The required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
The given starting weight for the diet program is 106 pounds. Because the weight is expected to be multiplied by 1.04 pounds each week, the weight will develop exponentially with an initial value of 106 pounds and a growth factor of 1.04 pounds. Then, for the weight after weeks, the exponential function is given by,
W = W(n) = Pb'
Here P = 106 and b = 1.04
Hence the required formula is,
⇒ W = 106 × 1.04ⁿ
Thus, the required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.
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The question seems to be incomplete the correct question would be
A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week. Then, find the exponential function for the weight after weeks.
Michael earned some Money doing odd jobs last summer and put it in a savings account that earns 13% interest compounded quarterly after 2 years there is 100.00 in the account how much did Michael earn doing odd jobs
Michael earned some Money doing odd jobs last summer and put it in a savings account that earns 13% interest compounded quarterly after 2 years there is 100.00 in the account How much did Michael earn doing odd jobs?
____________________________________
13% interest compounded quarterly
after 2 years there is 100.00
_________________________________-
interest compounded
A = P(1 + r/n)^nt
A= Final amount
P= Principal Amount
r= interest
n= number of compounding periods (year)
t= time (year)
_____________________
Data
A= 100.00
P= Principal Amount (The question)
r= interest (0.13)
n= number of compounding periods (4)
t= time (2)
_________________
Replacing
A = P(1 + r/n)nt
P = A / ((1 + r/n)^nt)
P = 100.00/ ((1 + 0.13/4)^4*5)
P= 100.00/ (1.0325^20)
P= 52
________________
Michael earns doing odd jobs 52 dollars.
In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Select all the equations that are equivalent to the formula PV = nRT.
The equations that are equivalent to the formula PV = nRT are V = nRT/P, n = PV/RT and R = PVnT. Option B, C and D
How to determine the equationsFrom the information given, we have that;
The Ideal Gas law is represented as;
PV = nRT
Given that;
P is the pressure V is the volumeT is the temperaturen is the amount of gasR is a physical constantSubject of formula is described as the variable expressed in terms of other variables in an equation.
It is made to stand on its own on one end of the equality sign.
Let's make 'V' the subject of formula
Divide both sides by the coefficient of V which is the variable 'P', we have;
V = nRT/P
Making 'R' the subject of formula, we have
R = PV/ nT
Making 'n' the subject of formula, we have;
n = PV/RT
Hence, the equations are options B, C and D
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The complete question:
In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Which of the equations below are equivalent to the formula PV = nRT? Select all that apply. A. P = VnRT B. V = nRT/P C. n = PV/RT D. R = PVnT E. T = nR/PV
Answer:Pv=NRT
Step-by-step explanation:
Given the triangle ABC with the points A = ( 4, 6 ) B = ( 2, 8 ) C = ( 5, 10 ) and it's dilation, triangle A'B'C', with points A' = ( 2, 3 ) B' = ( 1, 4 ) C' = ( 2.5, 5 ) what is the scale factor?
Answer:
Explanation:
Given A = (4, 6) B = (2, 8) C = (5, 10)
[tex]\begin{gathered} AB=\sqrt{(2-4)^2+(8-6)^2} \\ \\ =\sqrt{8} \\ \\ BC=\sqrt{(5-2)^2+(10-8)^2} \\ \\ =\sqrt{8} \end{gathered}[/tex]SImilarly, for A' = (2, 3) B' = (1, 4) C' = (2.5, 5)
[tex]\begin{gathered} A^{\prime}B^{\prime}=\sqrt{(1-2)^2+(4-3)^2} \\ \\ =\sqrt{2} \\ \\ B^{\prime}C^{\prime}=\sqrt{(2.5-1)^2+(5-4)^2} \\ \\ =\sqrt{3.25} \end{gathered}[/tex]
Since it is a dilation, AB/A'B' should be the same as BC/B'C', but that is not the case here.
Select all rational numbers
help ASAP please
15 points
The resulting rational number is √100
Rational numbers:
A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.
Given,
Here we have the following list of numbers
√75, -√25, 2√7, √100, √0.36, √0.0144, √3/7 , -√36/49
Now, we need to identify whether these are the rational numbers or not.
AS per the definition of rational number,
When we take the root for the value √75, we get 8.660 that is a non-whole square root, 8.660 is not a rational number.
The value -√25 takes the negative value so it is not a rational number.
The number 2√7, this one also produce on-whole square root, so this one is not a rational number.
The value of √100 is 10, and it is a rational number.
The value of √0.36 is 0.6 which is less than 0, so it is not a rational number.
The value of √0.0144 is 0.012 which is less than 0, so it is not a rational number.
The value of √3/7 this one also produce on-whole square root, so this one is not a rational number.
The value -√36/49 takes the negative value so it is not a rational number.
Therefore, the rational number is √100.
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Find the area of the triangle below.9 cm6 cm2 cm
We recall that the area of a triangle is defined by the product of the triangle's base times its height divided by 2.
So we notice that in our image, we know the height (6 cm), and we also know the base of the triangle (2 cm)
Therefore the triangles are is easily estimated via the formula:
[tex]\text{Area}=\frac{base\cdot height}{2}=\frac{2\cdot6}{2}=6\, \, cm^2[/tex]Then the area is 6 square cm.
The following are the distances (in miles) to the nearest airport for 13 families.10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39Notice that the numbers are ordered from least to greatest.Give the five-number summary and the interquartile range for the data set.
We have the next given set for distances (in miles) to the nearest for 13airport families:
10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39
The minimum is the least number value. Then:
Minimum =10
In this case, we have 13 data, so :
- The middle number is the median:
10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39
Now, the lower quartile is given by the next equation:
[tex]=(n+1)\ast\frac{1}{4}[/tex]Replacing:
[tex]\begin{gathered} =(13+1)\ast\frac{1}{4} \\ =14\ast\frac{1}{4} \\ =3.5=4 \end{gathered}[/tex]The lower quartile is in the fourth position:
Lower quartile = 15
The upper quartile is given by the next equation:
[tex]\begin{gathered} =(n+1)\ast\frac{3}{4} \\ =(13+1)\ast\frac{3}{4} \\ =10.5=11 \end{gathered}[/tex]The upper quartile is located in the 11th position:
Upper quartile = 34
The interquartile range is given by:
IQR=upper quartile - lower quartile
IQR=34-15
The interquartile range =19
See if anybody can answer this. A concession stand sells lemonade for $2 each and sports drinks for $3 each. The concession stand sells 54 cups of lemonade and sport drinks. The total money collected for these items is $204. How much money was collected on sports drinks?
The initial directions are in the pic below. I’m sending 2 pics now. And the other 2 soon. For a total of 4.
Recall that the rule of transformation of a point reflected over the y-axis is as follows:
[tex](x,y)\rightarrow(-x,y).[/tex]Therefore, the transformed coordinates of the vertices of the triangle are:
[tex]\begin{gathered} N(4,6)\rightarrow N^{\prime}(-4,6), \\ P(1,6)\rightarrow P^{\prime}(-1,6), \\ Q(3,4)\rightarrow Q^{\prime}(-3,4)\text{.} \end{gathered}[/tex]Therefore, the image of the triangle is the triangle with the above vertices.
Answer:
write an equation that gives the proportinal relationship of the graph
Answer:
y=5x
Explanation:
The slope-intercept form of the equation of a line is:
[tex]y=mx+b\text{ where }\begin{cases}m=\text{slope} \\ b=y-\text{intercept}\end{cases}[/tex]First, we find the slope of the line by picking two points from the line.
• The points are (0,0) and (3,15).
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{15-0}{3-0}=\frac{15}{3} \\ \implies m=5 \end{gathered}[/tex]Next, the line crosses the y-axis at y=0.
Therefore, the y-intercept, b=0.
Substitute m=5 and b=0 into the slope-intercept form:
[tex]\begin{gathered} y=5x+0 \\ \implies y=5x \end{gathered}[/tex]The equation that gives the proportional relationship of the graph is y=5x.
a store sells gift cards in preset amount. You can purchase gift cards for $20 or $30 . You spent $380 on gift cards. let x be the number of gift cards for $20 And let y be your gift cards for $30 . Write an equation in standards for to represent this situation
ANSWER= 20x+30y=380
but what ab this one
What are three combinations of gift cards you could have purchased?
The equation that represent the situation is as follows:
20x + 30y = 380The three combination of the gift cards you can purchase is as follows:
13 and 410 and 67 and 8How to represent equation in standard form?The store sells gift cards. One can purchase gift cards for $20 or $30 .
You spent $380 on gift cards. let x be the number of gift cards for $20 And let y be your gift cards for $30 .
The equation in standard form to represent the situation is as follows:
The standard form of a linear equation is A x + By = C. A, B, and C are
constants, while x and y are variables.
Therefore,
x = number of gift cards for 20 dollars
y = number of gift card for 30 dollars
Hence,
20x + 30y = 380
The three combination one could have purchased is as follows:
20(13) + 30(4) = 38020(10) + 30(6) = 38020(7) + 30(8) = 380learn more on equation here: https://brainly.com/question/7222455
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The amounts of money three students earn at their jobs over time are given in the tablesStudent ETime (hr) Amount Earned2$15.005$37.508$60.00Student FTime (hr) Amount Earned3$27.006$54.0010$90.00Student GTime (hr) Amount Earned1$8.504$34.007S59.50According to the tables, which statement is true?Student E cams the most amount of money per hourStudent E cars more money per hour than studentStudent Goarns the least amount of money per hourStudent G earns less money per hour than student F
the answer is:
Student G earns less money per hour than student F
Mr. Edmonds is packing school lunches for a field trip for the 6th graders of Apollo Middle school. He has 50 apples and 40 bananas chips. Each group of students will be given one bag containing all of their lunches for the day. Mr. Edmonds wants to put the same number of apples and the same number of bananas in each bag of lunches. What is the greatest number of bags of lunches Mr. Edmonds can make? How many apples and bananas will be in each bag?
The greatest number of bags of lunches Mr. Edmonds can make = 40, And , in each bag there will be one apple and one banana chips bag.
In the above question, the following information is given :
Mr. Edmonds wants to pack lunches for the schools field trip where he wants to put the same number of apples and the same number of bananas in each bag of lunches
We are given that,
Number of available bananas chips packs = 40
Number of available apples = 50
We need to find the greatest number of bags of lunches Mr. Edmonds can make
As the pair should be an even number and we have less number of banana chips bags than apples. So the number of lunches which can be packed with equal number of apples and banana chips bags depend on banana chips bags
Therefore, the greatest number of bags of lunches Mr. Edmonds can make = 40
And , in each bag there will be one apple and one banana chips bag.
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a sample size 115 will be drawn from a population with mean 48 and standard deviation 12. find the probability that x will be greater than 45. round the final answer to at least four decimal places
B) find the 90th percentile of x. round to at least two decimal places.
The probability that x will be greater than 45 is 0.1974.
The 90th percentile of x is 63.3786
Given,
The sample size drawn from a population = 115
The mean of the sample size = 48
Standard deviation of the sample size = 12
a) We have to find the probability that x will be greater than 45.
Here,
Subtract 1 from p value of the z score when x = 45
Then,
z = (x - μ) / σ
z = (45 - 48) / 12 = -3/12 = -0.25
The p value of z score -0.25 is 0.8026
1 - 0.8026 = 0.1974
That is,
The probability that x will be greater than 45 is 0.1974.
b) We have to find the 90th percentile of x.
Here,
p value is 0.90
Then, z score will be equal to 1.28155
Now find x.
z = (x - μ) / σ
1.28155 = (x - 48) / 12
15.3786 = x - 48
x = 15.3786 + 48
x = 63.3786
That is,
The 90th percentile of x is 63.3786
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Consider the following when d = 14 ft. Give both exact values and approximations to the nearest hundredth.(a) Find the circumference of the figure.ftftx(b) Find the area of the figure.ft?x7A²teh
(a)Recall that the circumference of a circle is given by the following formula:
[tex]C=\pi d.[/tex]Where d is the diameter of the circle.
Substituting d=14 ft in the above formula, we get:
[tex]C=\pi(14ft)\approx43.98ft\text{.}[/tex](b) Recall that the area of a circle is given by the following formula:
[tex]A=\frac{\pi d^2}{4}.[/tex]Substituting d=14 ft in the above formula, we get:
[tex]A=\frac{\pi(14ft)^2}{4}=49\pi ft^2\approx153.94ft^2.[/tex]Answer:
(a)
Exact solution:
[tex]14\pi ft.^{}[/tex]Approximation:
[tex]43.98\text{ ft.}[/tex](b) Exact solution:
[tex]49\pi ft^2\text{.}[/tex]Approximation:
[tex]153.94ft^2.[/tex]what is the slope of the line which goes through the points (-2, -9) and (2, 11) the slope of the line is___
We know the equation of a line is given by:
[tex]y=mx+b[/tex]where m is its slope and b its interpcetion with y - axis.
We know the slope equation is
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]If (x₁, y₁) = (-2, -9) and (x₂, y₂) = (2, 11) then replacing in the slope equation
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{11-(-9)}{2-(-2)} \\ =\frac{11+9}{2+2} \\ =\frac{20}{4}=5 \end{gathered}[/tex]Answer: the slope of the line is 5I don't understand any of this (for a practice assessment)
Answer:
a. The total weight
b. 2 times the weight of Jet
c. The weight of Fido
d. The total weight
Explanation:
We know that Fido weighs 10 pounds more than Jet and together they weigh 46 pounds. So, if j represents Jet's weight, the bar model is:
Now, we can answer each part as:
a. 46 represents the total weight of the small dogs
b. 2j represents 2 times the weight of Jet
c. j + 10 represents the weight of Fido because its weight is the weight of Jet j added to 10.
d. 2j + 10 also represents the sum of the weights of the small dogs.
So, the answers are:
a. The total weight
b. 2 times the weight of Jet
c. The weight of Fido
d. The total weight
0. Taylor earned the following amount each day. One dollar on the first day Three dollars on the second day Nine dollars on the third day Twenty-seven dollars on the fourth day
Question:
Solution:
Answer:
[tex]f(t)=3^{(t-1)}[/tex]Step-by-step explanation:
one dollar of the first day = 3^0
three dollars on the second day = 3^1
nine dollars on the third day = 3^2
twenty-seven dollars on the fourth day = 3^3
Numbers increase 3 times a day, it is an exponential function, powers of 3
The function is going to be:
[tex]f(t)=3^{(t-1)}[/tex]How can use theorem 7-4 to find missing segments? (7-4 is similarity) :)
Given
AD = 6.4
BD = 3.6
Find
AC,BC and DC
Explanation
Using Pythogoras theorem in triangle ADC
[tex]AC^2=DC^2+6.4^2------(1)[/tex]Using PT in triangle BDC
[tex]BC^2=DC^2+3.6^2-------(2)[/tex]Adding equation (1) and (2)
[tex]\begin{gathered} AC^2+BC^2=DC^2+3.6^2+DC^2+6.4^2 \\ AC^2+BC^2=2DC^2+53.92 \end{gathered}[/tex]Using PT in triangle ABC
[tex]10^2=AC^2+BC^2[/tex]Equating above 2 equations
[tex]\begin{gathered} 100=2DC^2+53.92 \\ DC^2=23.04 \\ DC=4.8 \end{gathered}[/tex]Putting this value of DC in equation (2)
[tex]\begin{gathered} BC^2=4.8^2+3.6^2 \\ BC^2=23.04+12.96 \\ BC=6 \end{gathered}[/tex][tex]\begin{gathered} 10^2=AC^2+BC^2 \\ 100=AC^2+36 \\ AC=8 \end{gathered}[/tex]Final Answer
AC = 8
BC = 6
DC = 4.8
three more than the difference of five and a number
Answer:
5x+3
Step-by-step explanation:
Three more than means we add 3
The product of 5 and a number means some number multiplied by 5 call it 5x
so three more than 5x is 5x+3.
NO LINKS!! Please help me with this probability question. 4a
=====================================================
Explanation:
mu = 500 = mean
sigma = 100 = standard deviation
We'll need the z score for x = 620
z = (x - mu)/sigma
z = (620-500)/100
z = 1.20
The task of finding P(x > 620) is equivalent to P(z > 1.20)
Use a Z table or a Z calculator to find that
P(Z < 1.20) = 0.88493
which leads to
P(Z > 1.20) = 1 - P(Z < 1.20)
P(Z > 1.20) = 1 - 0.88493
P(Z > 1.20) = 0.11507
This converts to 11.507% and rounds to 11.5%
About 11.5% of the students score higher than a 620 on the SAT.
-------------------------
Another approach:
Open your favorite spreadsheet program. The command we'll be using is called NORMDIST. The template is this
NORMDIST(x, mu, sigma, 1)
x = 620 = critical valuemu = 500 = meansigma = 100 = standard deviationThe 1 at the end tells the spreadsheet to use a CDF instead of PDF. Use 0 if you want a PDF value.If you were to type in [tex]\text{=NORMDIST(620,500,100,1)}[/tex] then you'll get the area under the normal distribution to the left of x = 620
This means [tex]\text{=1-NORMDIST(620,500,100,1)}[/tex] will get us the area to the right of 620. The result of that calculation is approximately 0.11507 which leads to the same answer of 11.5% as found earlier.
When using a spreadsheet, don't forget about the equal sign up front. Otherwise, the spreadsheet will treat the input as text and won't evaluate the command.
-------------------------
Another option is to use a TI83 or TI84 calculator.
Press the button labeled "2nd" in the top left corner. Then press the VARS key. Scroll down to "normalcdf"
The template is
normalcdf(L, U, mu, sigma)
L = lower boundaryU = upper boundarymu = mean sigma = standard deviationThe mu and sigma values aren't anything new here. But the L and U are. In this case L = 620 is the lower boundary and technically there isn't an upper boundary since it's infinity. Unfortunately the calculator wants a number here, so we just pick something very large. You could go for U = 99999 as the stand in for "infinity". The key is to make sure it's more than 3 standard deviations away from the mean.
So if you were to type in [tex]\text{normalcdf(620,99999,500,100)}[/tex] then the calculator will display roughly 0.11507, which is in line with the other answers mentioned earlier.
As you can see, there are many options to pick from. Searching out "normal distribution calculator" or "z calculator" will yield many free options. Feel free to pick your favorite.
Put these numbers in order from least to greatest. -27/36, 6, 18/40, 5/20
We have four numbers. We have to know that negative numbers are "smaller" than positive numbers, and when numbers are far away from zero are even "bigger".
The least number is -27/36. It is a negative number.
We can also see that we have some fractions. A fraction is a part of "a whole".
So, as we can see 6 is not a fraction. Therefore, 6 is the greatest number from this list.
So we have the least and the greatest: -27/36 and 6, respectively.
We also need to compare 18/40 and 5/20. What fraction is bigger?
In order to compare them, we need to have two fractions with the same denominator. Then, the fraction with the greatest numerator is "bigger" than the other fraction.
Let us see:
If we divide the numerator and the denominator of 18/40 by 2, we have:
18/2 = 9
40/2 = 20
Then, the equivalent fraction is 9/20 (or 9/20 is equivalent to 18/40). Now, we can compare them:
9/20 and 5/20. So, which one is the greatest? The one with the greatest numerator: 9/20.
Our final list is this way, from least to the greatest as follows:
-27/36, 5/20, 18/40 (9/20), 6.
Write the the function f(x) = -5(x + 5)² - 2 in the form f(x) = ax² +bx+c
start expanding the squared expression using the square of a binomial,
[tex](a+b)^2=a^2+2\ast a\ast b+b^2[/tex]then,
[tex]\begin{gathered} (x+5)^2=x^2+2\ast5\ast x+5^2 \\ (x+5)^2=x^2+10x+25 \end{gathered}[/tex]replace in the original function
[tex]-5(x^2+10x+25)-2[/tex]apply distributive and simplify
[tex]\begin{gathered} -5x^2-50x-125-2 \\ -5x^2-50x-127 \end{gathered}[/tex]Answer:
[tex]-5x^2-50x-127[/tex]Look at the circle below. D = 6 3What is the area of the circle if the diameter is 6 centimeters? Use 3.14 for pi. A 18.84 square centimetersB 28.26 square centimeters C 37.68 square centimeters D 113.04 square centimeters
we are asked to determine the area of a circle with a diameter of 6 cm. To do that we will use the following formula for the area of a circle:
[tex]A=\frac{\pi D^2}{4}[/tex]Replacing the value of the radius:
[tex]A=\frac{\pi(6\operatorname{cm})^2}{4}[/tex]Replacing the value of pi:
[tex]A=\frac{3.14(6\operatorname{cm})^2}{4}[/tex]Solving the operations:
[tex]\begin{gathered} A=\frac{3.14(36cm^2)}{4} \\ \\ A=3.14(9cm^2)=28.26cm^2 \end{gathered}[/tex]Write an equation of the line that is parallel to the line y=4x+2 and y-3x=6 are parallel, perpendicular, or neither.
Given:
The point is (-2,3).
The parallel line is y=4x+2.
This is of the form
[tex]y=mx+b_1[/tex]where slope m=4.
We know that the slope of the parallel lines is equal.
Thus we get the slope m =4 for the required line.
Consider the line equaiton
[tex]y=mx+b[/tex]Substitute x= -2,y=3, and m =4 in the equation to find the value of b.
[tex]3=4(-2)+b[/tex][tex]3=-8+b[/tex]Adding 8 on both sides of the equation, we get
[tex]3+8=-8+b+8[/tex][tex]11=b[/tex]We get b=11.
Substitute m=4 and b=11 in the equation, we get
[tex]y=4x+11[/tex]Hence the line equation that passes through the point (-2,3) and parallel to y=4x+2 is
[tex]y=4x+11[/tex]An online bookstore is having a sale. All paperback books are $6.00 with a flat shipping fee of $1.25. you purchase "b" booms and your total is "c". What is the independent variable?$6.00"c" cost"b" books$1.25
Let:
c = total
a = cost of each book
w = flat shipping fee
Therefore, the total is given by:
[tex]c=ab+w[/tex]where:
b = number of books
[tex]c=6x+1.25[/tex]The independent variable is:
"b" books
40. Coach Hesky bought 3 new uniforms for his basketball team. He spent a total of $486. If the same amount was spent on each uniform, how much did he spend per player? .
new uniforms = 3
Total amount spent = $486
Amount spent per player = $486 /3 = $162
Write the equation of the line through the given point. Use slope-intercept form. (-5,2); perpendicular to y = - 2/3x +5
Explanation
Step 1
we have a perpendicular line, its slope is
[tex]\begin{gathered} y=\frac{-2}{3}x+5 \\ \text{slope}=\frac{-2}{3} \end{gathered}[/tex]two lines are perpendicular if
[tex]\begin{gathered} \text{slope}1\cdot\text{ slope2 =-1} \\ \text{then} \\ \text{slope}1=\frac{-1}{\text{slope 2}} \end{gathered}[/tex]replace
[tex]\text{slope1}=\frac{\frac{-1}{1}}{\frac{-2}{3}}=\frac{-3}{-2}=\frac{3}{2}[/tex]so, our slope is 3/2
Step 2
using slope=3/2 and P(-5,2) find the equation of the line
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-2=\frac{3}{2}(x-(-5)) \\ y-2=\frac{3}{2}(x+5) \\ y-2=\frac{3}{2}x+\frac{15}{2} \\ y=\frac{3}{2}x+\frac{15}{2}+2 \\ y=\frac{3}{2}x+\frac{19}{2} \end{gathered}[/tex]Given the following absolute value function sketch the graph of the function and find the domain and range.
ƒ(x) = |x + 3| - 1
pls show how did u solve it
In order to sketch the graph we need to find the vertex and two more points to connect with the vertex.
To do so set the inside of absolute value to zero:
x + 3 = 0x = - 3The y-coordinate of same is:
f(-3) = 0 - 1 = - 1.So the vertex is (- 3, - 1).
Since the coefficient of the absolute value is positive, the graph opens up, and the vertex is below the x-axis as we found above.
Find the x-intercepts by setting the function equal to zero:
|x + 3| - 1 = 0x + 3 - 1 = 0 or - x - 3 - 1 = 0x + 2 = 0 or - x - 4 = 0x = - 2 or x = - 4We have two x-intercepts (-4, 0) and (-2, 0).
Now plot all three points and connect the vertex with both x-intercepts.
Now, from the graph we see there is no domain restrictions but the range is restricted to y-coordinate of the vertex.
It can be shown as:
Domain: x ∈ ( - ∞, + ∞),Range: y ∈ [ - 1, + ∞)Answer:
Vertex = (-3, -1).y-intercept = (0, 2).x-intercepts = (-2, 0) and (-4, 0).Domain = (-∞, ∞).Range = [-1, ∞).Step-by-step explanation:
Given absolute value function:
[tex]f(x)=|x+3|-1[/tex]
The parent function of the given function is:
[tex]f(x)=|x|[/tex]
Graph of the parent absolute function:
Line |y| = -x where x ≤ 0Line |y| = x where x ≥ 0Vertex at (0, 0)Translations
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
Therefore, the given function is the parent function translated 3 units left and 1 unit down.
If the vertex of the parent function is (0, 0) then the vertex of the given function is:
⇒ Vertex = (0 - 3, 0 - 1) = (-3, -1)
To find the y-intercept, substitute x = 0 into the given function:
[tex]\implies \textsf{$y$-intercept}=|0+3|-1=2[/tex]
To find the x-intercepts, set the function to zero and solve for x:
[tex]\implies |x+3|-1=0[/tex]
[tex]\implies |x+3|=1[/tex]
Therefore:
[tex]\implies x+3=1 \implies x=-2[/tex]
[tex]\implies x+3=-1 \implies x=-4[/tex]
Therefore, the x-intercepts are (-2, 0) and (-4, 0).
To sketch the graph:
Plot the found vertex, y-intercept and x-intercepts.Draw a straight line from the vertex through (-2, 0) and the y-intercept.Draw a straight line from the vertex through (-4, 0).Ensure the graph is symmetrical about x = -3.Note: When sketching a graph, be sure to label all points where the line crosses the axes.
The domain of a function is the set of all possible input values (x-values).
The domain of the given function is unrestricted and therefore (-∞, ∞).
The range of a function is the set of all possible output values (y-values).
The minimum of the function is the y-value of the vertex: y = -1.
Therefore, the range of the given function is: [-1, ∞).
please give a VERY SHORT EXPLANATION NOT LONG! i inserted a picture of the question
If the amount of time spent is lesser than or equal to 250, so the price is $29, so we have the first part of the piecewise equation:
[tex]f(x)=29,\text{ x <= 250}[/tex]Then, for an amount of time greater than 250, the extra minutes are charged by 0.35 per minute, and this extra cost will add the fixed cost of $29, so the second part of the equation is:
[tex]f(x)=29+(x-250)0.35,\text{ x>250}[/tex]The option that shows the correct piecewise equation is option A.
Compute P(7,4)
From probability and statistics
The resultant answer from computing P(7,4) from probability and statistics is 840.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.So, P(7,4):
This is a permutation and can be calculated as:
ₙPₓ= n! / (n - x)!Here, n = 7 and x = 4Put the values in the given formula:
P(7, 4) = 7! / (7 - 4)!P(7, 4) = 7! / 3!P(7, 4) = 840Therefore, the resultant answer from computing P(7,4) from probability and statistics is 840.
To read more about probability:
brainly.com/question/25870256
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