Your pet groomer charges according to how much your dog weighs. For a dog that weighs 20 pounds or less, the groomer charges $25. For a dog that weighs more than 20 pounds and less than 50 pounds, the groomer charges $45. For any dog that weighs 50 pounds or more, the groomer charges $45 plus an additional $1 for each pound over 50. Using this situation, match each piece of the piecewise function with the corresponding domain restriction.
Answers
Explanation
Given: The pet groomer charges according to the dog weights as follows:
[tex]\begin{gathered} If\text{ }weight\leqslant20,then\text{ }charge=\text{ \$}25 \\ \\ If\text{ }weight\text{ }is\text{ }between\text{ }20\text{ }and\text{ }50,then\text{ }charge=\text{ \$}45 \\ \\ If\text{ }weight\geqslant50,then\text{ }charge=\text{ \$}45+\text{ \$}1\text{ }for\text{ }each\text{ }pound\text{ }over\text{ }50 \end{gathered}[/tex]Required: To match each piece of the piecewise function with the corresponding restriction.
This is achieved thus:
==> For the first function
[tex]\begin{gathered} f(x)=25 \\ \\ \text{ This function satisfies the condition for x is greater than zero but less than or equal to 20} \end{gathered}[/tex]==> For the second function
[tex]\begin{gathered} f(x)=45 \\ \\ \text{ This function satisfies the condition for x is greater than 20 but less than 50.} \end{gathered}[/tex]==> For the third function
[tex]\begin{gathered} f(x)=45+1(x-50) \\ \\ \text{ This function satisfies the condition for x is greater than or equal to 50} \end{gathered}[/tex]Hence, the answers are:
f(x) = 25 ==> 0 less than x less than or equal to 20
f(x) = 45 ==> 20 less than x less than 50
f(x) = 45 + 1(x - 50) ==> x greater than or equal to 50.
Related Questions
How many standard deviations is each student away from hiir school average? If the student GPA is higher than his school average, enter this as a positive number. If the student GPA is lower than his school average, enter this as a negative number.
Answers
Part A: Thuy
mean (average) of 2.8, and a standard deviation of 0.8
Thuy's score is 2.5
Calculate the z-score and we have
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{2.5-2.8}{0.8} \\ z=\frac{-0.3}{0.8} \\ z=-0.375 \end{gathered}[/tex]Therefore, Thuy is -0.375 standard deviations away from the mean.
Part B: Vichet
Doing the same as above, we have the following values
x = 86
μ = 78
σ = 10
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{86-78}{10} \\ z=\frac{8}{10} \\ z=0.8 \end{gathered}[/tex]Therefore, Vichet is 0.8 standard deviations away from the mean.
Part C: Kamala
x = 8.5
μ = 8.4
σ = 0.5
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{8.5-8.4}{0.5} \\ z=\frac{0.1}{0.5} \\ z=0.2 \end{gathered}[/tex]Therefore, Kamala is 0.2 standard deviations away from the mean.
The vertex of this parabola is at (-2, 5). Which of the following could be itsequation?4111-5(-2,5)10O A. y=3(x+ 2)² +5OB. y= 3(x-2)²-5OC. y= 3(x-2)² +5OD. y=3(x+2)²-5015
Answers
Given:
The vertex of this parabola is at (-2, 5).
Required:
Find the equation of the parabola.
Explanation:
The equation of the parabola in vertex form is:
[tex]y=a(x-h)^2+k[/tex]We can observe from the options that the value of a = 3 and vertex (h,k) is given (-2,5).
So the equation of the parabola will be:
[tex]y=3(x+2)^2+5[/tex]Young's rule find dosage for child. Adult dosage is 75mg. And the age of the child is 12. Calcuate child dosage in my.C=ad________ (a+12)
Answers
Given:
The adult dosage is 75mg and the age of the child is 12.
The formula to find the child's dosage is
[tex]C=\frac{ad}{a+12}[/tex]where a is the child's age, d is the usual adult's dosage and C is the child's dosage.
Required:
We need to find the child's dosage.
Explanation:
Consider the formula to find the child's dosage.
[tex]C=\frac{ad}{a+12}[/tex]Substitute a =12 and d =75 in the formula.
[tex]C=\frac{12\times75}{12+12}[/tex][tex]C=\frac{900}{24}=37.5\text{ mg.}[/tex]Final answer:
The child's dosage is 37.5mg.
In a cattle form of 10 cows and 5 pigs, two cattle are tested. What is the probability of choosing a cow and a pig for testing?10/5310/2110/10510/51
Answers
The Solution:
Given that:
Number of cows = 10
Number of pigs = 5
Total number of animals = 15
[tex]\begin{gathered} Pr(\text{Cow)}=\frac{\text{ number of cows}}{\text{ Total number of animals}}=\frac{10}{15} \\ \\ Pr(Pig\text{)}=\frac{\text{ number of pigs}}{\text{ Total number of animals}}=\frac{5}{15} \end{gathered}[/tex]We are required to find the probability of selecting a cow and a pig for testing.
[tex]\begin{gathered} Pr(\text{Cow and Pig)=Pr(Cow and Pig) or Pr(Pig and Cow)} \\ =2\times\text{ Pr(Cow and Pig)}=2\times\frac{10}{15}\times\frac{5}{14}=\frac{10}{3\times7}=\frac{10}{21} \end{gathered}[/tex]Therefore, the correct answer is [option 2]
Simplify.-1/2 (8w – 10x - 2) A -4w + 5x + 1 B 4w -5x - 1 C 4W-5x D -4w + 5x
Answers
Explanation:
To simplify we have to multiply each term in the parenthesis by -1/2:
[tex]-\frac{1}{2}(8x-10x-2)=-\frac{1}{2}\cdot8w-(-\frac{1}{2})\cdot10x-(-\frac{1}{2})\cdot2=-4w+5x+1[/tex]Answer:
A. -4w + 5x + 1
Indicate which sets are disjoint to the given set
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If the intersection of two sets is a null set or an empty set, then two sets A and B are disjoint sets. The intersection of a set is therefore empty.
Explain about the disjoined set?Disjoint sets are a pair of sets that do not share any elements. For instance, the sets A=2,3 and B=4,5 are not connected sets. However, set C=3,4,5 and set C=3,6,7 are not disjoint since 3 is a common element in both sets C and D.
Now that we are clear on the disjoint set's definition, let's go on to talking about some more important topics, such the notation and Venn diagram related to it. A B = is the notation used for this particular set. As an illustration, suppose A = 1, 2, 3, and B = 4, 5, 6, 7. A + B = then.
To learn more about disjoined set refer to:
https://brainly.com/question/28165517
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opposite value of -2.
Answers
The opposite value of a number can be found by switching the signal of the value.
So, to find the opposite value of -2, we need to switch the negative signal by a positive signal.
Therefore the opposite value of -2 is equal to 2.
The graph of 2x-3y=4 is shown. What is the domain ofthis function?
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The graph of the function is
As you can see in the graph, the function is linear, that is, it is a line that continues indefinitely in each direction.
By definition, The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
Regarding the domain of a linear function, any real number can be substituted for x and get a meaningful output.
As for the range of a linear function, for any real number, you can always find an x value that gives you that number for the output.
Therefore, the domain and range of this function are all real numbers.
[tex]\begin{gathered} D_f=\R \\ R_f=\R \end{gathered}[/tex]Solve the following system of linear equations using elimination -x+2y=-7 -2x+3y=-1
Answers
We are asked to solve via the elimination method the following system:
- x + 2 y = - 7
- 2 x + 3 y = - 1
so we pick to eliminate the term in x. and notice that in order to do that, we need to multiply the first equation by (-2) so our x term in it becomes "2 x" which is the exact OPPOSITE of the term "- 2 x " in the second equation.
Then we multiply the first equation by (-2) as shown below:
(-2) (- x + 2 y ) = (-2) ( - 7 )
2 x - 4 y = 14
now we combine term by term this transformed equation with the second equation in the system:
2 x - 4 y = 14
- 2 x + 3 y = - 1
____________
0 - 4 y + 3 y = 14 - 1
- y = 13
divide bith sides by (-1) to isolate y completely
y = 13 / (-1)
y = -13
Now we use this result in the original first equation to solve for x:
- x + 2 y = - 7
- x + 2 (-13) = - 7
- x - 26 = -7
add 26 to both sides
- x = 26 - 7
- x = 19
divide both sides by (-1) to isolate x completely
x = 19 / (-1)
x = - 19
Then our answer is: x = -19 and y = -13 which makes the coordinate pair: (-19, -13)
8a-4b=20 5a-8b=62What is a? What is b?
Answers
The given system of equations is:
8a - 4b = 20...............(1)
5a - 8b = 62...............(2)
Multiply equation (1) by 2
16a - 8b = 40........................(3)
Subtract equation (2) from equation (3)
11a = -22
a = -22/11
a = -2
Substitute a = -2 into equation (1)
8a - 4b = 20
8(-2) - 4b = 20
-16 - 4b = 20
4b = -16-20
4b = -36
b = -36/4
b = -9
Therefore the solution to the system of equations is:
a = -2 and b = -9
kyra brought a trick coin that landed on heads with a probability of 0.4. which frequency table would kyra most likely generate by flipping the coin many times ?
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Since the probability of landing heads with the trick coin is 0.4, we have:
[tex]\begin{gathered} P(heads)=0.4=\frac{36}{90} \\ \\ \Rightarrow P(tails)=1-P(heads)=1-\frac{36}{90}=\frac{54}{90} \end{gathered}[/tex]therefore, the first frequency table represents the behavior of the trick coin.
What is the area watered by the sprinkler? I can’t figure it out.
Answers
We are asked to determine the area of a circular sector. To do that we will use the following formula:
[tex]A=\frac{r^2\theta}{2}[/tex]Where:
[tex]\begin{gathered} r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}[/tex]Now, we convert the angle of 85° to radians using the following conversion factor:
[tex]1\pi=180\text{degrees}[/tex]Now, we multiply by the conversion factor:
[tex]\theta=85\times\frac{\pi}{180}=\frac{17\pi}{36}[/tex]Now, we substitute in the formula for the area:
[tex]A=\frac{(5m)^2(\frac{17\pi}{36})^2}{2}[/tex]Substituting the value of pi for 3.14
[tex]A=\frac{(5m)^2(\frac{17(3.14)}{36})^2}{2}[/tex]Solving the operations:
[tex]A=18.5m^2[/tex]Therefore, the area is 18.5 square meters.
In 2015, there were 759 laptops at lightning high school. Starting in 2016, the school bought 75 more laptops at the end of each year. The function T(x)=75x+759 can be used to determine the total number of laptops at the school x year after 2015. What is the project total number of laptops at Lightning High School at the end of 2020?
Answers
the total number of laptops ar lightning school at the end of 2020 is 1134
Explanation
Step 1
Let
x represents the year after 2015=2020-2015=
x=5
In 2015, there were 759 laptop, Starting in 2016, the school bought 75 more laptops at the end of each year,it is
[tex]\begin{gathered} T(x)=75x+759 \\ \end{gathered}[/tex]let's check
in 2015
[tex]\begin{gathered} x=0 \\ T(0)=75\cdot0+759 \\ T(0)=759 \end{gathered}[/tex]Step 2
now, we need the total for 2020
[tex]\begin{gathered} x=\text{ number of years after 2015} \\ x=2020-2015=5 \\ \text{replace} \\ T(x)=75\cdot x+759 \\ T(5)=75\cdot5+759 \\ T(5)=375+759 \\ T(5)=1134 \end{gathered}[/tex]Hence, the total number of laptops ar lightning school at the end of 2020 is 1134
The last answer option is D = The number of years until the population reaches 2 million .I was just not able to fit it in . I just need a brief explanation with the answer
Answers
where
t = numbers of years since 1990
Therefore,
523 represents the y-intercept which is the predicted number of dear in the united states in 1990.
= Initial Knowledge Check Divide 4 ? - 6 2- 23 Simplify your answer as much as p
Answers
The given expression is
[tex]\frac{4z^7-6z^5}{2z^3}[/tex]First, we factor out the third power of z, and factor 2.
[tex]\frac{2z^3(2z^4-3z^2)}{2z^3}[/tex]Now, we simplify to get the final expression
[tex]2z^4-3z^2[/tex]The divisions made were
[tex]\begin{gathered} \frac{4z^7}{2z^3}=2z^4 \\ \frac{6z^5}{2z^3}=3z^2 \end{gathered}[/tex]Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function bewritten using function notation?
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If x is the independent variable, we have that y is the dependent variable.
Using function notation, let's say that y is our function, that is, y = f(x).
So we need to isolate the variable y in the equation:
[tex]\begin{gathered} 9x+3y=12 \\ 3y=12-9x \\ y=\frac{12-9x}{3} \\ y=4-3x \end{gathered}[/tex]So our function is:
[tex]f(x)=-3x+4[/tex]Can u help me answer question 23 BTW this is lesson 6 the distributive property
Answers
For the expression
3(x + 7) we simply multiply 3 by each term inside the parenthesis:
3(x + 7) = 3 · x + 3 · 7
= 3x + 21
Answer: 3(x + 7) = 3x + 21Find decimal notation for 800%.800% =
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In mathematics, a percentage is a number or ratio expressed as a fraction of 100
For example
A% is
[tex]A\text{ \%=}\frac{\text{ A}}{100}[/tex]The question was given to figure out
[tex]800\text{ \%}[/tex]Therefore,
[tex]\begin{gathered} 800\text{ \%= }\frac{\text{800}}{100} \\ 800\text{ \%= 8} \end{gathered}[/tex]Hence,
800 % = 8
I need help with unions, intersections, and complements involving 2 sets
Answers
Here, we want to get the set resulting from the given set operations
a) This set is the complement of the intersection of the subsets C and D
The intersection refers to that set that has its members as the elements present in both subsets
The intersection here is;
[tex]\mleft\lbrace8\mright\rbrace[/tex]Now, the complement here are the other elemnts present in the universal set
We have this as;
[tex]\mleft\lbrace1,2,4,7\mright\rbrace[/tex]b) Here, we want to get a union
The complement of set C are the elements that not present in set C but are in the universal set
So, the union here is are the list of elements in both set, without no repetitions
[tex]\begin{gathered} C^{\prime}\text{ = }\mleft\lbrace2,4\mright\rbrace \\ D\text{ = }\mleft\lbrace2,8\mright\rbrace \\ C^{\prime}\text{ U D = }\mleft\lbrace2,4,8\mright\rbrace \end{gathered}[/tex]If Jim could drive a Jetson's flying car at a coristant speed of 370 km/hr across oceans and space, approximately how long (in Millions of years, in 10^6 years)would he take to drive to a nearby star that is 12.3 light-years away? Use 9.461 x 10^12 km/light-year and 8766 hours per year (365.25 days).
Answers
Given:
Jim could drive a Jetson's flying car at a constant speed of 370 km/hr
We will find the time could take to drive to a nearby star that is 12.3 light-years away
Given light year = 9.461 x 10^12 km
And the number of hours per year = 8766 hours
The time = Distance over the speed
so, the time =
[tex]\frac{12.3\times9.461\times10^{12}}{370}=3.145\times10^{11}hours[/tex]Divide the answer by the number of hours per year
[tex]\frac{3.145\times10^{11}}{8766}=35.88\times10^6years=35.88\text{ }Millionsofyears[/tex]So, the answer will be 35.88 Millions of years
Use the format below to write a sequence of rigid motions and dilation that takes square ABCD to square EFGH. Remember that corresponding points in the names of the figures need to correspond in your transformations.Your transformations should take this form: translate ___ by directed line segment __ which will take point _ to point _. Then, rotate the image using center _ by angle __. Finally, ___ by scale factor 2/5.
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Translate square ABCD by the direct line segment AE, which will take point A to point E. Then, rotate the image using center point A by angle 135° (=90°+45°). Finally, scale square ABCD by scale factor 2/5.
For how many integers x is the equation 22x+1 = 3x - 3 true?
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REmember that
the speed is equal to divide the distance by the time
so
speed=d/t
in this problem we have
speed=3.6x10^4 miles/hour
d=7.2x10^8 miles
substitute in the formula
[tex]3.6\cdot10^4=\frac{7.2\cdot10^8}{t}[/tex]solve for t
[tex]\begin{gathered} 3.6\cdot10^4=\frac{7.2\cdot10^8}{t} \\ t=\frac{7.2\cdot10^8}{3.6\cdot10^4} \\ t=2.0\cdot10^4\text{ hours} \end{gathered}[/tex]therefore
answer is option DFactor W^2 + 24W + 23
Answers
Here, we want to factorizze the given expression
To do this, we will have to rewrite the mid-expression
We need two values of variable w which when added will give 24W and which when multiplied will give 23w^2
We have this as;
[tex]\begin{gathered} w^2+24w+23=w^2+w\text{ + 23w + 23} \\ =\text{ w(w+1) + 23(w+1)} \\ =\text{ (w+23)(w+1)} \end{gathered}[/tex]What is the vertex of (3,-3)
Answers
Question:
Solution:
Note that the standard quadratic form of a quadratic polynomial is given by the following equation:
[tex]ax^2+bx+c\text{ = }y[/tex]so that, the vertex form of a quadratic equation is
[tex]y\text{ = a(}x-h)^2+k[/tex]where (h,k) is the so-called vertex. Thus, according to this, we can say that the equation that represents a vertex (h,k)=(3,-3) is
[tex]y\text{ = 5(}x-3)^2\text{-}3[/tex]then, we can conclude that the correct answer is:
[tex]y\text{ = 5(}x-3)^2\text{-}3[/tex]what expression can be used to suntract 2/3 - 4/9
Answers
From the options, we have that:
[tex]\frac{2}{3}\cdot\frac{3}{3}=\frac{6}{9}[/tex]Then, 6/9 is an equivalent fraction to 2/3. Therefore, the expression that can be used to subtract 2/3 - 4/9 is:
[tex]\frac{6}{9}-\frac{4}{9}[/tex]That is. the answer is option C.
mark me best !!
Is either x=9 or = 15 a solution to ×-3= 12
Answers
Is either x=9 or = 15 a solution to ×-3= 12
x-3 = 12
x= 12+3
x= 15
______________
Answer
x= 15
_______________
x=9
×-3= 12
9-3 = 12
6 ≠ 12
what is the perimeter? I have a photo attached of the problem.
Answers
Ok the solution is related to the fact that the sides of the trapezoid are tangents to the circle. This means that if we divide each of the four sides of the trapezoid by the point where they touch the circle we have 4 pair of segment with the same size. What I mean is that:
[tex]\begin{gathered} \bar{RS}=\bar{RQ}=8 \\ \bar{QP}=\bar{PW}=7 \\ \bar{WV}=\bar{VU}=11 \\ \bar{TU}=\bar{TS}=12 \end{gathered}[/tex]Therefore the perimeter is given by:
[tex]8+8+7+7+11+11+12+12=76[/tex]-Find the x and y intercepts of the equation: 2x – 7y = – 56The intercepts are:x intercept =,0)y intercept = (0,
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
2x - 7y = - 56
Step 02:
x-intercept:
y = 0:
2x - 7(0) = - 56
2x = 56
x = 56 / 2
x = 28
( 28 , 0)
y-intercept:
x = 0:
2(0) - 7y = 56
- 7y = 56
y = 56 / (-7)
y = - 8
( 0 , - 8)
The answer is:
x-intercept: ( 28 , 0)
y-intercept: ( 0 , - 8)
the polynomial of degree 3 p x have the root of Multiplicity 2 at x equals 3 and a root of Multiplicity 1 at x equals negative 5 the Y intercept is y equals -27 find a formula for p x
Answers
Answer:
P(x) = (x - 3 )^2 (x + 5) - 72
Explanation:
We are told that the polynomial has a root of multiplicity 2 at x = 3. This means (x - 3)^2 is present in the polynomial. Alos, the root at x = -5 has a multiplicity 1, meaning (x + 5) is also present; therefore, we can write our polynomial as
[tex]P(x)=(x-3)^2(x+5)[/tex]Now, the y-intercept of P(x) is -27, meaning
[tex]P(0)=-27[/tex][tex]\begin{gathered} P(0)=(0-3)^2(0+5)+c=-27 \\ 9\cdot5+c=-27 \\ 45+c=-27 \\ \boxed{\therefore c=-72.} \end{gathered}[/tex]Hence, the equation for the polynomial is
Ron is planning for the back to school rush at his store. Last year he estimated that he would need 168 notebooks. Explain how Ron can find the percent error of his estimate
Answers
To calculate the percent error, he will need the real value and the estimated value.
In this problem, we only know the value of the estimated value.
If we would know both values just substitute them in the equation and solve for percent error.
[tex]\text{ Percent error = }\frac{estimated\text{ value - real value}}{estimated\text{ value}}\text{ x 100}[/tex]