The minimum value of Y is -6 and the maximum value is 10. The range is {-6, 1, 2, 3, 10}.
What is the domain and how is the range calculated range ?Domain of Y = -x³ + 2: A = {-2, -1, 0, 1, 2}. The equation is defined for all x in the set A.
Range of Y = -x³ + 2: To find the range, we need to find the minimum and maximum values of Y for x in the set A. Using the formula Y = -x³ + 2, we can substitute the values of x from the set A and find the corresponding values of Y:
x = -2, Y = -(-8) + 2 = 10
x = -1, Y = -(-1) + 2 = 3
x = 0, Y = -(0) + 2 = 2
x = 1, Y = -(1) + 2 = 1
x = 2, Y = -(8) + 2 = -6
Thus, the minimum value of Y is -6 and the maximum value is 10. The range is {-6, 1, 2, 3, 10}.
Relation Y = -x³ + 2 is a function: A relation is a function if every input x in the domain corresponds to only one output Y in the range. To check if the relation is a function, we need to ensure that no two different inputs in the domain result in the same output.
For this relation, every input x in the domain results in only one unique output Y, so the relation is a function.
Function Notation: If the relation is a function, we can write it in function notation as: f(x) = -x³ + 2, where f is the function name and x is the input.
Evaluating f(-5), f(0) and f(1):
f(-5) = -(-125) + 2 = 127
f(0) = -(0) + 2 = 2
f(1) = -(1) + 2 = 1
Thus, f(-5) = 127, f(0) = 2 and f(1) = 1.
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Use a graphing calculator to solve (1/2)^7x+1=-9
Answer:approximatly -1.63092975357148
Step-by-step explanation:To solve the equation (1/2)^7x+1 = -9, we first need to get all the terms on one side of the equation by subtracting 1 from both sides. This gives us (1/2)^7x = -10.
Next, we need to get x by itself, so we take the log base 2 of both sides.
This gives us log base 2 of (1/2)^7x = log base 2 of -10.
The log base 2 of (1/2)^7 is -7, so we have -7x = log base 2 of -10
Finally, we divide both sides by -7 and get x = log base 2 of -10/-7
Using a calculator we can calculate this value which is approximatly -1.63092975357148
x = log base 2 of -10/-7 = -1.63092975357148
Example 4: ABC~FED
A) Write the scale factor.
B) Find the value of x.
C) Find measure of f
D) Find the value of y.
E) Find the value of z.
The required values are A) 5/3, B) 15, C) 20, D) 86°, E) 15°.
What is Similarity in triangles?Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal. Consequently, if A = X and AB/XY = AC/XZ, then ABC XYZ.
According to question:Because of similarity, Corresponding angles are equal and corresponding sides are Proportional.
So,
In ΔABC
∠A = 180 - 60 - 36
∠A = 180 - 96 = 86°
Which is equal to ∠F
So,D) angle ∠F = 86°
A) Scale factor = AB/EF
= 5/3
So Scale factor is 5/3.
We can say length of side ΔABC = 5/3 Side of ΔDEF.
So, For x
25 = 5x/3
x = 15
For y
y = 5(12)/3
y = 20
And value of z,
4z = 60 degree
z = 15 degree.
Thus, required values are A) 5/3, B) 15, C) 20, D) 86°, E) 15°
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Adam, Barry and Charlie are brothers.
Here is some information about their ages
• Adam is twice as old as Barry
• Charlie is three years younger than Barry
• The sum of all their ages is 53
How old is Barry?
For the sum of ages of Adam, Barry, and Charlie is 53 , Barry is 14 years old.
Number of brothers are three.
Adam, Barry and Charlie.
Let us consider 'x' years be the age of Barry.
Adam age is equal to (2x) years.
And Charlie age is equal to ( x - 3 )years.
Sum of their ages = 53
Substitute the value of Adam, Barry and Charlie age we get,
⇒ x + 2x + x - 3 = 53
⇒ 4x = 53 + 3
⇒ 4x = 56
⇒ x = 56 / 4
⇒ x = 14 years
Barry is 14 years old.
Adam = 2(14 )
= 28 years
Charlie = 14 - 3
= 11 years
Therefore, as per the information about the ages of Adam, Barry and Charlie , the Barry is 14 years old.
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Which of the following is a factor of 4x2 + 23x + 15
A: (4x + 5)
B: (2x + 3)
C: (4x + 3)
D: (2x + 5)
Jonathan compared the ounces in and prices of several different cereals at the grocery store. Here are his results:
Ounces Price (in dollars)
32 $3.89
28 $2.79
42 $4.19
8 $1.00
27 $3.15
12 $2.25
Find the line of best fit for the data. Round any decimals to the hundredths place.
Estimate the price when you have a weight of 48 ounces.
State the correlation coefficient and then explain what it means in the context of the problem.
PLLLLLZZZZZ HELP!!!
Answer:
20
Step-by-step explanation:
To find the line of best fit, we can use the equation for a linear regression: y = mx + b, where y is the price, x is the weight in ounces, m is the slope of the line, and b is the y-intercept.
To estimate the price when the weight is 48 ounces, we can plug in x = 48 into the equation: y = mx + b, and solve for y.
The correlation coefficient, denoted by r, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.
In this case, the correlation coefficient means that how strong and direction of the relationship between the price and weight of cereal. A correlation coefficient of 1 means that there is a perfect positive correlation between the two variables, which means that as the weight of the cereal increases, so does the price. A correlation coefficient of -1 means that there is a perfect negative correlation between the two variables, which means that as the weight of the cereal increases, the price decreases. A correlation coefficient of 0 means that there is no correlation between the two variables, which means that there is no relationship between the weight of the cereal and the price.
Maya is spending money at the average rate of 3 dollars per day. After 14 days she has 68 dollars left. The amount of money left depends on the amount of days that have passed.
Answer:
$110 is what she started with
Step-by-step explanation:
1/10(x+16)=-2(3-X)
X=?
Answer: 2) x=60
Step-by-step explanation:
Set up a system of equations for the given information by filling in the boxes with the coefficients of the variables and the constant values, where is the amount invested in stocks, is the amount invested in bonds, and is the amount invested in CD's.
If there is no visible coefficient, then enter
for the coefficient.
If a specific variable is not present in the equation, then enter
for the coefficient.
Country Day's scholarship fund receives a gift of $200000. The money is invested in stocks, bonds, and CDs. CDs pay 5% interest, bonds pay 2.9% interest, and stocks pay 10.9% interest. Country day invests $20000 more in bonds than in CDs. The total amount earned from the investments is $11165.
Total amount invested:
+ +
=
Total amount earned from investements:
+ +
=
Relation of bonds and CDs:
+ + =
Answer: Total amount invested:
= 200000
Total amount earned from investements:
0.109x + 0.029y + 0.05z = 11165
Relation of bonds and CDs:
= +20000
Step-by-step explanation:
calculate the sample covariance. b. calculate the sample correlation coefficient. c. describe the relationship between x and y.
The relationship between x and y can be described based on the value of the sample correlation coefficient.
Sample covariance measures the degree to which two variables are linearly related and the direction of their linear relationship. The formula for sample covariance is:
[tex]Cov(x,y) = (1/(n-1)) * \Sigma(x-\bar x)(y- \bar y)[/tex] where,
[tex]\bar x[/tex] and [tex]\bar y[/tex] are the sample means of x and y, respectivelyn is the sample size.The sample correlation coefficient, also known as Pearson's correlation coefficient, measures the degree to which two variables are linearly related and the direction of their linear relationship. It is a normalized version of the sample covariance, with a value between -1 and 1. The formula for the sample correlation coefficient is:
r = Cov(x,y) / (s1 * s2) where,
s1 and s2 are the sample standard deviations of x and y, respectively.To calculate the sample covariance and sample correlation coefficient, we need to have a sample of data containing the variables x and y. Once we have the data, we can calculate the sample means, and sample standard deviations, and then use the formulas above to calculate the sample covariance and sample correlation coefficient.
The relationship between x and y can be described based on the value of the sample correlation coefficient.
A value close to 1 indicates a strong positive linear relationshipA value close to -1 indicates a strong negative linear relationship A value close to 0 indicates no linear relationship.Learn more about covariance here:
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The complete question is:
Given a sample of data containing the variables x and y, calculate the sample covariance and the sample correlation coefficient, and describe the relationship between x and y.
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Graph △ABC with vertices A(2,3), B(2,0), and C(3,2) and its image after a 90 degrees clockwise rotation about the origin and a reflection in the y-axis.
The coordinates of the final image are
A'' (3, 2)
B'' (0, 2)
C'' (2, 3)
How to find the coordinates of the final imageThe coordinates of the preimage are A(2,3), B(2,0), and C(3,2)
The transformation rule for a 90 degrees clockwise rotation is
(x, y) → (y,-x)
hence we have
A(2,3), → (3,-2)
B(2,0) → (0,-2)
C(3,2) → (2,-3)
The transformation rule for reflection in the y axis is
(x, y) → (x,-y)
hence we have
A'(3,-2) → (3, 2)
B'(0,-2) → (0, 2)
C'(2,-3) → (2, 3)
The image is plotted and attached
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To make ends meet, Ms.
Farnsby works three jobs. Her total income last year was $48,000. Her income from teaching was just $6000 more than her income from house painting. Royalties from her textbook sales were one-seventh of the total money she received from teaching and house painting. How much did she make from each source last year?
The money that a organisation earns in return for their labour or products is referred to as income.She make from each source last year $6000.
What is income?The money that a person or organisation earns in return for their labour or products is referred to as income.
Salary, rent, capital gains, company revenue, and income from other sources are a few typical sources of income. Understanding how each type of income is taxed is not always simple, and you may require an income tax calculator to do so.
Let t=teaching income, p=painting income, and b=book sales income.
t=p+6000 b=(t+p)/7 b+t+p=48000 (t+p)/7 +p+6000+p=48000 substitute (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000 multiply each side by 7 to eliminate the fraction.
substitution (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000
2p+6000+7p+42000+7p=336000
16p+48000=336000
16p=336000-48000
16p=288000 \s16p/16=288000/16
p=$18,000.
t=18000+6000
t=$24,000.
b=(24000+18000)/7
=42000/7
=$6000.
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15% off 84.75 pls help
Answer: If you take 15% off of 84.75, the new amount would be 71.8875. This can be calculated by multiplying 84.75 by 0.15 (15% written as a decimal), and then subtracting that result from 84.75.
Using powers of 10, give a low and high estimate for the number of teachers in the U. S
0.0000732 = 7.32 x 10⁻⁵
The power of 10 will be the number of places the original decimal point was moved and it will be positive as it was moved towards the left side.145,000 = 1.45 x 10⁵
Now, According to the question:
If the number is given in the decimal notation, move the decimal point to the right side of its original position and place the decimal point after the first non zero digits. The power ten will be the number of places the original decimal point was moved and it will be negative as it was moved towards the right side.
0.0000732 = 7.32 x 10⁻⁵
If the whole number greater than 10 is to be changed into the power of 10, then move the decimal point to the left side of its original position and place the decimal point after the first digit. The power of 10 will be the number of places the original decimal point was moved and it will be positive as it was moved towards the left side.
145,000 = 1.45 x 10⁵
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using these data, estimate the mean and standard deviation for hand grip-strength for this population. what assumption about the distribution do you need to make? g
Hand-grip strength is a sign of general toughness and a good indicator of significant consequences.
For grip strength measurements, current, population-specific reference values are required to interpret the results appropriately.
Objectives
To offer grip-strength reference values and formulae based on population for US citizens ages 18 to 85.
Methods
In this cross-sectional study, hand-grip data from 1232 participants, aged 18 to 85, were taken from the database of the 2011 normative phase of the US National Institutes of Health Toolbox project. Equations and descriptive reference values were derived from the data.
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The question is incomplete
the standard deviation for hand grip strength. what Objectives and Methods of the distribution
a researcher randomly draws samples of iq scores for 50 individuals. what proportion of samples will have means less than 80?
A whopping 95% of people fall within the IQ ranges of 70 and 130. 99.7% of people in the world have IQs between 55 and 145. Only about 0.3% of people have IQ scores that fall outside of this range (less than 55 or higher than 145).
According to the one-standard-deviation rule, 32 percent of the population has an IQ score that is at least 15 points off from 100: 16 percent have IQs over 115, and 16 percent have IQs below 85.
The equation IQ=mc100, where m is the mental age and c is the chromological age, determines a person's IQ. Find the range of their mental ages if a group of 12-year-old youngsters has an IQ between 80 and 140.
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Every quadrilateral that has exactly one pair of parallel sides
Answer:
False. This may be true with a trapezoid but not with a square or rectangle, seeing they have 2.
Step-by-step explanation:
Hope it helps! =D
Lauren deposited $300 to start her savings account. After one year, she had $312 in
her account. If she did not deposit or withdraw any money that year, how much
interest did she earn?
N
Answer:
12 dollars
Step-by-step explanation:
she started with 300 and didn't add any money or take any away... sooo she earned $12 in interest
ABCD → A’B’C’D’ is a reflection. Use this to answer the questions below.
All the solution of the blank words are given below.
What is a reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.
Given:
Figure ABCD is the pre-image.
And A'B'C'D' is the image.
The line of the reflection is y = 0.
The coordinates of the output:
A'(3, -6), B;(1, -1), C'(11, - 1) and D'(6, -6)
Therefore, all the blank words are given above.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor this expression completely and then place the factors in the proper location on the grid. Note: Place factors alphabetically in the grid!
mn-4m-5n+20
The factors of the expression mn-4m-5n+20 are (m-5)(n-4)
What are expressions?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, an expression mn-4m-5n+20, we need to factorize it,
On factorizing the expression, mn-4m-5n+20, we get,
= mn-4m-5n+20
= m·n-4·m-5·n+5·4
= m(n-4)-5(n-4)
= (m-5)(n-4)
Hence, the factors of the expression mn-4m-5n+20 are (m-5)(n-4)
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Which of the following expressions are equivalent to 16a^3b^2 - 8a^5b^5 + 12a^4b? Select all that apply.
Answer:
um i don't know.... 99
Step-by-step explanation:
99 +12
adding fractions with unlike denominators worksheets
The simplification of the addition of two or more fraction with unlike denominator is:
Convert the denominator with like terms and then add the numerators.
Method of simplification of addition of fraction with unlike denominator is:
Calculate the least common multiple of all the denominator of unlike fraction.Convert the denominator of the fraction with like terms.Now add the numerator of the given fraction.Example : ( 1 / 2) + ( 3 / 5 )Least common multiple of 2 and 5 is 10.Multiply by ( 5 / 5) to ( 1/ 2) which is equal to ( 5 / 10 ).Multiply ( 2/ 2 ) to ( 3 /5 ) we get ( 6 /10).Add like fraction ( 5/10) + ( 6 /10) = ( 5+ 6 ) /10Result is 11 /10.Therefore, to simplify unlike fractions find least common multiple and add the like fractions.
The given question is incomplete, I answer the question in general according to my knowledge:
Simplification of adding fractions with unlike denominators with example?
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i need the answer because i dont know
The functions f and have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.
What is a graph ?
Graph can be defined as the visual representation of the given data using ordered pairs.
Graph of f(x)
You can read the y-intercept on the graph. It is the value of y-coordinate when x = 0; so ti is y = 6.
The axis of simmetry is the vertical line that split the graph into two symmetrical forms. That is the same that the vertical line that passes through the vertex. You can see that it is x = 2
2) Table of values of g(x)
The y-intercept is the value of y-coordinate when x = 0, so it is y = 8.
The axis of symmetry is x = 2.
Hence, The functions f and have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.
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12.5% as a fraction (simplified)
Answer: 12.5% is 1/8
Answer: 25/2 would be your answer, as it is already in it's simplest form. I hope this helps! :)
Step-by-step explanation:
The y-intercept of f(x) has the same value as the
x-intercept of f inverse
y-intercept of f inverse
x-intercept of f
The function f-1(x) has range including all values greater than or equal to 0;therefore, the _____ does also
range of f
domain of f
domain of f inverse
The y-intercept for function f(x) has the same value as the x-intercept of f-inverse.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
As
we can see from figure that y-intercept for f(x)=3
and x-intercept for f inverse = 3
Hence,
The y-intercept for function f(x) has the same value as the x-intercept of f-inverse
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Answer:
x-intercept
domain of f
Step-by-step explanation:
i just did it
Roberto's parents open a savings account for him by depositing $250 on his birthday. The account earns simple interest at an annual rate of 5%. How much will be in Roberto's account after 5 years
To calculate the amount of money in Roberto's savings account after 5 years, you can use the formula for simple interest:
I = Prt
Where:
I = Interest earned
P = Principal (original amount of money in the account)
r = Annual interest rate (expressed as a decimal)
t = Number of years
In this case, the principal is $250, the annual interest rate is 5% (or 0.05 as a decimal), and the number of years is 5.
So, you can plug these values into the formula:
I = 250 * 0.05 * 5
To find out the total amount of money in the account after 5 years, you need to add the interest to the principal:
250 + I = 250 + (250 * 0.05 * 5) = 250 + 62.5 = $312.5
Roberto's account will have $312.5 after 5 years.
A number is doubled and the result is increased by 8. If the final result is 36. What is the number?
Answer:
14
Step-by-step explanation:
This question can be expressed as the following linear equation:
2x+8=36, where x is our unknown number.
From here,
2x+8=36
2x=28 (-8 both sides)
x=14 (/2 both sides)
Therefore the number is 14
Solve for x.
y = x-11
y = 15
Simplify your answer as much as possible.
The solution for the given equations is x = 26, y = 15.
What is the linear equation in two variables?
A linear equation in two variables is an equation that can be written in the form of "ax + by = c", where a, b, and c are constants, and x and y are the variables.
To solve the equation y = x-11 for x, we can add 11 to both sides of the equation, resulting in y+11 = x.
To solve the equation y=15 for x, we can substitute 15 in the place of y in the first equation
15 = x - 11
So, x = 26
Hence, the solution for the given equations is x = 26, y = 15.
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What are the missing angle measures in triangle abc? 1.4° and 88.6° 18.6° and 71.4° 35.5° and 54.5° 44.4° and 45.6°
The missing angle measures in triangle ABC are 35.5° and 54.5°.
We know that,
In the right triangle ABC
∠A +∠B =90° ( by complementary angles)
We find the measure of angle B.
we know that
[tex]tanB = \frac{opposite side angle B}{adjacent side angle B}[/tex]
According to the question,
Opposite side angle B= 7 in
Adjacent side angle B = 5in
So, [tex]tanB = \frac{7}{5}[/tex]
[tex]B = arc tan(\frac{7}{5})[/tex]
B = 54.5°
Then, we find the measure of angle A
A + B = 90°
A = 90°-B
A = 90° - 54.5° ( using subtraction)
A = 35.5°
So, The angles measured in triangle ABC are 35.5° and 54.5°.
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It takes 2 h for students to plabt seeds in 3/8 of a community garden. Vanessa says it will take 4 h for the students to plant seeds for the whole garden. Is vanessa corect? Explain your reasoning
Students can plant seeds in a whole community garden in 5 1/3 h. Hence, Vanessa is not correct.
In the example question, students must plant seeds in 3/8 of a community garden in two hours.
The children will need 4 hours to plant the seeds for the entire garden, according to Vanessa.
We must confirm whether Vanessa is correct.
Within two hours, students plant seeds in 3/8 of the community garden.
Students can therefore plant seeds in 1 community garden in = 2/(3/8) h.
In one of the community gardens, students can sow seeds in = 2/3 * 8 hours.
In one of the communal gardens, students can plant seedlings in 16/3 hours.
In one of the communal gardens, students can sow seeds in 5 1/3 hours.
Students can therefore plant seeds in the entire community garden in 5 1/3 hours. Hence, Vanessa is not correct.
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What is the equation of the line that passes through the point (3,-6) and has a slope of -3?
Answer:
y = -3x + 3
Step-by-step explanation:
the equation of a line in point-slope form is.
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - (-6) = -3 (x - 3)
y+6 = -3x+9
Answer:
y = -3x+3
Step-by-step explanation:
Remember that y = mx+c
The slope is m aka the gradient and we know that that's -3.
So just chuck it into the equation:
y = -3x + c
We still have to find c (which is the y intercept)
So substitute the point (3,-6) into the equation
We will have: -6 = -3(3) +c
Once you do algebra you'll get 3=c
So substitute that back into the equation (without the point (3,-6) since we only need the equation)
y = -3x + 3