The solution of the given equation is between 4 and 5.
What is solution of an equation?
The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all possible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.
Consider the given equation,
x^3 - 6x = 72
Subtract 72 from both sides,
x^3 - 6x - 72 = 72 - 72
x^3 - 6x - 72 = 0
After solving this equation we get
x ≈ 4.63902
This value is exactly between the 4 and 5.
Hence, the solution of the given equation is between 4 and 5.
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pretty please can someone answer this for me????? ty
The value of the function f(1)-f(-7) = -11
What is a function?A function from a set X to a set Y assigns to each element of X exactly one element of Y.
Given are a function,
For x = 1, take -x²-3x
f(1) = -1²-3 = -4
For x = -7, take |x+5|-9
f(-7) = |-7+5|-9 = -7
f(1)-f(-7) = -7-4 = -11
Hence, The value of the function f(1)-f(-7) = -11
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Before doing laundry, an unlucky student must recover from illness. The number of days the student is ill is determined as follows. We toss a fair coin and we roll a fair 6-sided die. If the coin is heads, the student is ill for n days, where n is the outcome of the die roll. If the coin is tails, the student is ill for 2n days, where n is the outcome of the die roll. What is Ex(u)? Example: If the die roll is 5, the student delays for U = 5 days if the coin toss is heads and U = 10 days if the coin toss is tails.
The student will be out of class for 2n days if the coin comes up tails, where n is the result of the die roll, which the probability will be 25.
An unfortunate student must recover from illness before washing laundry. The following formula is used to calculate the student's illness duration. We roll a fair 6-sided die and toss a fair coin. The student is absent from class for n days if the coin comes up heads, where n is the result of the die roll.
Ex(u) = (1/2)(1/6)*5+(1/2)(1/6)10+(1/2)(1/6)15+(1/2)(1/6)20 + (1/2)(1/6)25+(1/2)(1/6)*30
Probability = 25
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A daycare center has a weekly revenue of $15,000. The daycare director has created a monthly budget using the following percentages for expenses:
Percent
Employee Wages 40%
Building Rent 5%
Supplies 15%
Equipment 5%
Educational Licensing 2%
Food 13%
Utilities 10%
Maintenance 5%
Emergency/Repair 5%
Which balance sheet correctly represents the daycare's income, expenses, and balance?
A: Income
Amount
Weekly Income $15,000.00
Total Monthly Income $65,000.00
Expenses
Percent Amount
Employee Wages 40% $26,000.00
Building Rent 5% $3,250.00
Supplies 15% $9,750.00
Equipment 5% $326.29
Educational Licensing 2% $1,300.00
Food 13% $8,450.00
Utilities 10% $6,500.00
Maintenance 5% $3,250.00
Emergency/Repair 5% $3,250.00
$65,000.00
Balance
Income $65,000.00
Expenses $65,000.00
Balance $0
B; Income
Amount
Weekly Income $15,000.00
Total Monthly Income $30,000.00
Expenses
Percent Amount
Employee Wages 40% $12,000.00
Building Rent 5% $1,500.00
Supplies 15% $4,500.00
Equipment 5% $1,500.00
Educational Licensing 2% $600.00
Food 13% $3,900.00
Utilities 10% $3,000.00
Maintenance 5% $1,500.00
Emergency/Repair 5% $1,500.00
$30,000.00
Balance
Income $30,000.00
Expenses $30,000.00
Balance $0
C; Income
Amount
Weekly Income $15,000.00
Total Monthly Income $60,000.00
Expenses
Percent Amount
Employee Wages 40% $24,000.00
Building Rent 5% $3,000.00
Supplies 15% $9,000.00
Equipment 5% $3,000.00
Educational Licensing 2% $1,200.00
Food 13% $7,800.00
Utilities 10% $3,000.00
Maintenance 5% $3,000.00
Emergency/Repair 5% $1,500.00
$60,000.00
Balance
Income $60,000.00
Expenses $60,000.00
Balance $0
D; Income
Amount
Weekly Income $15,000.00
Total Monthly Income $67,500.00
Expenses
Percent Amount
Employee Wages 40% $27,000.00
Building Rent 5% $3,375.00
Supplies 15% $10,125.00
Equipment 5% $3,375.00
Educational Licensing 2% $1,350.00
Food 13% $8,775.00
Utilities 10% $6,750.00
Maintenance 5% $3,375.00
Emergency/Repair 5% $3,375.00
$67,500.00
Balance
Income $67,500.00
Expenses $67,500.00
Balance $0
The balance sheet that correctly represents the daycare's income, expenses, and balance is given as follows:
C; Income
Amount
Weekly Income $15,000.00
Total Monthly Income $60,000.00
Expenses
Percent Amount
Employee Wages 40% $24,000.00
Building Rent 5% $3,000.00
Supplies 15% $9,000.00
Equipment 5% $3,000.00
Educational Licensing 2% $1,200.00
Food 13% $7,800.00
Utilities 10% $3,000.00
Maintenance 5% $3,000.00
Emergency/Repair 5% $1,500.00
$60,000.00
Balance
Income $60,000.00
Expenses $60,000.00
Balance $0
How to obtain the balance sheet?The first step in obtaining the balance sheet is obtaining the total monthly income.
The weekly income is of $15,000, while a month is composed by four weeks, hence the monthly income is of:
4 x $15,000 = $60,000.
Then the percentages of each expenses are applied to find the values, for example, 40% of that is for employee wages, hence:
0.4 x 60,000 = $24,000.
From the percentages stated in the problem, 100% of the income is turned into expenses, hence the balance will be of zero and option C is correct.
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approximately what does the box portion of a boxplot display? group of answer choices the upper quarter of the data the middle half of the data the lower quarter of the data the middle quarter of the data
The box portion of a boxplot display the middle half of the data.
We know that a box and whisker plot which is also known as a box plot.
It represents the five-number summary of dataset.
This five-number summary is nothing but the minimum, first quartile, median, third quartile, and maximum.
In box and whisker plot, we draw a box from the first quartile to the third quartile.
In bosplot, the left and right sides of the box are the lower and upper quartiles.
The box covers the 50% of the data is found. It covers the interquartile range.
Therefore, the box portion displays the middle half of the data.
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Using the factor theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?.
The polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3 thanks to the factor theorem.
What is Factor Theorem?A factor theorem is a tool used in mathematics to thoroughly factor polynomials.
It is a theorem that connects the polynomial's zeros and factors.
The factor theorem states that (x-a) is a factor of f(x) if f(a)=0 and f(x) is a polynomial of degree n 1 and 'a' is any real number.
So, the Factor Theorem states that P(k) must equal zero if (x - k) is a factor of polynomial P(x).
A polynomial function with the zeros 2, 3, and -3 is provided to us. As a result, we can set k = 2, 3, -3.
The Factor Theorem states that P(2), P(3,) and P(-3) must all equal 0.
Tests of each option reveal that only option A is accurate:
f(x) = x³ – 2x² – 3x + 6
Testing each of the three results in:
[tex]\begin{aligned}f(2) & =(2)^3-2(2)^2-3(2)+6 \\& =(8)-(8)-(6)+(6) \\& =0 \stackrel{\checkmark}{=} 0 \\f(\sqrt{3}) & =(\sqrt{3})^3-2(\sqrt{3})^2-3(\sqrt{3})+6 \\& =(3 \sqrt{3})-(6)-(3 \sqrt{3})+6 \\& =0=0 \\f(-\sqrt{3}) & =(-\sqrt{3})^3-2(-\sqrt{3})^2-3(-\sqrt{3})+6 \\& =(-3 \sqrt{3})-(6)+(3 \sqrt{3})+6 \\& =0=0\end{aligned}[/tex]
Therefore, with the help of the factor theorem, polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3.
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Complete question:
Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3, and negative radical 3?
a. f(x) = x3 – 2x2 – 3x + 6
b. f(x)= x3 – 2x2 + 3x + 6
c. f(x) = x3 + 2x2 – 3x + 6
d. f(x) = x3 + 2x2 – 3x – 6
On 2 May 2000, a man borrowed a sum of money from a bank at 6.5% p.a. simple interest and on 2 September 2000, the interest amounted to $137.50. Calculate the amount of money he borrowed.
The amount of money borrowed by the man from the bank on on 2 May 2000 is $6346.15.
Explain the term simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.The formula for calculating simple interest;
SI = P R T/100,
where
P stands for principal, R for rate of interest, and T for time period. Here, the rate (r%) is expressed as r/100, where r% is the percentage rate.In the case of simple interest, the principal is the amount of money that does not change over the course of a year.
Time = 4/12 year
For the given values-
137.50 = P × 6.5 × 4 /1200
P = 137.50 × 1200 / 6.5 × 4
P = $6346.15
Thus, the amount of money borrowed by the man from the bank on on 2 May 2000 is $6346.15.
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f a circle has an area that is 225 pi square feet or more, what are the possible diameters d for the circle?
The diameter of the circle is 30 feet.
What is diameter?
The center of the circle is the midpoint of a line segment that connects two points on the circle's perimeter, and this line segment is indicated by the diameter of a circle.
The diameter of a circle is precisely equal to twice the radius' length.
Let us suppose the diameter of a circle is D then, the area is computed according to the formula
[tex]A = \frac{\pi D^2}{4}[/tex]
where
A is the area and D is the diameter.
Plug A = 225 pi in the above equation,
[tex]225 \pi =\frac{\pi D^2}{4} \\225 = \frac{D^2}{4} \\D^2 = 900\\D = 30[/tex]
Hence, the diameter of the circle is 30 feet.
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Y= -4 cos 5x -10 please answer this someone
The trigonometric function, Y = -4·cos 5·x - 10 is undefined at Y = 0, but the function arranged as Y = -4·cos(5·x - 10) has an x-intercept at x = π/10 + 2
What is a trigonometric function?A trigonometric function indicates the relationship between angles and the lengths of sides of angles.
The specified function can be presented as follows;
Y = -4·co(5·x) - 10
There are two unknown variables
The number of equations is one
The number of equations is less than the number of unknowns, the equation is said therefore, to be undetermined.The function, at Y = 0, can be evaluated as follows;
Y = 0 = -4·co(5·x) - 10
cos(5·x) = 10/(-4) = -2.5
5·x = arccos(-2.5) = Undefined
However, when the function is; Y = -4·cos((5·x) - 10), we get;
At Y = 0
0 = -4·cos((5·x) - 10)
cos((5·x) - 10) = 0/(-4) = 0
5·x - 10 = arccos(0) = π/2
Therefore;
x = (π/2 + 10)/5 = π/10 + 2
(-π/2 + 10)/5
An x-intercept is at x = π/10 + 2
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b. suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. how likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm?
The average waist size of the population is 85 cm, and the standard deviation is 15 cm. then A sample mean waist size of at least 86.3 cm has a 0.931 probability of occurring.
We can use the Z-score formula to find the probability.
Z = (86.3 - 85) / (15 / sqrt(277))
Z = 0.2 / 0.106
Z = 1.89
The probability of a sample mean waist size of at least 86.3 cm is 0.931.
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Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k=1k=1 successes given the probability p=p=9/10 of success on a single trial.
(Report answer accurate to 4 decimal places.)
P(X=k)=
By using Binomial Distribution, it can be calculated that -
P(X = 1) = 0.0005
What is Binomial Distribution?
Binomial distribution is a discrete type probability distribution whose probability density function is given by
P(X = x) = [tex]{n \choose x} p^xq^{n - x}[/tex]
Where p is the probability of success and q is the probability of failure
Here, Binomial Distribution of probability is used
k = 1
p = 0.9
q = 1 - 0.9 = 0.1
n = 5
P(X = 1) = [tex]{5 \choose 1} (0.9)^1(0.1)^{5 - 1}[/tex]
= 0.00045
= 0.0005
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5. Find the value of x.
48
8x
Answer:
Step-by-step explanation:
try 6
Answer: 6
Step-by-step explanation: 6 x 8 = 48
What is the value of x?
1/4 (6x - 2) = x - 2
Answer:
Step-by-step explanation:
0
Answer:
x = 3
Step-by-step explanation:
1/4 (6x - 2) = x - 2
1.5x - 0.5 = x - 2
1.5x = x - 1.5
0.5x = 1.5
x = 3
Could you please give me brainliest for this? Thank you!
ANSWER PLSSSSSS
This scatter plot shows the number of magazines checked out and the number of books checked out.
Choose the statement that is best supported by the data in the scatter plot.
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
1The data shows a positive linear association between the number of magazines checked out and the number of books checked out.
2The data shows a positive linear association between the number of magazines checked out and the number of books checked out.
3The data shows a non-linear association between the number of magazines checked out and the number of books checked out.
4The data shows no apparent association between the number of magazines checked out and the number of books checked out.
The correct statement regarding the scatter plot is given as follows:
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
What is the scatter plot?The scatter plot, as shown by the image given at the end of the answer, is a series of points of the data-set in the following format:
(Number of books checked out, Number of magazines checked out).
From the graph, the points are given as follows:
(2,4), (3,6), (4,0), (4,2), (5,7), (6,5), (7,2), (9,1).
Inserting these points into a linear regression calculator, the line of best fit is given as follows:
y = -0.36x + 5.18
Which has a negative slope, meaning that it is a negative linear relationship and the first option is correct.
Missing InformationThe scatter plot is given by the image shown at the end of the answer.
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5 parts!!! 100 pionts I WILL GIVE BRANLIST
part 1 Using the table provided above, list the average gas price for 2010.
part 2 Find the linear regression equation that models the data above. Round to the nearest thousandth if needed.
part 3 List the domain of the linear regression equation in interval notation. Round to the nearest thousandth if needed.
part 4 List the range of the linear regression equation in interval notation. Round to the nearest thousandth if needed.
part 5 Use the linear regression equation to predict how much you expect gas to cost in 2025?
1. The average gas price for 2010 is of: $2.22.
2. The linear regression equation is given as follows: y = 0.176x + 0.5.
3. The domain is: [0,∞).
4. The range is: [0.5,∞).
5. Gas is expected to cost $4.55 in 2025.
How to obtain the linear regression equation?The linear regression is obtained inserting the points of the table into a linear regression calculator.
The variables of the problem are given as follows:
Input x: number of years after 2002.Output y: cost of gas.Hence the points are given as follows:
(0, 0.7), (1,1.04), (2, 1.15), (3, 1.38), (4, 1.86), (5, 1.70), (6, 2.55), (7, 1.29), (8, 2.22), (9, 2.56).
Inserting these points into a calculator, the equation is given as follows:
y = 0.176x + 0.5.
The estimate for 2025 is the numeric value when x = 23, as 2025 is 23 years after 2002, hence:
y = 0.176(23) + 0.5 = $4.55.
The domain and the range are given as follows:
Domain: values of 0 and greater, representing the number of years after 2002.Range: values of 0.5 and greater, representing the costs.More can be learned about linear regression at https://brainly.com/question/29613968
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PLEASE HELP!!!!
Suppose you are developing an Excel spreadsheet that finds the unit
price of any object. You plan to put the number of units in cell E2, and
the price of the object in cell D2.
What formula should you write in cell C2 to find the unit price?
The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.
What is the unit price?
The average price of a product is calculated by dividing the total sales revenue by the total units sold. Managers must define "comparable" units when a single product is sold in variants, such as bottle sizes.
To find the unit price of an object, You divide the price by the Object. We need to find how much an object cost per unit.
Let, us consider an Example we have 50lbs of Kulfi (Object) that cost 8.00 dollars(price).
To find the Unit cost, We take the 8.00 and divide it by 50, which results in 0.16 cents per pound. We can check this by multiplying 0.16 by 50=8.00
So, Object= Number of units in cell = C2
Price of Object = B2
Unit Price Formula = D2
Therefore, by considering the above example.,
Object = C2 = 50
Price = B2 = 8.00
D2 Formula= Price of Object/ Number of Units
Therefore, The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.
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if you repeated the experiment with a glass of water that had 5 teaspoons of salt and another glass that had 10 teaspoons, what do you think would happen?
This procedure demonstrates that there is room between matter particles. The existence of salt ions is indicated by their accommodation in water.
1. When salt is dissolved in water, the chemical bond between the salt atoms is broken by the water molecule.
2. When a teaspoon of salt is added to water, the salt molecules fill any open places in the water. Since water is a fluid with atoms that may move around freely, when salt is dissolved in it, these open spaces are filled, making salt particles invisible.
3. The resulting solution becomes denser. The mass of the solution increases when salt is added to water. As a result, the solution's density rises.
4. This procedure demonstrates that there is room between matter particles. The existence of salt ions is indicated by their accommodation in water.
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Pls help
, I really need an answer for this rn
Answer: 34.00 and 2.10
Step-by-step explanation:
Help me please I’m begging and crying
Answer:
x=-12
Step-by-step explanation:
it would be -2=-x-14 then solve as normal algebraic equation
add 14 to each side 12=-x
then divide by -1 on each side so you get x=-12 for the final answer hope this helps
(a) residents of a city have monthly incomes (in dollars) that are distributed around an unknown mean, with a standard deviation of 500 dollars. the incomes are recorded for a random sample of 36 residents. an average value of 1500 dollars is obtained. what is the 90%-confidence interval for the population mean estimate?
The 90% confidence interval for the population mean estimate is (1362.9167,1637.0833).
Given that,
n=36 residents
Standard deviation = 500 dollars
Mean u = 1500 dollars
X = 1500 dollars
(1-α)% = 90%
(1-α)= 0.9
α = 0.10
α/2 = 0.05
Z α/2 = Z 0.05
Z α/2 = 1.645
90%-confidence interval for the population mean estimate is
=X ± Z α/2 (σ/√n)
= 1500 ± (1.645)(500/√36)
=(1362.9167,1637.0833)
Therefore, the 90%-confidence interval for the population mean estimate is (1362.9167,1637.0833).
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the number 120 is increased by 50%, and the result is then decreased by 30% to give the number x. what is the value of x?
Answer:
x = 126
Step-by-step explanation:
1. 120 + 120(.50) = 180
2. 180 - 180(.30) = 126
Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2075x
What is an expression that represents the total amount that Zoe paid?Expression are simply used to illustrate the datathat are given. It should be noted that it's usually represented by the variables given.
From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.
The expression will be:
= x + (5% × x) + (15% × 1.05x)
= x + 0.05x + 0.1575x
= 1.2075x
Therefore, the expression based on the above will be 1.2075x.
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What is the measure of angle A in this triangle?
Enter your answer in the box.
m∠A=
The measure of angle A in this triangle is 50°.
How to calculate the angle?It is important to note that a triangle has three sides and the total angle is 180°.
Therefore A = 2x - 10
B = 70
C = x + 30
The angles will be illustrated thus:
2x - 10 + 70 + x + 30 = 180
3x + 90 = 180
3x = 180 - 90
3x = 90
Divide
x = 90/3
x = 30
Therefore A will be:
= 2x - 10
= 2(30) - 10
= 60 - 10
= 50°
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a rectangular block of mass m has dimensions as shown. in terms of m, a, b and c, find the rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces. b. let m
The answer of the given question is A rectangular block of mass m has an inertia moment of Bh3/3.
What is moment of inertia?When a body resists having the direction of its rotation along an axis changed by the application of a torque, this resistance is referred to as having moment of inertia. There are four types of axes: internal, external, fixed, and moving. It is possible to calculate the moment of inertia (I), which is always expressed in terms of that axis, by adding the results of multiplying each particle's mass by the square of its distance from the axis within the particular body. Moment of inertia is the same as mass in linear momentum when calculating the angular momentum of a rigid body.
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how many ways are there to deal hands from a standard playing deck to four players if: (a) each player gets exactly 13 cards. (b) each player gets seven cards and the rest of the cards remain in the deck?
Th number of possible ways for
a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)
b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)
In this question, we have been given that there are four players. the select cards from the standard deck of 52 cards.
We need to find the number of possible ways for given situations.
(a) each player gets exactly 13 cards.
Using combination, we get an expression,
^{52}C_13 * ^{39}C_13 * ^{26}C_13 * ^{13}C_13
= 52! / (13! 13! 13! 13!)
= 53644737765488792839237440000
(b) each player gets seven cards and the rest of the cards remain in the deck
Using combination, we get an expression,
^{52}C_7 * ^{45}C_7 * ^{38}C_7 * ^{31}C_7 * ^{24}C_24
= 52! / (7! 7! 7! 7! 24!)
Therefore, a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)
b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)
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compare continuous functions f, g, and h, and match the statements with the function they best describe. drag each description to the correct location on the table. this function has the highest y-intercept.this function is increasing over the longest interval.this function is decreasing over the longest interval.this function has the lowest y-intercept.
From the given properties of the functions,
Function 'f' is decreasing in the longest interval [-0.8, 0.6]Lowest y-intercept → y = -1 (function g)Highest y-intercept → y = 3 (function h)Function 'h' in increasing in the longest interval → (-∞, ∞)Functions given in the picture are 'f', 'g' and 'h'.
From the graph given for function 'f',
y - intercept = 1
Increasing in the interval → (-∞, -0.8] and (0.6, ∞)
Decreasing in the interval → [-0.8, 0.6]
From the table given for the function 'g',
Decreasing in the interval → [-2, 2]
y-intercept = -1
For function 'h',
h(x) = 4x³ + 3
Table of the input-output values for function will be,
x h(x)
-2 -29
-1 -1
0 3
1 7
2 35
Therefore, function 'h' will increase in the interval → (-∞, ∞)
y-intercept → y = 3
Therefore, from these properties of the functions we conclude,
Function 'f' is decreasing in the longest interval [-0.8, 0.6]Lowest y-intercept → y = -1 (function g)Highest y-intercept → y = 3 (function h)Function 'h' in increasing in the longest interval → (-∞, ∞)To know more about Function check the below link:
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1/2(x-8)+1=2(1/8x-1)
Answer:4
Step-by-step explanation:
distribute 1/2 into x-8 and distribute 2 into 1/8x-1 on other side
1/2x-4+1=1/4x-2
combine like terms
1/4x=1
multiply both sides by 4 to solve x
x=4
(1 point) find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have distinct digits :
The number of positive integers with exactly four decimal digits that is positive integers between 1000 and 9999 is 4536.
The positive integers between 1000 and 9999 inclusive have 4 digits.
The first digit cannot be zero because otherwise, it will become a digit integer.
So, the first digit can be filled in 9 ways.
The second digit can be filled by 9 different ways.
Because the second digit cannot be the same as that of the first digit but zero can be the second digit.
The third digit can be filled by 8 different ways.
The fourth digit can be filled in 7 different ways.
Number of four decimals digits = 9 * 9 * 8 * 7
= 81 * 8 * 7
= 81 * 56
= 4536 digits.
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A company is producing picture frames as well as the glass for the front of the frames. The amount of wood required for the frame is represented by the function W(x), and the amount of glass is represented by the function G(x). The frames have lengths represented by the function f(x) and widths represented by g(x). Which statement describes the combined functions W(x) and G(x)? The amount of glass required has a constant rate of change, but the amount of wood does not. The amount of wood required has a constant rate of change, but the amount of glass does not. Both the amount of wood required and the amount of glass required have a constant rate of change. Neither the amount of wood required nor the amount of glass required has a constant rate of change.
The correct statement regarding the rate of change of the functions is given as follows:
The amount of wood required has a constant rate of change, but the amount of glass does not.
How to obtain the rate of change of the functions?The rate of change of a function is obtained as the change in the output of the function divided by the change in the input of the function.
For the wood function, we have that when x is increased by one, the output of the function W(x) is increased by 10, hence the rate of change is constant.
For the glass function, we have that:
When x increases by one from 2 to 3, the output G(x) increases by 21.When x increases by one from 3 to 4, the output G(x) increases by 33.Hence the rate of change is not constant, and then the second statement is the correct statement.
Missing InformationThe table is given by the image shown at the end of the answer.
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the weights of a certain dog breed are approximately normally distributed with a mean of 53 pounds, and a standard deviation of 6.2 pounds. use your graphing calculator to answer the following questions. write your answers in percent form. round your answers to the nearest tenth of a percent. a) find the percentage of dogs of this breed that weigh less than 53 pounds. % b) find the percentage of dogs of this breed that weigh less than 46 pounds. % c) find the percentage of dogs of this breed that weigh more than 46 pounds. %
(i) The percentage of dogs of this breed that weigh less than 53 pounds P(X<53) = 50.0%
(ii) The percentage of dogs of this breed that weigh less than 46 pounds P(X<46) = 15.2%
(iii) The percentage of dogs of this breed that weigh more than 46 pounds P(X>46) = 84.8%
What is Standard Deviation?
The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values of the set tend to be near to the mean (also known as the expected value), whereas a high standard deviation shows that the values are spread out over a larger range.
Solution:
Mean weight (μ) = 53 pounds
Standard deviation (σ) = 6.2 pounds
The z-score for any given weight, 'X', is given by the following expression;
z = (X - μ)/σ
(i) P(X<53)
Since 53 pounds is exactly the mean weight, 50% of the dogs weight more than 53 pounds while 50% weight less than 53 pounds.
P(X<53) = 50.0%
(ii) P(X<46)
z = (46-53)/6.2
z = -1.12
this is equivalent to 15.2 percentile
P(X<46) = 15.2%
(iii) P(X>46)
P(X>46) = 100% - P(X<46) = 100% - 15.2%
P(X>46) = 84.8%
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If the cos 0 = 5/13 and tan 0 = 12/5, what is sin 0?
Answer:
sin(x) = 12/13
Step-by-step explanation:
cos^(-1)(5/13) = 0.176
tan^(-1)(12/5) = 0.176
sin(0.176 radians) = 12/13
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