends would be:
69 + 58 + 45 + 120 + 76 = 368
358 ÷ 73.6 seconds
The average of my group of friends would be 73.6 seconds.
According to the above, to identify the average profit per hour of my neighbors who own their lawns, you must use the same formula to obtain the result.
Note: This question is incomplete because the are some information missing. However I can answer it based on my prior general knowledge.
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Please anyone i need help on this now.
Direct variation between x and y.
The equation for this direct variation is y = 2.25 x.
We have,
The relationship between x and y is a direct variation because y increases as x increases, and the ratio between y and x is constant.
Now,
To find the equation of direct variation, we can use the formula y = kx, where k is the constant of proportionality.
To solve for k, we can use any pair of values given. For example, using
(4, 9):
9 = k x 4
k = 9/4
k = 2.25x
Therefore,
Direct variation between x and y.
The equation for this direct variation is y = 2.25 x.
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the perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm. the length of side p is 4 cm and the lengths of q and r are equal
The lengths of q and r are 2.5 , 2.5 respectively if the perimeter of an isosceles triangle pqr is 9 cm.
What is a triangle ?
triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.
Given ,
The perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm.
the length of side p is 4 cm
Let the lengths of q and r are x and y respectively.
The perimeter of an isosceles triangle = (p+2q)
So,
p+2q = 9
4+2q = 9
2q = 9-4
2q = 5
q = 5/2
q = 2.5 cm
Hence , the lengths of q and r are 2.5 , 2.5 cm respectively .
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If we spin the spinner 10 times, what is the best prediction possible for the number of times it will land on yellow or purple? 3 blue,5 yellow, 2 red.
Answer:
Yellow = 5 times and I think you meant blue since there is no purple so blue = 3 times
Step-by-step explanation:
There is ten in all and half of the spaces are yellow, or 50%. Out of ten times, you should land on it about half, or 5. For blue, there are 3 spaces, or 30%. Out of ten times, you should lamd on it about three.
Which of the following is not a factor in capacity planning?
a) approach used to measure capacity
b) economies of scale
c) prepare to deal with capacity in "chunks"
d) proximity to suppliers
e) identify the best operating level
The option that is not a factor of capacity planning is the option d
d) Proximity to suppliers
What is capacity planning?The process of ascertaining the production capacity an organization needs in order to meet changing demand for the products and services of the organization is known as capacity planning.
The factors considered in capacity planning are factors which include the capacity measurement approach, the economies of scale, preparedness to deal with the capacity in chunks, and activities towards identifying the best operating level.
Therefore, from the listed options, the option that is not a factor in capacity planning is the option (d) proximity to suppliers
Other aspects of the operations of an organization, such as supply chain management and logistics can be affected by the proximity of suppliers, but the proximity of suppliers is not directly linked to the determination process for the production capacity needed to meet the market demand.
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how to determine if a function crosses the horizontal asymptote
To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.
1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.
2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.
3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.
4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.
If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.
It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.
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What is the r-value of the following data to three decimal places?
X. Y
4. 23
5. 12
8. 10
9. 9
13. 2
Note that the r-value of the above data is : -0.903 (Option A)
What is R-value?In mathematics, the r-value typically refers to the correlation coefficient, which measures the strength and direction of the linear relationship between two variables.
With regard to the above data:
A) Find the Sum of the X values: 4 +5+8+9+13 = 39
B) Find the Sum of the Y values: 23 +12 +10 +9 +2 = 56
C) Find the Sum of x^2: 4^2 + 5^2 + 8^2 + 9^2 +13^2 = 355
D) The sum of the Y^2's: 23^2 + 12^2 + 10^2 + 9^2 + 2^2 = 858
E) Sum of x *y's: 4*23 + 5*12 + 8*10 + 9*9 + 13*2 = 339
N = number of sets = 5
Numerator of r = (E - A*B/N) = 339-39*56/5 = 339 - 436.8 = -97.8
Denominator of r = SQRT(C-A^2/N) x SQRT(D-B^2/N) =
SQRT(355-39^2/5) x SQRT(858-56^2/5) =
SQRT(50.8) x SQRT(230.8) =
7.1274 x 15.1921 =
108.2803
r = -97.8 / 108.2803
r = -0.903
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What is 56/5 simplest form???
Answer:
9 1/3
Step-by-step explanation:
this is what i think and i hope im right
Answer:
11 1/5
Step-by-step explanation:
You can do 56 divided by 5 to answer this.
56 / 5 = 11 and 1/5
11 1/5
What is the experimental probability of spinning an even number?
Answer:
The probability of spinning and even number on the spinner is 0.4.
Step-by-step explanation:
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Complete the statements.
f(4) is
f(x) = 4 when x is
Someone explain please
Answer:
SA = 94 ft²
Step-by-step explanation:
To find the surface area of a rectangular prism, you can use the equation:
SA = 2 ( wl + hl + hw )
SA = surface area of rectangular prism
l = length
w = width
h = height
In the image, we are given the following information:
l = 4
w = 5
h = 3
Now, let's plug in the information given to us to solve for surface area:
SA = 2 ( wl + hl + hw)
SA = 2 ( 5(4) + 3(4) + 3(5) )
SA = 2 ( 20 + 12 + 15 )
SA = 2 ( 47 )
SA = 94 ft²
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Calculate the Land Transfer Tax on a house for 248000
Answer:Calculate the Land Transfer Tax on a house for 248000
Calculation example
1.multiply $55,000 by 0.5% (55,000 × 0.005) = $275.
2.multiply the amount exceeding $55,000 up to $250,000 by 1.0% (195,000 × 0.01) = $1,950.
3.multiply the amount exceeding $250,000 up to $400,000 by 1.5% (150,000 × 0.015) = $2,250.
Step-by-step explanation:
.It makes sense to measure the number of students in a class in partial quantities.
True or False
consider the trial on which a 2 is first observed in successive rolls of a six-sided die. let a be the event that 2 is observed on the first trial and b be the event that at least two trials are required to observe a 2. what is p(a s b)?
The probability that a 2 is observed on the first trial or at least two trials are required to observe a 2 is 7/36.
Let's break down the possible outcomes of the experiment to find P(A or B):
A: 2 is observed on the first trial (probability of A = 1/6).
B: 2 is not observed on the first trial, but is observed on the second, third, fourth, etc. trial (probability of B = 5/6 * 1/6 + 5/6 * 5/6 * 1/6 + 5/6 * 5/6 * 5/6 * 1/6 + ...)
We can write the probability of B as a geometric series:
B = 5/6 * 1/6 + 5/6 * 5/6 * 1/6 + 5/6 * 5/6 * 5/6 * 1/6 + ...
B = (5/6 * 1/6) * (1 + 5/6 + (5/6)^2 + (5/6)^3 + ...)
B = (5/36) * (1 / (1 - 5/6)) (using the formula for an infinite geometric series)
B = 5/36
Therefore, P(A or B) = P(A) + P(B) - P(A and B) = 1/6 + 5/36 - 0 (since A and B are mutually exclusive events).
P(A or B) = 7/36
So the probability that a 2 is observed on the first trial or at least two trials are required to observe a 2 is 7/36.
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Find the volume of the solid generated by revolving the region bounded by the given line and curve about the x-axis: y =sqrt(36-x^2), y = 0
V = π(72 - 12) = 360π cm^3.
The volume of the solid generated by revolving the region bounded by the given line and curve about the x-axis can be found using the formula V = π∫y^2 dx.
In this case, y = sqrt(36-x^2) and y = 0.
Substituting these values into the formula, we get V = π∫ (sqrt(36-x^2))^2 dx.
Integrating, we get V = π/3(36x - x^3/3) + C, where C is a constant.
We can solve for V by evaluating the integral from x = 0 to x = 6. Doing this gives us V = π(72 - 12) = 360π cm^3.
Therefore, the volume of the solid generated by revolving the region bounded by the given line and curve about the x-axis is 360π cm^3.
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In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded continuously, what will the membership be in 2020?
Answer:
5563.85 But round the nearest whole number is 5564
Step-by-step explanation:
Formule is P=Ie^(r)(t)
If, In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded continuously, then 5563.85 is the population in 2022.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
In 2010 the Network Club membership was 2,500.
Annual growth rate of approximately 8%
8% is converted to decimal value by dividing 8 with 100
8/100=0.08
\(P=Ie^{rt}\)
p is the final population
I is the initial population
\(p=Ie^{0.08(10)}\)
\(p=2500e^{0.8}\)
p=5563.85
Hence, 5563.85 is the population in 2020.
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Let u denote the unemployment rate, f the job finding rate, and s the separation rate. The law of motion for the unemployment rate is (where Δu=u t+1 −u t is the change in the unemployment rate): a. Δu=fu−s(1−u). d. Δu=fu+s(1−u). b. Δu=su−f(1−u). e. Δu=su+f(1−u). c. Δu=s(1−u)−fu.
The law of motion for the unemployment rate is given by the equation: Δu = fu - s(1 - u). The correct option is (a) Δu = fu - s(1 - u).
The equation represents the change in the unemployment rate (Δu) over time. Let's break down the components of the equation:
- fu represents the job finding rate (f) multiplied by the current unemployment rate (u). This term represents the number of unemployed individuals who find jobs and transition into employment, which decreases the unemployment rate.
- s(1 - u) represents the separation rate (s) multiplied by the difference between one and the current unemployment rate (1 - u). This term represents the number of individuals who become separated from their jobs and enter unemployment, which increases the unemployment rate.
Therefore, the equation Δu = fu - s(1 - u) combines the effects of job finding and separation rates on the change in the unemployment rate.
Thus, the correct option is (a) Δu = fu - s(1 - u)
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Given the points X(-9, 2) and Y(5, -4), find the length of XYXY. Round to the nearest hundredth.
Answer:
15.23
Step-by-step explanation:
the length of XY =√(5+9)²+(-4-2)²
=√14²+(-6)²
=√196+36
=√232
= 15.23
\(\\ \rm\longmapsto XY=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
\(\\ \rm\longmapsto XY=\sqrt{(5+9)^2+(-4-2)^2}\)
\(\\ \rm\longmapsto XY=\sqrt{(14)^2+(-6)^2}\)
\(\\ \rm\longmapsto XY=\sqrt{196+36}\)
\(\\ \rm\longmapsto XY=\sqrt{232}\)
\(\\ \rm\longmapsto XY=15.2\)
simplify 6 (n - 4) - 4n
1.) A scale drawing of a building was made using the scale 15 cm = 120 ft. If the
scale drawing is 45 cm tall, how tall is the actual building?
Answer:
Actual tall building = 360 ft
Step-by-step explanation:
15 cm-----> 120ft
45 cm-----> x ft
x=(45*120)÷15=5400 ÷15 =360 ft
What is the value of x?
Enter your answer in the box.
x=?
Answer:23/3
Step-by-step explanation:
6/48=5/3x+7
1/8=5/(3x+7)
3x+7=40
3x=23
x=23/3
Please help me find the equation for b. This is due today in my math class
Answer:
I suppose the equation would be something like b = 6x, where x is equal to the amount of chocolate chips and b equals to amount of butter.
Use the drawing tool(s) to form the correct answer on the provided grid.
Lisa and Penny are guests at a beachside hotel. Lisa is laying on a towel at the beach which is 50 feet from the base of the hotel. When she looks up at an angle of 54.5 degrees, she can see her sister Penny waving to her from the hotel window.
Draw a scale representation of the triangle that models the situation and can be solved to find the straight-line distance between Penny and Lisa. Round calculations to the nearest foot. Each unit on the grid represents five feet.
Answer:
86 ft
Step-by-step explanation:
You want the straight line distance from a location 50 ft from a hotel to a window that has an angle of elevation of 54.5°.
CosineThe cosine relation between sides and angles in a right triangle is ...
Cos = Adjacent/Hypotenuse
The 50 ft distance is adjacent to the angle, and we want to find the hypotenuse. Using this equation, we can solve for the length we want:
Hypotenuse = Adjacent/Cos
ApplicationUsing the numbers in the problem statement, we find the straight-line distance to be ...
LW = LH/cos(54.5°) = (50 ft)/0.580703 ≈ 86 ft
The distance between Penny and Lisa is about 86 feet.
__
Additional comment
We don't know what drawing tools you have available. The attached diagram was drawn by locating the window at 50tan(54.5°) up from the base of the hotel. The tool provided the length of LW as 86.1.
We could have use a rotation tool to create the angle of 54.5°, or a line graphing tool to draw the line through (50, 0) with slope tan(-54.5°). Then an intersection tool could have located the window at the point of intersection of that line and the y-axis.
The calculation we did above is about the easiest for determining the distance mathematically (not having the tool measure it).
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Evaluate and solve for the variable and please show your work.
-2=y+5
x – 7 = 4 + 10
–2x + 3x – 5 = 6 – 21
70 = 7m
4 – 14 = 5x
2y + 3y = 4 – 6 – 13
Answer:
Step-by-step explanation:
-2 = y + 5
- y -2 = 5
- y = 5 + 2
- y = 7
y = -7
-2x + 3x – 5 = 6 – 21
x – 5 = 6 – 21
x – 5 = -15
x = -15 + 5
x = -10
70 = 7m
7m = 70
m = 10
4 – 14 = 5x
-10 = 5x
5x = -10
x = -2
2y + 3y = 4 – 6 – 13
5y = 4 – 6 – 13
5y = -15
y = -3
Answer:
I took I quiz and the answers are correct
Step-by-step explanation:
:) :) :) :) :) :) :)
Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, r, in beats per minute, can be approximated by the formulas r = 143 minus 0.65 a for women r = 165 minus 0.75 a for men, where a represents the person’s age. if the desirable heart rate for a man is 135 beats per minute, how old is he? a. 22.5 years old b. 40 years old c. 45 years old d. 42.5 years old
Age will be 40 years old.
R, in beats per minute, can be approximated by the formulas, where a represents the person's age.
where R= 143 - 0.65a for women.... (1)
and R= 165 - 0.75a for men,..... (2)
So by implementing these two equation we get a = 40
If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.
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I don’t know 6-8 I need help. Please do not write random I fr need help
In functions, value of x = 45 and y = 45
What is function in math?
A quantitative expression, rule, or law that describes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions occur widespread, and they are essential for defining physical links in the sciences.6) x = 15
y = 49
3x = 3 * 15 = 45
y - 4 = 49 - 4 = 45
7) 3x + 23 = 4x
4x - 3x = 23
x = 23
y = 4 * 23 = 92°
8) y + 12 = 5x °
3x + 50 =
According to the question
y + 12 = 3x + 50
5x = 3x + 50
2x = 50
x = 25
y + 12 = 5x °
y = 5 * 25 - 12
y = 125 - 12 = 113
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use a maclaurin series in this table to obtain the maclaurin series for the given function. f(x) = 9 cos x 7
The Maclaurin series for the given function f(x) = 9 cos(x) * 7 is:
f(x) = 63 * Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...
To obtain the Maclaurin series for the given function f(x) = 9 cos(x) * 7, follow these steps:
STEP 1: First, identify the base function. In this case, it is cos(x).
STEP 2: The Maclaurin series for cos(x) is given by the following formula:
cos(x) = Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...
STEP 3: Now, we need to incorporate the constants 9 and 7 into the series. We do this by multiplying the series by 9 * 7:
f(x) = 9 * 7 * Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...
STEP 4: Simplify the series:
f(x) = 63 * Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...
So, the Maclaurin series for the given function f(x) = 9 cos(x) * 7 is:
f(x) = 63 * Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...
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please help i have test tmrw
Answer:
170 ft²
Step-by-step explanation:
4ft = 48 in
You then multiply 48 by each given side.
48 in · 4.25in = 204 in
Divide by 12 to get answer in feet.
204 in ÷ 12 = 17
So the actual length of the side labeled 4.25 in is 17 ft.
48 · 2.5 = 120
Divide by 12 to get the answer in feet.
120 ÷ 12 = 10
The actual length of the side labeled 2.5in is 10 ft.
Area= L x W
Area= 17ft · 10ft = 170 ft²