Which function could represent the data in
the table below?
X -2 -1 0 1
F(x) 3 1 -1 -3
he data in the table appears to be modeled by the function f(x) = -x^2 + 2.
To see this, let's plug in the values for x in the table and see if the resulting values for f(x) match the values in the table:
f(-2) = (-2)^2 + 2 = 4 - 2 = 2
f(-1) = (-1)^2 + 2 = 1 - 1 = 0
f(0) = 0^2 + 2 = 2
f(1) = 1^2 + 2 = 1 + 2 = 3
We can see that the resulting values for f(x) match the values in the table, so f(x) = -x^2 + 2 is a function that could represent the data.
Solve for X
6y = 2x + 10
Answer: x=3y−5
Step-by-step explanation: 6y=2x+10
Swap sides so that all variable terms are on the left hand side.
2x+10=6y
Subtract 10 from both sides.
2x=6y−10
Divide both sides by 2.
2
2x
=
2
6y−10
Dividing by 2 undoes the multiplication by 2.
x=
2
6y−10
Divide 6y−10 by 2.
x=3y−5
stephanie is ordering a pizza for a friends birthday. she wants to offer both meat and vegetarian options. a pepperoni pizza costs $8.00 and the vegetarian pizza costs $13.00. stephanie has $90 to spend on pizza and she wants to have at least 4 pizzas.
Part A: Create a system of inequalities to represent this situation where x represents the number of pepperoni pizzas and y represents the number of vegetarian pizzas she could order.
Part B: Give an example of one solution that would describe how many of each pizza she could buy.
Part A. The system of inequalities to this context is x + y ≥ 4 and
8x + 13y ≤ 90.
Part B. An example of one solution is (x, y) is (4, 4), where she buys 4 pizzas of each type which satisfies x + y ≥ 4.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
From the given information 'x' represents the number of pepperoni pizzas and 'y' represents the number of vegetarian pizzas.
Given, She wants to have at least 4 pizzas which is,
x + y ≥ 4...(1)
Also given that a pepperoni pizza costs $8.00 and a vegetarian pizza costs $13.00 and she has $90 to spend.
Therefore, 8x + 13y ≤ 90...(2)
An example of a solution is (x, y) ⇒ (4, 4) where she buys 4 pepperoni pizzas and 4 vegetarian pizzas.
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Question 1
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A pharmacy technician receives the following prescription:Hydrocortisone 2.5% cream
and Aquaphor in 1:1 Quantity: 4 oz total. What quantity of hydrocortisone powder, in g.
should be entered on the compounding record?
The quantity of hydrocortisone powder, in g, should be entered on the compounding record as 56.7 g
What quantity of hydrocortisone powder, in g should be entered on the compounding record?Generally, To determine the quantity of hydrocortisone powder to be used in the compounding of this prescription, you will need to know the percentage of the final preparation that will be made up of hydrocortisone.
Since the prescription calls for a 1:1 mixture of hydrocortisone cream and Aquaphor, and the final quantity is to be 4 oz, each component will make up half of the final preparation. Therefore, the final preparation will be 50% hydrocortisone.
To determine the quantity of hydrocortisone powder needed, you will need to multiply the final desired quantity of the preparation by the percentage of the preparation that is made up of hydrocortisone. In this case, the desired final quantity is 4 oz, and the preparation is 50% hydrocortisone, so the calculation is:
4 oz * 50% = 2 oz
Since there are 28.35 grams in an ounce, the total quantity of hydrocortisone powder needed in grams is:
2 oz * 28.35 g/oz = 56.7 g
Therefore, you should enter a quantity of 56.7 g of hydrocortisone powder on the compounding record for this prescription.
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1/4(2x + 1.2) = 3(0.7x + 3) - 5 1/2
what is the solution?
show your work please!!
Answer:
Step-by-step explanation:
Simplify parentheses : 0.5x+0.3=2.1x+9-5.5
Combine like terms : 0.5x+0.3=2.1x+3.5
Isolate the variable : -1.6x=3.2
Divide by -1.6 on both sides : x=-2
Answer: the answer is in the picture
have a nice one
Step-by-step explanation:
A local ice cream shop sold a scoop for $2 the first year they opened and had 1000 customers each day. The price for ice cream increases by 10 cents each year because times are tough. However, 10 fewer people buy ice cream each year. Create a revenue equation. What price should they sell the ice cream to maximize the daily profit?
The answer is $6, but I want an explanation as to why
To be profitable and ensure your finances are healthy, look at both your total revenue as well as your net revenue.
What drives our total revenue calculation?A simple way to solve for revenue is by multiplying the number of sales and the sales price or average service price (Revenue = Sales x Average Price of Service or Sales Price).With that being said, not all revenues are equal.Total Revenue = Number of Units Sold X Cost Per UnitTotal Sales X Cost Per Unit equals Total RevenueThe total revenue equation can be used to determine revenue for both goods and services.Think "quantity times price" to help yourself remember.To learn more about total revenue calculation refer to:
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Question 12
Solve -3 + m2 9 or 1+ 2m 19. Write the solution using set-builder notation.
The solution to the linear inequality written in set-builder notation is {m | m ∈ R and m ≥ 12 or m ≤ 9}
Solving Linear inequalitiesFrom the question, we are to solve the given linear inequality.
The given linear inequality is
-3 + m ≥ 9 OR 1 + 2m ≤ 19
Solving -3 + m ≥ 9
-3 + m ≥ 9
Add 3 to both sides of the equation
-3 + 3 + m ≥ 9 + 3
m ≥ 12
Solving 1 + 2m ≤ 19
1 + 2m ≤ 19
Subtract 1 from both sides of the equation
1 - 1 + 2m ≤ 19 - 1
2m ≤ 18
Divide both sides by 2
2m/2 ≤ 18/2
m ≤ 9
Thus,
m ≥ 12 OR m ≤ 9
In set-builder notation
{m | m ∈ R and m ≥ 12 or m ≤ 9}
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Determine the value of b in the equation b3 = −27.
b = −3
b = 3
b = −9
b = 9
The FBI determined the true average time between felony acts in the US with a 95% confidence interval of (2.3, 5.7) seconds. Which of the following (if any) are correct? There is a 95% probability that the true average is between 2.3 and 5.7 seconds 95% of all felonies happen in 2.3 seconds to 5.7 seconds We are 95% confident the true average is between 2.3 and 5.7 seconds 95% of the time the true average will be between 2.3 and 5.7 seconds 95% of the time confidence intervals like this capture the true average time between a felony A new confidence interval has a 95% probability of capturing the sample average
95% of the time confidence intervals like this capture the true average time between a felony.
The average of the true ranges throughout the given period is known as the average true range (ATR). ATR calculates volatility by accounting for any gaps in price movement. 14 periods, which can be intraday, daily, weekly, or monthly, are typically used in the ATR calculation. Utilize a shorter average, such as 2 to 10 periods, to gauge recent volatility. Use 20 to 50 periods for volatility over longer time spans.
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The window frame is a regular octagon. It is made from eight pieces of wood shaped like congruent isosceles trapezoids. What are m∠ A, m∠ B, m∠ C, and m ∠D ?
m ∠A=___
m∠ B=____
m∠ C=___
m ∠D=___
The values of the angles are m∠ A = 112.5°, m∠ B = 67.5°, m∠ C = 67.5°, and m ∠D = 112.5°
How to find the values of m∠ A, m∠ B, m∠ C, and m ∠D?
Considering the regular octagon, the sum of angles in an octagon is 1080°. This implies each angle in the octagon will be 1080/8 = 135°
Thus, you can label the angle as shown in the image attached
c + m<A + 135° = 360° (the sum of angle at a point is 360°)
Since c = m<A (identical sides)
m<A + m<A + 135° = 360°
2 m<A = 360-135
m<A = 225/2 = 112.5°
m<B + m<A = 180° (Between two parallel lines, consecutive interior angles add up to 180°)
m<B + 112.5° = 180°
m<B = 180-112.5 = 67.5°
m<C = <B (base angles of isosceles trapezoids are equal)
m<C = 67.5°
m<D = m<A (base angles of isosceles trapezoids are equal)
m<D = 112.5°
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Which of the expressions below has a 1 in the ones place of the difference? Select all that apply.
A) 43.45 – 13.22
B) 17.56 – 15.98
C) 7.54 – 6.32
D) 12.54 – 10.67
Answer: D 12.54-10.67
1. Simplify the following expression which creates an equivalent expression.
7x-8x+14-26-3x
Answer:
-4x-12
Step-by-step explanation:
7x-8x-3x = -4x
14-26 = -12
-4x-12
How do I find x?
Please help me, I tried everything :(
Answer:
70
Step-by-step explanation:
I believe that since these are complementary angles, you are supposed to add two to get 180. In this case, there is a 110, so 70 more would be 180, but i could be wrong. you can delete my answer if it is wrong :(
Explain how to translate the phrase into an algebraic expression. The difference between four times a number and 10
Translating the phrase into an algebraic expression for the difference between four times a number and 10 is 4x - 10.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Let the number be given as x.
Therefore, 4 times will number will be 4x.
Then, difference between four times a number and 10 will be:
= 4x - 10
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Simplify: 3x^2-9x over x^2-2x-3
Answer:
[tex] \frac{(3x(x - 3))}{(x - 3)(x + 1)} = \frac{3x}{x + 1} [/tex]
There are 11 books stacked on a shelf. The red books are 1 inch high and the blue books are 2 inches high. The height of the books is 14 inches. Use a graph to estimate the number of red books and the number of blue books on the shelf.
Red books are 8 and blue books are 6.
What is inches?The smallest unit of measurement is the inch (or inches, in plural). A foot is made up of twelve inches. In the metric system, one inch is equivalent to 2.54 cm. When measuring shorter distances, such the breadth of an eraser or the length of a pencil, inches are employed.
Give conditions
Total books = 11
Red book height = 1 inches
Blue book height = 2 inches
Total height = 14 inches
We assume that
8 red books and 3 blue books = 11 books { first condition is satisfied}
In inches case:
8 * 1 = 8 { red book height 1 inches}
3 * 2 = 6 {blue book height 2 inches}
total height = 8 +6 = 14 inches {second condition is satisfied}
since red books are 8 and blue books are 6.
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Mathamathics for 9th
The equation of the line is y=3÷5x+4.
How to find the slope of a curve at a given point?A straight line that meets a curve only once and does not pass entirely through it is said to be tangential. The point of tangency is the intersection of the curve and the tangent. We are aware that the slope at any point on the line y=mx+cy=mx+c equals mm. The same is true for curves. When we refer to a curve's slope, we actually mean its point-to-point tangent slope.We employ the subsequent steps to calculate slope:In order to get dy/dx of an equation, we must first differentiate the provided equation.After differentiating, we will have the slope equation.To find the slope, enter the value of x into the equation.Here, we need to figure out the slope of this curve.
if two lines are perpendicular to each other and both of their slopes exist, the product of their slopes is equal to -1.
k1 = -9-6÷1-(-4)
= -5÷3
k2-k1 = -1
∴k2= 3÷5
y-1= 3÷5[x-(-5)]
y= 3÷5÷x+4
Hence, The equation of the line is y=3÷5x+4.
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Determine which set of side measurements could be used to form a right triangle.
04, 11, 20
16, 21, 25
5, 13, 25
3, 4, 5
Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )
What is the Pythagoras Theorem ?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
For a triangle to be Right Angled , It should obey the Pythagoras Theorem
[tex]c^{2} = a^{2}+b^{2}[/tex]
c = hypotenuse
a = perpendicular side
b = base
Hence
if c = 5 , a = 3 and b = 4
Then
[tex]c^{2} = a^{2}+b^{2}[/tex]
[tex]5^{2}= 3^{2}+4^{2}[/tex]
25 = 3 + 16
25 = 25
So
It obeys the Pythagoras Theorem
Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )
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What equation represents this function?
What is the domain and range of this function?
The equation is [tex]36x-y=145[/tex].
The domain is (∞,-∞), {x,x∈R}.
What is the domain of a function?
The domain of a function is the set of all conceivable values that are acceptable as inputs, or alternatively, it can be interpreted as the full set of potential values for independent variables. The denominator of the fraction is not equal to zero, and the digit under the square root bracket is positive, which is an indicator of the domain.
Let us first take any 2 coordinates of the function, say (-143,-2) and (0,-71).
let us take the slope of these 2 points,
[tex]m=\frac{x_{2}-x_{1} }{y_{2}- y_{1} } \\m=\frac{-71+143}{0+2} \\m=\frac{72}{2} \\m=36[/tex]
Now, using the slope, we can find the required equation:
[tex]y-y_{1} =m (x-x_{1} )\\y+143=36(x+2)\\36x-y=145\\[/tex]
The domain for the function is (∞,-∞), {x,x∈R}.
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Answer fast please.
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
12,18,27,...
Find the 7th term.
The 7th term of the sequence is 136.6875
How to determine the 7th of the sequence?From the question, we have the following sequence that can be used in our computation:
12, 18, 27....
In the above sequence, we can see that the previous term is multiplied by 1.5 to get the current term
Using the above as a guide,
So, we have the following representation
aₙ = 1.5aₙ₋₁
a₄ = 1.5 * 27
Evaluate the products
a₄ = 40.5
Solving further, we have
a₅ = 40.5 * 1.5
Evaluate the products
a₅ = 60.75
Solving further, we have
a₆ = 60.75 * 1.5
Evaluate the products
a₆ = 91.125
Solving further, we have
a₇ = 91.125 * 1.5
Evaluate the products
a₇ = 136.6875
Hence, the 7th term is 136.6875
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Find the standard error of the mean for each sampling situation (assuming a normal population).
Standard Error
a. σ = 28, n = 4
b. σ = 28, n = 16
c. σ = 28, n = 64
The standard error is decreasing on increasing number of Sample.
What is the standard error?
The population mean and sample mean are likely to deviate from one another, and the standard error of the mean, or simply standard error, shows how likely this is.
If a study were to be repeated using fresh samples drawn from a single population, it would be possible to calculate how much the sample mean would change.
The standard error is represented by a σ because it is a standard deviation. The subscript (M) indicates that the standard error in question is the standard error of the mean.
Now we will get the standard error for the following situations:
(a) σ_M = 12/√4 = 6
(b) σ_M = 12/√16 = 3
(c) σ_M = 12/√64 = 1.5
Hence from here, we can conclude that the standard error is decreasing on increasing number of Sample.
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if a sloth is traveling at its top speed of 0.067 m/s how long does it take the sloth to travel a 11.5 meter tree
The time required for the sloth to travel an 11.5-meter tree is
171.64 seconds.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A sloth is traveling at its top speed of 0.067 m/s.
∴ The time required for the sloth to travel an 11.5-meter tree is,
= (11.5/0.067) secs.
= 171.64 seconds.
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Help!
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Slope = -8, passing through (-4,-9)
Answer:
-25
Step-by-step explanation:
If Mars travels at 24,126 meters per second in orbit around the Sun and takes 1.88 earth years to complete its orbit, what is the total distance in miles Mars travels throughout its complete orbit? (Round your answer to the nearest whole number and do not include units or commas in your answer.) Note: There are 1,609 meters in a mile.
The total distance in miles Mars travels throughout its complete orbit will be 888 × 10⁶ miles.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, If Mars travels at 24,126 meters per second in orbit around the Sun and takes 1.88 earth years to complete its orbit,
First, we have to convert the unit from earth year to second obtained as,
1.88 earth year= 59287680 second
As we know that the distance is the multiplication of the speed and the time
Distance = speed × Time
Distance =24,126 m/sec × 59287680 second
Distance = 1.4 × 10¹² m
If 1 meter consists of 0,000621371 miles, the obtained distance is in miles.
1 metere = 0,000621371 miles
1.4 × 10¹² m=888 × 10⁶ miles
Thus, the total distance in miles Mars travels throughout its complete orbit will be 888 × 10⁶ miles.
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A sum of money was given to Arin, Greg, and James, the ratio is 2:5:7. James received $1180 more than Arin. How much total money was shared?
The total money was shared = $3304
What are proportion and ratio?
Two quantities are compared to form a ratio. An equality of two ratios is a proportion. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.
Aaron, Ben, and Charles split a sum of money in the following proportions: 2: 5: 7. What was the initial amount of money shared if Charles' part was 1180 higher than Aaron's portion?
——-
Ben:::: 5x
Charles:7x
Aaron:2x
———-
7x = 2x + 1180 in the equation
5x = 1180
x = 236
————-
2x + 5x + 7x = 14x
14x = 14*236 = $3304
—————————————
Hence the total money was shared = $3304
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Assume that you want to have $ 1900 saved in a sinking fund in 1 year. The account pays 3.5% compounded monthly. What should be your monthly payments?
Monthly Payment =
The monthly payment would be an amount of $163.875.
What exactly is a monthly payment?A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.
As per the given question, we have
Here P = $1900 , r = 3.5%, and T = 1 years
The total payback = P× r/100 × T + P
The total payback = 1900 × 3.5/100 × 1 + 1900
The total payback = 1900 × 0.04 × 4 + 1900
Apply the multiplication operation, and we get
The total payback = $1966.5
The total payback of the borrowings will be $1966.5 over a one-year period. The monthly payment for this will be,
The monthly payment = Total payback / No. of payment
The monthly payment = 1966.5/12
The monthly payment = $163.875
Therefore, the monthly payment would be an amount of $163.875.
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A yoga teacher sells yoga mats for $25 each and yoga DVDs for $14
each. If x represents the number of mats she sells and y represents
the number of DVDs she sells, write an expression that represents
the amount of money she receives from selling mats and DVDs. Tell
whether the expression should be minimized or maximized.
The required expression for the money spent is given as 25x + 14y.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given problem can be solved as follows,
The price for each yoga mat is $25 and each yoga DVD is $14.
As per the question, the expression for the amount of money spent can be written as,
25x + 14y
The expression can be minimised to reduced the money spent.
Hence, the expression for the money spent by yoga teacher is 25x + 14y and the given expression can be minimised to reduce the total cost.
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Mrs. McCoy bought three pieces of cloth. They were 4 yards, 5 yards, and 3 yards long. How many yards of cloth did she buy in all?
Answer:
12 yards
3+4+5=12
3+4=7
7+5=12
Answer:
12, needed to be multiplied ( which I don't think so) 60
Step-by-step explanation:
I really don't have a "step by step explanation" but 4+5=9+3=12
or: 4x5=20x3=60
a party rental company has chairs and tables to rent. there were two customers who rented both chairs and tables last week
A system of equations are 9x+7y=77 and 3x+5y=49. Therefore, cost to rent each chair is $1.75 and cost to rent each table is $8.75.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
a) From the table, first costumer brought 9 chairs and 7 tables per $77
Second costumer brought 3 chairs and 5 tables per $49
Let x be the cost (in dollars) to rent a chair
Let y be the cost (in dollars) to rent a table
Here, 9x+7y=77 --------(I)
3x+5y=49 --------(II)
b) Multiply equation (II) by 3
9x+15y=147 --------(III)
Subtract equation (I) from (III), we get
9x+15y-(9x+7y)=147-77
⇒ 8y=70
⇒ y=8.75
Substitute y=8.75 in (I), we get
9x+7×8.75=77
⇒ 9x+61.25=77
⇒ 9x=77-61.25
⇒ 9x=15.75
⇒ x=1.75
Therefore, the system of linear equations are 9x+7y=77 and 3x+5y=49.
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I need help for a grade
Answer:
36
Step-by-step explanation:
[tex]\frac{1}{4}(12^2)=\frac{1}{4}(144)=36[/tex]