Answer:
You should reverse the inequality sign when you multiply or divide both sides of an inequality by a negative number. Addition and subtraction never change the direction of the inequality sign. Multiplication and division do change the direction of the inequality, but only if the number you’re multiplying or dividing by is a negative number.
Step-by-step explanation:
Function
Which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x2? Check all
that apply.
O p(x)=14(x + 7)² +1
q(x) = -5(x+10)²-1
s(x)=(x-1)2 +0.5
g(x)=2x² +10x-35
t(x)=-2²2-4x-3
The functions that have a maximum and are transformed to the left and down of the parent function f(x) = x^2 are options O and Q.
To identify functions that have a maximum and are transformed to the left and down of the parent function f(x) = x^2, we need to analyze each of the given functions and determine their characteristics. Let's go through each option:
Option O: p(x) = 14(x + 7)^2 + 1
This function is a transformation of the parent function f(x) = x^2. It has a maximum point because the coefficient in front of the squared term is positive. However, it is transformed to the left by 7 units and down by 1 unit due to the shift in the parentheses. Therefore, option O satisfies the conditions.
Option Q: q(x) = -5(x + 10)^2 - 1
Similar to option O, this function also has a maximum point as the coefficient in front of the squared term is negative. It is transformed to the left by 10 units and down by 1 unit. Thus, option Q satisfies the given conditions.
Option S: s(x) = (x - 1)^2 + 0.5
This function is the parent function f(x) = x^2 with a vertical shift upward by 0.5 units. It does not have a maximum point or any horizontal or vertical transformations to the left or down. Hence, option S does not meet the requirements.
Option G: g(x) = 2x^2 + 10x - 35
This function is the parent function f(x) = x^2 multiplied by a positive constant (2). It does not have any horizontal or vertical transformations to the left or down. Therefore, option G does not satisfy the conditions.
Option T: t(x) = -2^2 - 4x - 3
This function is a linear function, not a quadratic one. Therefore, it does not have a maximum point or any transformations relative to the parent function f(x) = x^2. Thus, option T does not meet the requirements.
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Consider the probability that more than 39 out of 149 houses for lose power once a year. Assume the probability that a given house will lose power once a year is 2%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
To determine whether the normal curve can be used as an approximation to the binomial probability in this scenario, we need to verify the necessary conditions:
1. The number of trials, n, is sufficiently large.
2. The probability of success, p, is not extremely close to 0 or 1.
Let's check these conditions:
1. The number of trials, n, is 149, which is reasonably large.
2. The probability of success, p, is given as 2%. To check if p is not extremely close to 0 or 1, we can calculate np and n(1 - p) and check if both values are greater than or equal to 5.
np = 149 * 0.02 = 2.98
n(1 - p) = 149 * (1 - 0.02) = 146.02
Since both np and n(1 - p) are greater than or equal to 5, the condition is satisfied.
Therefore, both conditions necessary for using the normal curve as an approximation to the binomial probability are satisfied in this case.
We can approximate the binomial probability of more than 39 houses losing power once a year using the normal distribution.
Amy was scheduled for 12 intervals this week. One her first interval, she had a technical issue that prevented her working for 15 minutes. This issue was reported to and diagnosed by Arise Technical Support, in which they issued an individual Waiver. Amy also looked at her schedule wrong, and completely missed three intervals in a row. What was her CA%
The correct answer is Amy's Compliance Adherence percentage (CA%) is approximately 66.67%.
To calculate Amy's CA% (Compliance Adherence percentage), we need to determine the number of intervals she actually worked compared to the total number of intervals scheduled.
Total intervals scheduled: 12 intervals
However, there were two incidents that affected her adherence:
Technical Issue: Amy experienced a technical issue during her first interval, resulting in a 15-minute disruption. As Arise Technical Support issued an individual waiver, this interval is not counted as non-adherent.
Interval affected: 1
Waived interval: 1
Missed Intervals: Amy completely missed three intervals in a row due to mistakenly looking at her schedule incorrectly. These intervals count as non-adherent.
Intervals affected: 3
To calculate her CA%:
Total intervals worked = Total intervals scheduled - Waived intervals - Non-adherent intervals
Total intervals worked = 12 - 1 (waived) - 3 (non-adherent)
Total intervals worked = 8
CA% = (Total intervals worked / Total intervals scheduled) * 100
CA% = (8 / 12) * 100
CA% = 66.67%
Therefore, Amy's Compliance Adherence percentage (CA%) is approximately 66.67%.
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which is rights answer?
Use a graphing utility to create a scatter plot of the data, with t = 5 corresponding to 2005. Then use the regression feature to find the least square regression line and predict the population of New Jersey in 2045. Round to the nearest whole number.
A) 94,452
B) 17,193
C) 10,475
D) 437,079
The population of New Jersey in 2045 is (b) 10475
How to predict the population of New Jersey in 2045from the question, we have the following parameters that can be used in our computation:
The table of values
Using the least squares, we have the following summary
Sum of X = 105Sum of Y = 55956Mean X = 17.5Mean Y = 9326Sum of squares (SSX) = 437.5Sum of products (SP) = 18640The regression equation is
y = mx + b
Where
m = SP/SSX = 18640/437.5 = 42.60571
b = MY - bMX = 9326 - (42.61*17.5) = 8580.4
So, we have
y = 42.61x + 8580.4
In 2045, we have
y = 42.61 * 45 + 8580.4
y = 10497.85
Hence, the prediction is (b) 10475
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HELP PLEASE!!! What’s was the speed of the plane in still air and the speed of the wind in MPH?
The speed of the plane in still air is 180 mph while that of the wind is 30 mph.
What is an equation?An equation is an expression that shows how numbers and variables are related to each other.
Let a represent the speed of the plane in still air and b represent the speed of the wind.
Against the wind, the plane traveled 175 miles in 1 hour 10 min.
1 hour 10 min = 1 hr + (10/60)hr = 1.167 hr
Hence:
(a - b) = 175/1.167 (1)
Coming back, it spent 50 minutes = (50/60) hr = 0.833 hr
Hence:
a + b = 175 / 0.833 (2)
From both equations:
a = 180, b = 30
The speed of the plane in still air is 180 mph while that of the wind is 30 mph.
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Solve the system using an algebraic method for full credit. Graphing by hand or using technology will receive partial credit. State the method used and describe your first step in detail. List any solution(s) and describe the method you used below-2x power of 2 +5 Y=4x+5.
The given system of equations [tex]-2x^2 + 5y = 4x + 5[/tex] has infinitely many solutions, and the solution set is the set of all real numbers.
To solve the given system of equations using an algebraic method, we'll use the substitution method. The first step is to solve one of the equations for a variable and substitute that expression into the other equation.
Let's start by solving the second equation for y:
[tex]-2x^2 + 5y = 4x + 5[/tex]
Rearranging the equation, we have:
[tex]5y = 2x^2 + 4x + 5[/tex]
Dividing all terms by 5, we get:
[tex]y = (2x^2 + 4x + 5)/5[/tex]
Now, we substitute this expression for y in the first equation:
[tex]-2x^2 + 5((2x^2 + 4x + 5)/5) = 4x + 5[/tex]
Multiplying through by 5 to clear the fraction, we have:
[tex]-2x^2 + 2x^2 + 4x + 5 = 4x + 5[/tex]
The [tex]-2x^2[/tex] and [tex]2x^2[/tex] terms cancel out, and we're left with:
4x + 5 = 4x + 5
The equation simplifies to:
0 = 0
This equation is always true, indicating that the two equations represent the same line. Therefore, the system of equations has infinitely many solutions, and the solution set is all real numbers. We used the substitution method to arrive at this result.
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28n⁴ + 16n³ - 80n²
Factor completely show work pls
Answer:
4n²(7n-10)(n+2)
Step-by-step explanation:
28n⁴ + 16n³ - 80n².The first step is to factor out a 4n² or take common from each term:
28n⁴ + 16n³ - 80n² 4n²(7n² + 4n - 20)The next step is to factor 7n² + 4n - 20. We can do this by grouping:
7n² + 4n - 20 (7n² + 14n - 10n - 20)7n(n+2)-10(n+2)(n+2)(7n-10)Therefore, the complete factorization is:
4n²(7n-10)(n+2)The sum of 3x+2xy-22 and -x+7xy+11 is subtracted from 6x+8xy+35
Answer:
4x - xy + 46
Step-by-step explanation:
sum the first 2 expressions
3x + 2xy - 22 - x + 7xy + 11 ← collect like terms
= (3x - x) + (2xy + 7xy) + (- 22 + 11)
= 2x + 9xy + (- 11)
= 2x + 9xy - 11
now subtract this sum from the third expression
6x + 8xy + 35 - (2x + 9xy - 11) ← distribute parenthesis by - 1 )
= 6x + 8xy + 35 - 2x - 9xy + 11 ← collect like terms
= (6x - 2x) + (8xy - 9xy) + (35 + 11)
= 4x + (- xy) + 46
= 4x - xy + 46
Please look at the photo. It’s a graph so I can’t write it out. Thank you!
Answer:
The function r is neither even nor odd.
The function s is even.
The function g is even.
The function h is neither even nor odd.
In a certain video game, there is a mini-game where the main character can choose from a selection of twenty
presents. The presents are wrapped, so the character does not know what is in them. If 7 presents contain money, 3
presents contain gems, 6 presents contain ore, and 4 presents contain fish, what is the probability that the main
character does not choose a present that contains a gem?
Your answer should be an exact decimal value.
The probability of randomly selecting a present that does not contain a gem is
Answer:
There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.
The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.
hope it helps you...
On a map, 1 inch equals miles. If two cities are 3 inches apart on the map, how far are they actually apart?
Answer: as many miles as 3 inches is
Step-by-step explanation:
To determine the actual distance between two cities when given a scale on a map, we can use the concept of ratios and proportions.
In this case, we are told that 1 inch on the map represents a certain number of miles. Let's say that 1 inch on the map represents x miles.
We can set up the following proportion:
1 inch / x miles = 3 inches / y miles
Using cross-multiplication, we have:
1 inch * y miles = 3 inches * x miles
Simplifying the equation:
y miles = 3 inches * x miles
Now, we can substitute the given value of 3 inches for the distance on the map:
y miles = 3 inches * x miles
To find the actual distance between the cities (y miles), we need to know the value of x, which represents the number of miles represented by 1 inch on the map. Without that information, we cannot calculate the actual distance between the cities.
Choose the most reasonable Celsius temperature for a snowy day.
17°C 26°C -6°C
Choose the most reasonable Celsius temperature for a snowy day.
O A. 26°C
OB. 17°C
C. -6°C
The most reasonable temperature for a snowy day is given as follows:
C. -6°C
How to obtain the most reasonable temperature?Considering that it snows, the temperature is either negative or very low positive, as snow only happens on temperatures close to freezing (like 2º C) or negative.
17ºC and 26ºC are far from cold enough to generate snow, hence the most reasonable temperature for a snowy day is given as follows:
C. -6°C
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Please look at the photo for the question. Thank you.
The range of the quadratic function f(x) = 2x² + 8x - 5 is: (-∞, -13]
How to find the range of a quadratic function?The quadratic function is given as:
f(x) = 2x² + 8x - 5
To determine the range of a quadratic function, we will begin by analyzing the vertex of the parabola.
The vertex of the parabola with equation f(x) = ax² + bx + c is given by the coordinates (-b/2a, f(-b/2a)).
In the quadratic function f(x) = 2x² + 8x - 5, we have:
a = 2, b = 8, and c = -5.
The x-coordinate of the vertex is -b/2a = -8/(2*2)
= -8/4 = -2.
To find the y-coordinate of the vertex, we substitute x = -2 into the equation:
f(-2) = 2(-2)² + 8(-2) - 5
= 2(4) - 16 - 5
= 8 - 16 - 5
= -13
Therefore, the vertex of the parabola is (-2, -13).
Since the coefficient of the x² term (a = 2) is positive, the parabola opens upwards, indicating that the vertex is the minimum point of the function.
This means that the range of the function is all real numbers greater than or equal to the y-coordinate of the vertex, which is -13.
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The linear equation was solved using these steps.
Linear equation: 1
3
(12x + 15) = 7
Step 1: 4x + 5 = 7
Step 2: 4x = 2
Step 3: x = 1
2
The property that was used in step 1 was the
.
The property that was used in step 2 was the
.
The property that was used in step 3 was the
.
Answer:
Step-by-step explanation:
The properties used in each step of solving the linear equation are as follows:
Step 1: To isolate the variable term on one side of the equation, the property used is subtraction property of equality. Subtracting 5 from both sides of the equation maintains the equality.
Step 2: To solve for x, the property used is division property of equality. Dividing both sides of the equation by 4 gives the value of x.
Step 3: The expression x = 1/2 represents the final solution of the equation. This is not necessarily a specific property, but rather the result of performing the previous operations correctly.
Therefore, the properties used in each step are as follows:
Step 1: Subtraction property of equality.
Step 2: Division property of equality.
Step 3: Representation of the solution.
36 1/5 + 4 1/2 + 3/5
Answer:
41 3/10
Step-by-step explanation:
solved with wolfram alpha.
which is rights answer?
The correct option is the second one, this function does not have an inverse.
Does the function have an inverse?A function y = f(x) has in inverse only if the function is one-to-one.
That means that each output is linked to only one input.
In this case, we have an absolute value function:
y = |x - 2|
Notuice that if x = -2
y = |- 2 - 2| =4
And if x = 6
y = |6 - 2| = 4
So two inputs give the same outputs, thus, this function is not one-to-one, so it does not pass the horizontal line test, then it does not have an inverse.
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A fair die is rolled 100 times the results are shown below no:1. 2. 3. 4. 5. 6 below are these numbers 12. 16. 25. 18. 15. 24. What is the probability of getting 1? 2? 3? 4? 5? 6?
The probabilities of rolling each number on a fair die based on the given results are: 1 (12%), 2 (16%), 3 (25%), 4 (18%), 5 (15%), and 6 (24%).
To find the probability of getting each number (1, 2, 3, 4, 5, and 6) when rolling a fair die, we need to calculate the frequency of each number and divide it by the total number of rolls, which in this case is 100.
From the provided results, we can see the following frequencies for each number:
Number 1: 12 occurrences
Number 2: 16 occurrences
Number 3: 25 occurrences
Number 4: 18 occurrences
Number 5: 15 occurrences
Number 6: 24 occurrences
To calculate the probability of each number, we divide the frequency of each number by the total number of rolls (100):
Probability of getting 1: 12/100 = 0.12 or 12%
Probability of getting 2: 16/100 = 0.16 or 16%
Probability of getting 3: 25/100 = 0.25 or 25%
Probability of getting 4: 18/100 = 0.18 or 18%
Probability of getting 5: 15/100 = 0.15 or 15%
Probability of getting 6: 24/100 = 0.24 or 24%
It is important to note that these probabilities are specific to the data provided and may not perfectly represent the true probabilities of rolling each number on a fair die unless the sample is representative of the entire population of possible rolls.
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A hair salon owner collected data comparing the length of an appointment in hours at the salon and the amount of money spent by the customer. The data shown in the table is represented in the graph. Use the table and the graph of the data to answer the questions.
Part A: Determine the equation for the line of fit. Show all work and include all steps. (4 points)
Part B: Identify and interpret the slope in the context of this scenario. (3 points)
Part C: Demonstrate how to use your equation for the line of fit from Part A to predict the cost of a 6-hour hair salon appointment. Show all work and include all steps. (3 points)
The regression equation for the line is y = 50x - 25. The slope is 50 which means "Amount spent on hair increases by $50 per hour". The predicted cost for 6 hour salon appointment is $275.
Solving Linear Regression problemsThe equation of fit is defined generally as :
y = bx + cb = slope ; c = interceptslope = (75 - 25)/(2 - 1) = 50
Taking a pair of (x, y ) values : (2, 75)
75 = 50(2) + c
75 = 100 + c
c = -25
Hence, the fit equation is :
y = 50x - 25B.)
The slope interpretation means that the amount spent for every one hour increase is $50
Hence, the slope interpretation
C.)
Cost of 6 hours hair salon
y = 50(6) - 25
y = 300 - 25
y = 275
Hence, the cost would be $275
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Find the slope of the line containing the points ( 3, - 2 ) and ( 3, 4 ).
Answer:The slope of a line is its vertical change divided by its horizontal change, also known as rise over run. When you have 2 points on a line on a graph the slope is the change in y divided by the change in x. The slope of a line is a measure of how steep it is.
Step-by-step explanation:
The answer is:
undefined
Work/explanation:
We can use the slope formula to find the slope, but we notice something - the x co-ordinates of both points are identical. Whenever this phenomenon occurs, we understand that the line that passes through the points is vertical. That means its run is 0 (remember that Slope : rise/run) so whatever the rise is, we'll just have rise/0, which is an operation that cannot be done. So in this case, the slope's undefined.
Hence, the slope of the line which passes through (3,-2) and (3,4) is undefined.
Identify the radius and the center of a circle whose equation is (x – 5)² + y² = 81
Answer:
The center of the circle is (5,0) and the radius is 9.
Step-by-step explanation:
The center of the circle is (5,0) and the radius is 9.
The number of hours a student spent studying each week for 9 weeks is shown.
5, 8.5, 11, 13, 5.5, 9, 2, 4, 6.5
What is the value of the range for this set of data?
13
11
6
2
Answer: *11* is the correct answer.
Step-by-step explanation:
To find *range*, use the *formula*,
*Range= Highest value - Lowest value*
From the given data, we can see that, the *highest value* is *13* and *lowest value* is *2*. So, *13-2=11*.
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Find the missing length indicated x=
Using the concept of proportions and ratios on the similar triangles, the value of x is 48 units
What are similar triangles?Similar triangles are triangles that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are proportional. In other words, the ratios of the corresponding sides of similar triangles are equal.
The concept of similar triangles is based on the fundamental property that corresponding angles in similar shapes are equal, and the corresponding sides are proportional.
To determine the value of x, we can apply the concept of proportions and ratio on the similar triangle;
x / 36 = 64 / x
Cross multiplying both sides
x * x = 36 * 64
x² = 2304
x = √2304
x = 48 units
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find the average of all the multiples of 5 up to and including 20 for basic 4
The average of multiples of 5 UpTo and including 20 is 12.5
What is average?Average is the quotient obtained by dividing the sum total of a set of figures by the number of figures.
Average can therefore be expressed as;
average = sum of terms /number of terms.
The multiples of 5 including 20 are;
5, 10, 15 , 20
counting this numbers, they are 4
Their sum = 20 + 15 + 10 +5
= 50
Therefore the average is calculated as;
average = 50/4
= 12.5
Therefore the average of multiples of 5 UpTo and including 20 is 12.5
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What is the mass of a cylinder of lead with a radius of 1 centimeter and a height of 3 centimeters, given that the density of lead is ?
Answer:
106.78 g
Step-by-step explanation:
For lead, d = 11.33 g/cm³.
V = πr²h
m = Vd
m = π × (1 cm)² × 3 cm × 11.33 g/cm³
m = 106.78 g
The Mendez family is considering a mortgage loan of $349,000 at an annual interest rate of 6.55%.
(a) How much greater is their mortgage payment if the term is 20 years rather than 30 years?
(b) How much less is the amount of interest paid over the life of the 20-year loan than over the life of the 30-year loan?
a) The monthly payment of the 20-year mortgage is $394.92 greater than the monthly payment of the 30-year mortgage.
b) The total interest paid over the life of the 20-year loan is $171,307.60 less than the amount of interest paid over the life of the 30-year loan.
How the monthly payments and interests are determined:The monthly payments and the total interests over the two loan terms can be determined using an online finance calculator.
Mortgage Loan for 20 Years:N (# of periods) = 240 months (20 years x 12)
I/Y (Interest per year) = 6.55%
PV (Present Value) = $349,000
FV (Future Value) = $0
Results:
PMT = $2,612.33
Sum of all periodic payments = $626,960
Total Interest = $277,960
Mortgage Loan for 30 Years:N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 6.55%
PV (Present Value) = $349,000
FV (Future Value) = $0
Results:
PMT = $2,217.41
Sum of all periodic payments = $798,267.60
Total Interest = $449,267.60
Comparison of 20-year and 30-year Mortgages:
20 Years 30 Years Difference
Monthly payments $2,612.33 $2,217.41 $394.92 ($2,612.33 - $2,217.41)
Total Interest $277,960 $449,267.60 $171,307.60 ($277,960 - $449,267.60)
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What is the surface area of this solid?
OA. 226.08
B. 257.36
OC. 163.28
OD. 150.72
Answer:
S = π(2²) + 2π(2)(6) + π(2²) + π(2)(10)
= (4 + 24 + 4 + 20)π = 52π = 163.36
Letting π = 3.14, S = 52(3.14) = 163.28
The correct answer is C.
A solid oblique pyramid has a square base with an edge length of 2 cm. Angle BAC measures 45°.
A solid oblique pyramid has a square base with an edge length of 2 centimeters. Point B is the apex and point A is the center of the square base. Line B C is the height of the pyramid. Triangle B C A is a right triangle. Base A C has a length of 3.6 centimeters.
What is the volume of the pyramid?
2.4 cm3
3.6 cm3
4.8 cm3
7.2 cm3
The volume of the pyramid with a square base which has an edge length of 2 cm and a measure of an angle BAC is 45° is equal to 4.8 cm³.
What is the volume?In mathematics 'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m³, cm³, in³ etc.
A pyramid's edge length is 2 cm.
The bottom is square.
Base area = (2)²
A is the center of the square base B is the apex of the right triangle BCA.
m∠BAC = 45°
m∠ABC = 45°
AC = BC
AC length = 3.6 cm
BC height = 3.6 cm
Volume (pyramid) = (1 ÷ 3) × base area × height
Volume (pyramid) = (1 ÷ 3) × (2)² × 3.6
Volume (pyramid) = 4.8 cm³
Therefore, the dimension of a pyramid with only a square base, a 2 cm edge length, and a BAC angle of 45° is 4.8 cm³.
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how do you simplify 5 lbs and 24 ounces
5 lbs and 24 ounces is equivalent to 6.5 lbs.
To simplify 5 lbs and 24 ounces, we need to convert ounces to pounds and then add the pounds together.
This is because there are 16 ounces in 1 pound.
So, we can start by converting 24 ounces to pounds. We can do this by dividing 24 by 16.24/16 = 1.5 lbs.
Now, we add the 5 pounds to the 1.5 pounds to get the total weight.5 lbs + 1.5 lbs = 6.5 lbs.
Therefore, 5 lbs and 24 ounces is equivalent to 6.5 lbs.
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Alvin paddled for hours with a 7-km/h current to reach a campsite. The return trip against the same current took 10hours. Find the speed of the boat in still water.
Answer:You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Alvin paddled for 3 hours with a 7 -km/h current to reach a campsite. The return trip against the same current took 10 hours. Find the speed of the boat in still water. Alvin paddled for 3 hours with a 7 -km/h current to reach a campsite.
Step-by-step explanation:
What values of x
and y
satisfy the system of equations {8x+9y=−36 x+7y=1}
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475),
enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.
To solve the given system of equations:
Equation 1: 8x + 9y = -36
Equation 2: x + 7y = 1
We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:
From Equation 2, we can solve for x:
x = 1 - 7y
Substituting this value of x into Equation 1:
8(1 - 7y) + 9y = -36
8 - 56y + 9y = -36
-47y = -44
y = 44/47
Substituting the value of y back into Equation 2 to find x:
x + 7(44/47) = 1
x + 308/47 = 1
x = 1 - 308/47
x = (47 - 308)/47
x = -261/47
Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).
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