solution
3x+18/18
ans4
The weight, in pounds, of a newborn baby t months after birth can be modeled by the equation W=1.75t+6. What is the slope of the equation and what is its interpretation in the context of the problem?
Answer:
the slope is 1.75
Step-by-step explanation:
Interpretation: The weight of newborn is 6 lb at birth, and every month baby gained 1.75 lb. You replace x with month you want to know the weight. For example you can calculate the weight after 4 month : w= 1.75(4)+6= 13 lb
1. Which is an important aspect of a randomized survey's design?
A. The survey should always contain at least 5 questions.
B. Each survey question should have at most 3 choices.
C. The survey participants should be randomly selected.
D. The survey should have questions for multiple populations.
2. Identify the leading question.
A. How much would you be willing to pay for a new living room furniture set?
B. During what time of day are you most likely to watch TV?
C. How interested would you be in purchasing a blue car?
D. How much did you enjoy your great experience at our waterpark?
3. Frederick is creating a plan to conduct a randomized survey. He will be asking guests at a baseball stadium to rate their experience. At which location should he take the survey to ensure randomization?
A. the section of seats directly behind home plate
B. the hot dog stand
C. the stadiums front gate
D. the gift shop
Answer: 1) C- the survey participants should be randomly selected
2) C- how interested would you be in purchasing a blue car?
3) C- the stadiums front gate
Step-by-step explanation: I took the quick check.
Answer:
1. c
2. d
3. c
Step-by-step explanation:
how do i factor (x + 2)^2 - (y - 2)^2???
The factor of the difference of two squares (x + 2)² - (y - 2)² is (x + y)(x - y + 4).
Difference of two squaresIf for any two squares say a² and b², then their difference a² - b² = (a + b)(a - b).
Given the two squares (x + 2)² and (y - 2)²
then their difference will yeild the factors derived as follows;
(x + 2)² - (y - 2)² = [(x + 2) + (y - 2)][(x + 2) - (y - 2)]
open brackets
(x + 2)² - (y - 2)² = (x + 2 + y - 2)(x + 2 - y + 2)
collect like terms
(x + 2)² - (y - 2)² = (x + y + 2 - 2)(x - y + 2+ 2)
so
(x + 2)² - (y - 2)² = (x + y)(x - y + 4)
Thus, by application of the rule of difference of two squares, we have the factors of (x + 2)² - (y - 2)² to be (x + y 2 - 2) and (x - y + 2+ 2).
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Determine when the function is positive, negative, increasing, or decreasing.
Then describe the end behavior of the function.
The function is positive and increasing from 0 to 2.5, at negative and decreasing from 0 to -2.5, respectively.
How to find returns to scale?
Returns to scale involves an increase in an output more than when all the inputs increase proportionately.
Using the graph, there is a line segment from the origin to a point. at the middle of the third block making 2.5.
This shows an increase which is positive and on the other hand, there is a line segment from the origin towards left hand side on the number line showing a decrease and a negative from 0 to -2.5.
In conclusion, the line pointing upwards towards right hand side shows both positive and increase while the line pointing leftward shows decrease and negative.
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NO LINKS!! Please help me with these graphs
Answer:
See below.
Step-by-step explanation:
Each of the graphs shows a line segment, but because of the arrowheads, each situation is different.
Left graph.
The line segment has a point at each end. The graph is of just the line segment shown.
The lowest x-coordinate is -4.
The greatest x-coordinate is 3.
The lowest y-coordinate is 2.
The greatest y-coordinate is 5.
Domain: -4 ≤ x ≤ 3
Range: 2 ≤ x ≤ 5
In interval notation:
Domain: [-4, 3]
Range: [2, 5]
Middle graph.
The line segment has a point at the right endpoint but an arrowhead at the left. The graph is a ray that starts at point (2, 2), goes through point (-4, 5) and keeps going forever past point (-4, 5) in the direction of the segment.
The lowest x-coordinate is -∞.
The greatest x-coordinate is 2.
The lowest y-coordinate is 2.
The greatest y-coordinate is ∞.
Domain: x ≤ 2
Range: x ≥ 2
In interval notation:
Domain: (-∞, 2]
Range: [2, ∞)
Right graph.
The line segment has an arrowhead at each end. The graph is a line that includes the line segment shown. A line has no beginning and no end; therefore, it goes on in both directions forever.
The lowest x-coordinate is -∞.
The greatest x-coordinate is ∞.
The lowest y-coordinate is -∞.
The greatest y-coordinate is ∞.
Domain: all real numbers
Range: all real numbers
In interval notation:
Domain: (-∞, ∞)
Range: (-∞, ∞)
Answer:
1. Domain: [-4, 3] Range: [2, 5]
2. Domain: (∞, 2] Range: [2, ∞)
3. Domain: (-∞, ∞) Range: (-∞, ∞)
Step-by-step explanation:
Domain: The set of all possible input values (x-values).
Range: The set of all possible output values (y-values).
An open circle indicates the value is not included in the interval.
A closed circle indicates the value is included in the interval.
An arrow shows that the function continues indefinitely in that direction.
Note: Assume that each square on the given graphs is 1 unit.
Question 1
There are closed circles at both endpoints of the line: (-4, 2) and (3, 5).
Therefore, the values are the endpoints of the intervals.
Domain: [-4, 3]Range: [2, 5]Question 2
There is a closed circle at (2, 2).
There is an arrow at one endpoint, so as x → -∞, y → ∞.
Domain: (∞, 2]Range: [2, ∞)Question 3
There are arrows at the endpoints of the line.
Therefore, the domain and range are unrestricted.
Domain: (-∞, ∞)Range: (-∞, ∞)A2 Lesson 3.2 Practice
1. Does the graph shown represent a function for 0 < x < 6? Explain.
Yes, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The function is given in the represented graph
According to the given graph, we can see the value of the domain of the given function f(x) when the function includes all possible variables of x values of a function.
Here the domain of the given function is 0 < x < 6
Therefore, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.
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How to solve step by step
Water , Tonya drinks the recommended 8 cups of water per day how many gallons of water dose she drink per year ?Hint:( 1gallon = 16 cups)
Step-by-step explanation:
your teacher gave you the solution to the real problem of this question : how many cups are in 1 gallon. 16 cups.
and if you remember that a year has 365 days, then the rest is rant simple and straight forward :
8 cups per day
so
365 × 8 = 2920 cups per year.
2920 cups = 2920/16 = 182.5 gallons
therefore, she drinks 182.5 gallons of water per year.
What is the correct answer
Answer: See coordinate graph below.
Step-by-step explanation: Again, the black point is the original point and the red point is the reflected point.
Ordered pair of the reflected point:
D': (-6, 5)
Have a great day! :)
Suppose a basketball player has made 215 out of 322 free throws. If the player makes the next 2 free throws, I will pay you $32. Otherwise you pay me $24. Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
The expected value of the proposition is -$1007.41
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]
In which [tex]C_{x},x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{x},x= \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Suppose a basketball player has made 215 out of 322 free throws.
This means that p = 215/322 = 0.6677
2 free throws:
This means that
Probability of making two free throws.
This is P(X = 2).
P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]
P(X = 2) = [tex]C_{2},2.(0.6677)^2.(0.3323)^0[/tex] = 0.29629
Expected value:
If he makes both free throws, you earn $24. So 0.29629 probability of you earning $24.
Otherwise, you have to pay $32. 1 - 0.29629 = 31.70371 probability of you losing $32.
E = 0.29629*24 - 31.70371*32 = -1007.41
Hence, The expected value of the proposition is -$1007.41
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f(x) = 2x^4-8x²+5x-7
x=3
[tex]{ \pink{ \boxed{ \purple{ \sf{f(3) = 98}}}}}[/tex]
Step-by-step explanation:
[tex]{ \blue{ \tt{f(x) = 2 {x}^{4} - 8 {x}^{2} + 5x - 7}}}[/tex]
[tex]{ \blue{ \tt{f(3) = 2( {3})^{4} - 8( {3})^{2} + 5(3) - 7}}}[/tex]
[tex]{ \blue{ \tt{f(3) = 2(81) - 8(9) + 15 - 7}}}[/tex]
[tex]{ \blue{ \tt{f(3) = 162 - 72 + 8}}}[/tex]
[tex]{ \blue{ \tt{f(3) = 162 - 64}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \sf{f(3) = 98}}}}}[/tex]
Khalil filled an ablum with 104 postcards. If there are 4 postcards on each page, how many pages are in the ablum?
Step-by-step explanation:
so there sre 104 postcards .so what we do is 104 ÷ 4 post cards on each page , it will then = to 26 pages
If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?
Answer:
65c
Step-by-step explanation:
Help it’s due tmr…………..
Answer:
7
Step-by-step explanation:
13x - 7 + 30 = 30 + 84
13x - 7 + 30 - 30 = 30 - 30 + 84
13x - 7 = 84
13x = 84 + 7
13x = 91
x = 91 / 13
x = 7
The price of a toy usually costing £50 is increased to £65
Work out the percentage increase.
Answer:
[tex]\frac{50}{50\\}[/tex] [tex]= \frac{65}{50}[/tex]
Now cross-multiply
Let p represent the percentage
50(50) = 50(65) ; 2500p = 3250
now divide 2500 on both sides to find p
2500p/2500 and 3250/2500
p = 1.3 ; percentage change is equal to %1.3 increase
Write the equation of a line, in slope-intercept form, that is perpendicular to y = - 1/3 x + 4 and passes through the point (-2-5)
The equation of the line perpendicular to the given line is, y = 3x + 1.
What is slope of the line?
The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.
Consider, the given equation of line
[tex]y = -\frac{1}{3}x+4[/tex]
We have to find the equation of line passes through the point (-2, -5) and perpendicular to the given line.
Here, the point is (-2, 5).
First to find the slope of the line.
Since, the slope of the line, perpendicular to the given line is negative reciprocal of the slope of given line.
Here, the slope of given line is, -1/3.
So, the slope of perpendicular line is [tex]-(\frac{1}{(-\frac{1}{3}) }) = 3[/tex]
Therefore, the slope of the line is 3.
Now to find the equation of the line.
Consider, the point - slope form of the line
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex](x_1, y_1) = (-2, -5) , m = 3[/tex]
⇒
[tex]y-(-5)=3(x-(-2))\\y+5=3(x+2)\\y+5=3x+6\\y=3x+6-5\\y=3x+1[/tex]
Hence, the equation of line in slope - intercept form, is y = 3x + 1.
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You want to have $300,000 when you retire in 30 years. If you can earn 4% interest compounded continuously, how much would you need to deposit now into the account to reach your retirement goal?
An amount of $ 92,495.60 must be the initial deposit to become into $ 300,000 by compound interest.
How much money must be deposited to obtain a given quantity for retirement?
In this problem we must determine the initial deposit that must become into $ 300,000 by compound interest after a period of 30 years. Compound interest model is a model where money gains interest continuously, whose formula is:
C' = C · (1 + r / 100)ⁿ
Where:
C - Initial deposit, in monetary units.C' - Final deposit, in monetary units. r - Interest rate, in percentage.n - Number of periods, in years.If we know that C' = 300,000, r = 4 and n = 30, then the initial deposit is:
C = C' / (1 + r / 100)ⁿ
C = 300,000 / (1 + 4 / 100)³⁰
C = 92,495.60
The initial deposit must be $ 92,495.60.
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Please Help 2
If a runner traveled a distance of d(h)=/16h4 in time t(h) = 3h4 - 3h3 -5h2 what is the runner's speed?
The runner's speed If a runner traveled a distance of d(h)=/16h4 in time t(h) = 3h^4 - 3h^3 -5h^2 is 4 /3h^2 - 3h -5h.
How can the speed be calculated?The concept that will be used to calculate this is the concept of speed which is the ratio of the distance per time which can be expressed as
speed = distance/time
Then we were given distance as d(h)=/16h^4
time as t(h) = 3h^4 - 3h^3 -5h^2
Speed = [tex]\sqrt{16h^4} /3h^4 - 3h^3 -5h^2[/tex]
Then we will have 4h^2 /3h^4 - 3h^3 -5h^2
then take h^2 from both the numerator and denominator and then cancel them , then we will have
= 4 /3h^2 - 3h -5h.
Therefore, the first option is correct.
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The expression 45h +225 represents the total cost in dollars of
renting a large party tent from a local rental store for h hours. Jamal's
parents are willing to spend between $500 and $750 for the tent.
Part A. Write an inequality to represent the possible lengths of time
the tent can be rented.
Part B. Using your inequality in Part A, what is one possible length of
time the tent could be rented? Give your answer in number of hours.
Part A Write an inequality to represent the possible lengths of time
the tent can be rented
[tex]6.11\leq h\leq 11.66[/tex]
Part B. Using your inequality in Part A, what is one possible length of
time the tent could be rented
[tex]6hr 6min\leq h\leq 11hr39min[/tex]
The definition of a linear inequality
The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.
What does a linear inequality in mathematics look like?
What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being utilized in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).
Given That
45h+225 is total cost in dollars for renting tent and parents are willing to spend between $500 and $750 for the tent.
Part A
[tex]500\leq 45h+225\leq 750\\500-225\leq 45h+225-225\leq 750-225\\275\leq 45h\leq 525\\\frac{275}{45} \leq h\leq \frac{525}{45} \\6.11\leq h\leq 11.66[/tex]
Part B
[tex]6.11hr\leq h\leq 11.66hr[/tex]
6.11 hr = 366 minute approx.
11.66 hr = 699 minute approx.
[tex]6hr 6min\leq h\leq 11hr39min[/tex]
Hence this is the answer
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Rodrigo needs a total of 3 pounds of vegetables for a stew.
He already has 3/8 pound of onions and 1/3 pound of tomatoes.
How many more pounds of vegetables does he need to buy?
Using mathematical operations of addition and subtraction, Rodrigo needs to buy additional 2⁷/₂₄ pounds of vegetables.
What are mathematical operations?The basic mathematical operations are addition, subtraction, division, and multiplication.
These mathematical operations can be used to determine the results of mathematical expressions.
The total pounds of vegetables required for a stew = 3 pounds
Available pounds of vegetables:
Onions = 3/8 pounds
Tomatoes = 1/3 pounds
The total available pounds = 17/24 pounds
Additional pounds required = 3 - 17/24 pounds
= 2⁷/₂₄ pounds
Thus, based on addition and subtraction, Rodrigo needs additional 2⁷/₂₄ pounds of vegetables.
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3. what is the probability of drawing four red cards in a row without replacement.
out of a standard deck with 52 playing cards
Answer: There are 52 cards in a standard deck and half of them, 26 in all, are red.
Suppose that you are drawing 4 cards without replacement from a thoroughly shuffled deck. You have 26 cards choose 4 over 52 choose 4.
∴ P(pulling 4 cards from deck) = (264)(524)
The total number of restaurant-purchased meals that the average person will eat
in a restaurant, in a car, or at home in a year is 169. The total number of these
meals eaten in a car or at home exceeds the number eaten in a restaurant by
13. Twenty more restaurant-purchased meals will be eaten in a restaurant than
78 meals are eaten in a restaurant, 58 meals are eaten in a car, 33 meals are eaten at home and the question is solved by using linear equations.
What is the linear equation?
A linear equation is an algebraic equation of the form y =mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given that the total number of meals is 169.
Assume that,
a = number of meals eaten in a restaurant
b = number of meals eaten in a car
c = number of meals eaten at home
a + b + c = 169 .....(i)
Since the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13.
Thus b + c = a + 13 .....(ii)
Again twenty more restaurant-purchased meals will be eaten in a restaurant than at home.
a = 20 + c .....(iii)
Subtract equation (ii) from (i)
a + b + c - b - c = 169 - a - 13
2a = 156
Divide both sides by 2
a = 78
Substitute a = 78 in equation (iii)
78 = 20 +c
c = 58
Putting c =58 and a =78 in equation (ii)
b + 58 = 78 + 13
b = 33
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Question:
The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 169. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.
F(x)=3x^4-4x^3+x^2+6x-2
The rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).
We will use the synthetic division method to determine the rational zeros and linear factors of given polynomials.
Polynomials are divided via synthetic division.
The procedure entails of synthetic division:
Step 1: Create a synthetic divide.
Step 2: Bring the leading coefficient down to the bottom row.
Step 3: Divide this by the value stated in the bottom row.
Step 4: Finally, add the column you defined in step 3.
This can proceed as:
Given: f(x) = 3x⁴- 4x³ + x² + 6x - 2
3x⁴ - 4x³ + x² + 6x - 2 = 0
We will put x = -1 in f(x). In this case, replace x with -1. This will be:
f(-1) = 3 * 1⁴ - 4 * 1³ + 1² + 6 * 1 - 2 = 0
Since f(-1) = 0, so (x + 1) is a factor of f(x).
Using synthetic division:
-1)....3....-4....1....6....-2
.........3.....-7...8....-2..|..0
Remainder = 0
Quotient = 3x³ - 7x² + 8x - 2
For 3x³ - 7x² + 8x - 2, f(1/3) = 0, so (x - 1/3) is a factor.
1/3)....3....-7....8....-2
..........3.....-6...6...|..0
Remainder = 0
Quotient = 3x² - 6x + 6 = 3(x² - 2x + 2)
Because x² - 2x + 2 has no more rational zeros or linear components. The rational zeros are hence x = -1 and x = 1/3.
Thus, the rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).
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Shaquana's car used 8 gallons of gas to drive 312 miles. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided
A table of equivalent ratios for the miles and gallons of gas driven is as follows:
Miles Gallons
39 1
117 3
312 8
The data points are plotted in the graph shown in the image attached below.
What is a proportional relationship?In Mathematics, a proportional relationship can be modeled or represented by the following mathematical expression:
x = ky
Where:
x represents the miles.y represents the gallons.k represents the constant of proportionality.In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.
Next, we would calculate the constant of proportionality (k) as follows:
Constant of proportionality (k) = x/y
Constant of proportionality (k) = 312/8
Constant of proportionality (k) = 39.
When x = 39, the value of y is given by:
y = x/k
y = 39/39
y = 1 gallons.
When y = 3, the value of x is given by:
x = ky
x = 39 × 3
x = 117 miles.
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A movie producer wants to cast a dog and a cat in her next film, and the talent agency
has 18 dogs and 24 cats to choose from.
How many different dog-cat options are possible for the producer? (please explain)
Step-by-step explanation:
there are 18 dogs to choose 1 dog.
therefore, these are 18 options.
for each of these 18 options there are 24 cats to choose from.
so, altogether, there are
18×24 = 432
dog-cat options.
There are are 432 ways to choose dog-cat options are possible for the producer.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
Total Number of Dogs= 18
Total Number of cats= 24
so, the number easy to select
= 18 x 24
= 432
Hence, there are 432 ways to choose dog-cat options are possible for the producer.
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Question 3(Multiple Choice Worth 1 points)
(02.04 MC)
In triangle DEF, if mZD = (2x)°, mZE = (2x - 4)º, and mZF = (x + 9)°, what is the value of x?
A)35
B)37
C)44
D)71
By using property of triangle and trapezium, it is obtained that
a) value of x is 35°
b) Third option is correct
What is a triangle and trapezium?
Triangle is a three sided two dimensional figure.
Trapezium is a quadrilateral whose one pair of opposite side is parallel and another pair of opposite side is non parallel
Here property of triangle is used
[tex]m \angle D = (2x)^{\circ}, \ m\angle E = (2x - 4)^{\circ}, m \angle F = (x +9)^{\circ}[/tex]
[tex]m \angle D + m\angle E + m \angle F = 180\\2x + 2x - 4 + x + 9 = 180\\5x + 5 = 180\\5x = 180 - 5\\5x = 175\\x = \frac{175}{5}\\x = 35^{\circ}[/tex]
In the second question, if the trapezoid is rotated 90° clockwise, then (x, y ) will change to (y, -x) and new coordinate of A is (1, 5)
Third option is correct
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Use the formula F = mg-3t²
m = 4, g = 6 and t = 2
Find the equation of a line perpendicular to -5x + y = 9 that passes through the
point (0, -9)
The equation of a line perpendicular to -5x + y = 9 that passes through the point (0, -9) is [tex]y = -\frac{1}{5}x -9[/tex]
How to find the equation of a line?The equation of the line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptPerpendicular lines follows the following rules as follows:
m₁ m₂ = -1
Let's find the slope of -5x + y = 9 .
y = 5x + 9
Hence,
slope = 5
Let's find the slope of the equation of the line that passes through (0, -9) and perpendicular to -5x + y = 9 .
5m₂ = -1
m₂ = -1 / 5
m₂ = - 1 / 5
Therefore, let's find the y-intercept of the line using (0, -9)
-9 = - 1 / 5(0) + b
b = -9
Therefore, the equation of the line is y = - 1 / 5 x - 9
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If housekeeping normally takes 10 minutes to prepare a patient’s room, how many rooms can one housekeeper be expected to handle in an 8 hour shift
The Monty Corporation has a staff of sales people who are paid a monthly salary of $1,600.00 plus an incremental commission based on the table below. If Sally sells $29,700.00, what is her total gross pay for the month
Answer:
Step-by-step explanation:
-28,100 if you subtract 29,700.00 - 1,600.00 = -28,100