The given transformation is 8 units left.
The pre-image vertices are A(1,-4), B(1,-6), C(5,-6), and D(5,-4).
Using the transformation, we have:
[tex]\begin{gathered} A^{\prime}(1-8,-4)=A^{\prime}(-7,-4) \\ B^{\prime}(1-8,-6)=B^{\prime}(-7,-6) \\ C^{\prime}(5-8,-6)=C^{\prime}(-3,-6) \\ D^{\prime}(5-8,-4)=D^{\prime}(-3,-4) \end{gathered}[/tex]The image below shows the graph of the image
five pounds of sugar cost $4.05 how much sugar do you get per dollar? round your answer to the nearest hundredth, if necessary.
Given:
The cost of five pounds of sugar is $4.05.
Explanation:
To determine the amount of sugar that individual get for 1 dollar, divide 4.05 by 5.
Divide 4.05 by 5 to determine the amount of sugar individual get per dollar.
[tex]\frac{4.05}{5}=0.81[/tex]
Suppose you are choosing at random from the numbers 1 through 12 (inclusive). If the event E is "the number is even," find the set representing E. Express your answer as a bracketed set in the form {a,b,c,d}.
The set numbers from 1 to 12(inclusive) is:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
The set even numbers are:
2, 4, 6, 8, 10, 12
Given that the event E is "the number is even"
Therefore, the set representing the event E as a bracketed set is:
[tex]E=\mleft\lbrace2,4,6,8,10,12\mright\rbrace[/tex]
ill send a pic of the question :) plsss help me
We have the next information
4 cups of water
1 cup lemon concentrate
in total, we have 5 cups of lemonade
5 ----- 100%
1 ------ x
x is the percentage of lemon concentrate
[tex]x=\frac{100}{5}=20[/tex]the percentage of lemon concentrate in the lemonade is 20%
Solve each system of equations please show your work! 3x+y-2z=22 x+5y+z=4 x=-3z
The solution of the system of equations are x = - 6 , y = 44 and z = 2
Given,
The system of equations;
3x + y - 2z = 22
x + 5y + z = 4
x = -3z
We have to solve the given equations;
Substitute x = -3z in both equations;
3x + y - 2z = 22
⇒ 3 × -3z + y - 2z = 22
⇒ - 9z + y - 2z = 22
⇒ - 11z + y = 22
And,
x + 5y + z = 4
⇒ - 3z + 5y + z = 4
⇒ 5y - 2z = 4
Solve the equations - 11z + y = 22 and 5y - 2z = 4
We get,
⇒ y = 44 and z = 2
So, x = - 3z
⇒ x = - 3 × 2
⇒ x = - 6
Thus, The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
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Find the rule for the following sequence. Then find the 45th term.
Answer:
[tex]a_{45}=221[/tex]Step-by-step explanation:
Arithmetic sequences are represented by the following equation;
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ where, \\ a_1=\text{ first term} \\ d=\text{ common difference} \\ n=\text{ nth term} \end{gathered}[/tex]The common difference is the difference between the consecutive terms:
[tex]\begin{gathered} d=6-1=5 \\ d=11-6=5 \\ d=16-11=5 \end{gathered}[/tex]Therefore, the equation that represents this sequence:
[tex]a_n=1+5(n-1)[/tex]Now, if we want to find the 45th term, substitute n=45:
[tex]\begin{gathered} a_{45}=1+5(45-1) \\ a_{45}=1+5*(44) \\ a_{45}=1+220 \\ a_{45}=221 \end{gathered}[/tex]Coach De Leon purchases sports equipment. Basketballs cost $20.00 each and soccer balls cost $18.00 each. He has a budget of $150.00. The graph shown below represents the number of basketballs and soccer balls he can buy given his budget constraint.
Solution:
Cost of a basketball = $20.00
Cost of a soccer ball = $18.00
Budget of Coach De Leon = $150.00
Check the given combinations can be purchased within the budget.
3 soccer balls, basket
An electrician charges $25 per hour plus a one-time service fee of $50. Write an equation to
represent the cost, y, he charges for x hours of service. How much would he charge for 3 hours of
service.
The equation that represents the cost and the charges for the service is y = $25x + $50. And the he charges $125 for 3 hours of service.
Equation:
An equation state that the value of two mathematical expressions is equal.
For example,
2x + 5 = 7
is an equation.
Given,
An electrician charges $25 per hour plus a one-time service fee of $50.
Here we need to find the equation for the given situation and we have also find the charge for the 3 hour of service.
Let us consider the equation of the line y = mx + c, where m represents the constant change and c represents the fixed constant.
While we apply these equation to the given situation we can get the value of
m = $25
And the value of
c = $50.
Therefore, the equation of the situation is
y = $25x + $50.
We have already now that the y represents the cost and the x represents the hour of service.
Now we have to find the service charge for 3 hours,
So we have to apply the value of x as 3 then we get,
=> y = $25 (3) + $50
=> y = $75 + $50
=> y = $125
Therefore, the cost for 3 hours is $125.
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27. A race consists of 7 women and 10 men. What is the probability that the top three finishers were(a) all men (b) all women (c) 2 men and 1 woman (d) 1 man and 2 women
Given 7 women and 10 men;
a) the top 3 are all men:
[tex]\begin{gathered} ways\text{ to choose 3 men out of 10 men is:} \\ 10C_3=\frac{10!}{(10-3)!3!} \\ \Rightarrow\frac{10!}{7!3!}=\frac{10\times9\times8\times7!}{7!\times3\times2\times1} \\ \Rightarrow\frac{10\times9\times8}{3\times2\times1}=120 \\ \text{ways to choose 3 men from 17 people(10men +7women) is:} \\ 17C_3=\frac{17!}{(17-3)!3!} \\ \Rightarrow\frac{17!}{14!\times3!}=\frac{17\times16\times15\times14!}{14!\times3\times2\times1} \\ \Rightarrow\frac{17\times16\times15}{3\times2\times1}=680 \end{gathered}[/tex]Therefore, the probability that the top 3 are all men is:
[tex]P_{all\text{ men}}=\frac{120}{680}=0.1765[/tex]b) the top 3 are all women:
[tex]\begin{gathered} \text{ways to choose 3 women from 7 women is:} \\ 7C_3=35 \\ \text{ways to choose 3 women from 17 people is:} \\ 17C_3=680 \end{gathered}[/tex]Therefore, the probability that the top 3 are all women is:
[tex]P_{\text{all women}}=\frac{35}{680}=0.0515[/tex]c) 2 men and 1 woman;
[tex]\begin{gathered} ways\text{ to choose 2 men out of 10 men is:} \\ 10C_2=45 \\ \text{ways to choose 1 woman from 7 women is:} \\ 7C_1=7 \\ \text{Thus, ways to choose 2 men and 1 woman }=45\times7=315 \end{gathered}[/tex]Therefore, the probability that the top 3 finishers are 2 men and 1 woman is:
[tex]P=\frac{315}{680}=0.4632[/tex]d) 1 man and 2 women;
[tex]\begin{gathered} \text{ways to choose 1 man from 10 men is;} \\ 10C_1=10 \\ \text{ways to choose 2 women from 7 women is:} \\ 7C_2=21 \\ \text{Thus, ways to choose 1 man and 2 women is 10}\times21=210 \end{gathered}[/tex]Therefore, the probability that the top 3 finishers are 1 man and 2 women is:
[tex]P=\frac{210}{680}=0.3088[/tex]Convert 6 kg per inch to g per m 6 points
We can do this conversion in this way:
[tex]\frac{6\operatorname{kg}}{i}\cdot\frac{1000gr}{\operatorname{kg}}\cdot\frac{1i}{0.0254m}=23622.047g/m[/tex]Then, the answer is 23622.047g/m.
Find the sum of the arithmetic series given a1 =2, an =35 an n = 12
Given:
[tex]a_1=2,a_n=35,n=12[/tex]Required:
Find the sum of the arithmetic series.
Explanation:
The sum of the arithmetic series when the first and the last term is given by the formula.
[tex]S_n=\frac{n}{2}(a_1+a_n)[/tex]Substitute the given values in the formula.
[tex]\begin{gathered} S_n=\frac{12}{2}(2+35) \\ =6(37) \\ =222 \end{gathered}[/tex]Final Answer:
Option D is the correct answer.
If I take a 45 min. break at 2:15pm what time do I come back?
The break time is 2:15 pm.
The time interval for break is 45 min.
Determine the time at which interval ends.
[tex]\begin{gathered} 2\colon15+00.45=2\colon60 \\ =3\colon00 \end{gathered}[/tex]So break ends (individual come back) at 3:00.
What’s the correct answer answer asap for brainlist
Answer:
Progressive Era
Step-by-step explanation:
A person randomly selects one of four envelopes. Each envelope contains a check that the person gets to keep. However, before the person can select an envelope, he or she must pay $ 15 to play. Determine the person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks.
The person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks is $5.
In the given question,
A person randomly selects one of four envelopes.
Each envelope contains a check that the person gets to keep.
However, before the person can select an envelope, he or she must pay $15 to play.
We have to determine the person's expectation if two of the envelopes contain $5 checks and two of the envelopes contain $35 checks.
As we know that when the person have to select envelope then they have to pay $15.
Total number of envelop = 4
From the 4 envelop 2 have $5 each and 2 have $35 each.
So the probability of getting envelop of $5 = 2/4 = 1/2
Probability of getting envelop of $35 = 2/4 = 1/2
Let x be the amount a person gets after selecting the envelop.
So E(x) = $5×1/2 + $35×1/2
Taking 1/2 common on both side
E(x) = 1/2 ($5+$35)
E(x) = 1/2×$40
E(x) = $20
But he have to pay $15 before selecting the envelop.
So required expectation = $20−$15 = $5
Hence, the person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks is $5.
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hello this the the problem Im stuck on. I need to know where to plot the point on the graph aswell. ty
Given:
The rent for trucks is $3750.
The additional charge per ton of sugar is $150.
To write: The equation relating the total cost C and amount of sugar S.
Explanation:
The equation represents the total cost C and the amount of sugar S is given by,
[tex]C=3750+150S[/tex]Let us find the three coordinates to plot the graph.
When
[tex]S=0[/tex]Then,
[tex]\begin{gathered} C=3750+150(0) \\ =3750 \end{gathered}[/tex]When
[tex]S=1[/tex]Then,
[tex]\begin{gathered} C=3750+150 \\ =3900 \end{gathered}[/tex]When
[tex]S=2[/tex]Then,
[tex]\begin{gathered} C=3750+150(2) \\ =3750+300 \\ =4050 \end{gathered}[/tex]So, the coordinates are,
[tex](0,3750),(1,3900),(2,4050)[/tex]The equation represents the total cost C and the amount of sugar S is given by,
[tex]C=3750+150S[/tex]The graph is,
11. Let the supply and demand functions for sugar is given by the following equations. Supply: p = 0.4x Demand: p = 100 - 0.4x (a) Find the equilibrium demand.
SOLUTION:
Step 1:
In this question, we are given the following:
Let the supply and demand functions for sugar be given by the following equations. Bye
Supply: p = 0.4x
Demand: p = 100 - 0.4x
a) Find the equilibrium demand.
Step 2:
At Equilibrium,
[tex]\begin{gathered} \text{Supply}=\text{ Demand} \\ 0.\text{ 4 x = 100 - 0. 4 x} \end{gathered}[/tex]collecting like terms, we have that:
[tex]\begin{gathered} 0.4\text{ x + 0. 4 x = 100} \\ 0.8\text{ x = 100} \end{gathered}[/tex]Divide both sides by 0.8, we have that:
[tex]\begin{gathered} x\text{ = }\frac{100}{0.\text{ 8}} \\ x\text{ = 125} \end{gathered}[/tex]
Step 3:
Recall that:
[tex]\begin{gathered} \text{Equilibrium Demand : p = 100 - 0. 4 x } \\ we\text{ put x = 125, we have that:} \\ p\text{ = 100 - 0. 4 (125)} \\ p\text{ =100 -50} \\ p\text{ = 50} \end{gathered}[/tex]CONCLUSION:
Equilibrium Demand:
[tex]p\text{ = 50 units}[/tex]Match each function on the left with the ordered pairs on the right.
We have to match the functions with the corresponding ordered pair.
The easiest way is to pick an ordered pair and replace (x,y) in the function to verify if the equality stands or not. If it does stand, then the ordered pair is part of the function.
Then, we start with (-8,9) and function y = 6x+9. Replacing x and y, we get:
[tex]\begin{gathered} (x,y)=(-8,9) \\ y=6x+9 \\ 9=6\cdot(-8)+9 \\ 9=-48+9 \\ 0=-48\longrightarrow\text{False} \end{gathered}[/tex]As this equation does not verify for (-8,9), this ordered pair does not belong to the function.
We repeat the same process with the next function, y = -9x-1:
[tex]\begin{gathered} (x,y)=(-8,9) \\ y=-9x-1 \\ 9=-9(-8)-1 \\ 9=72-1 \\ 9=71\longrightarrow\text{False} \end{gathered}[/tex]As with the previous function, the equation does not verify.
The next function is y = -1x+1:
[tex]undefined[/tex]Previous Answer: 12 Things to consider! • What are the solid/solids of the figure? • What are you being asked to find? • What are you being given? The volume is 60mi?. What is the height of the Pyramid of Giza?
The length of base is l = 5.
The width of base is b = 4.
The volume of pyramid is V = 60.
The formula for the volume of the pyramid is,
[tex]V=\frac{1}{3}l\cdot b\cdot h[/tex]Determine the height of the pyramid.
[tex]\begin{gathered} 60=\frac{1}{3}\cdot5\cdot4\cdot h \\ h=\frac{60\cdot3}{20} \\ =9 \end{gathered}[/tex]So height of the pyramid is 9 mi.
When you multiply possible options in each scenario to get the total number of combinations, this is referred to as the fundamental _____ principle.
Fundamental counting principle.
It is also called the counting rule, applying this principle we can know the number of outcomes by multiplying the options of each event together.
Given Hx)= vx and g(x) = \» ,which is the graph of (fºg)(x)?-2-222&DONE
Answer:
Step-by-step explanation:
A composite function is created when one functions is substituted into another function.
Given:
[tex]\begin{gathered} f(x)=\sqrt[]{x}\text{ and g(x)=}\lvert x\rvert \\ \text{Then, (f }\circ g)(x)\text{ would be f(g(x))} \end{gathered}[/tex]Therefore,
[tex](f\circ g)(x)=\sqrt[]{\lvert x\rvert}[/tex]Now, graphing this function...
Solve this system of equations by graphing. First graph the equations, and then type the solution.y=–4/3x–5x=–3
we have the system
y=–4/3x–5 ------> equation A
x=–3 ------> equation B
Using a graphing tool
see the attached figure
the solution of the system of equations is the intersection point both lines
the solution is the point (-3,-1)combine like terms
(x+3)+(9+x)
Answer:
[tex]x^{2}[/tex]+12x+27
Step-by-step explanation:
First, you need to distribute. You multiply x by 9 and x, and then multiply 3 by 9 and x, which results in 9x + [tex]x^{2}[/tex] +27 +3x.
Second, you collect like terms. In this case, there is only one like term, which is x. The results of this should be [tex]x^{2}[/tex] + 27 + 11x.
Lastly, reorder the terms properly, and you're done!
Hope this helps.
the x intercept of a functions is called?
In this case, the answer is very simple:
x
Divide polynomial and monomial 49c^2 d^2 - 70c^3 d^3 - 35c^2d^4 /7cd^2
start separating the fraction into smaller fractions
[tex]\frac{49c^2d^2}{7cd^2}-\frac{70c^3d^3}{7cd^2}-\frac{35c^2d^4}{7cd^2}[/tex]then, divide each of the fractions
[tex]7c-10c^2d-5cd^2[/tex]some animals on farms eat hay to get energy. A cow can eat 24 pounds of hay each day Write and evaluate an expression to find how many pounds a group of 12 cows can eat in two weeks. will send image
1 day a cow can eat = 24 pounds
1 day 12 cows can eat = 24 x 12
2 weeks = 14 days
therefore:
12 cows can eat in two weeks = 24 x 12 x 14 or 12 ( 24x14 )
answer: A. 12(24x14)
Write the equation of this line in point-slope form: The line passes through (−2,22) and (4,-8).
Write the equation of this line in point-slope form: The line passes through (−2,22) and (4,-8).
step 1
Find the slope of the line
m=(-8-22)/(4+2)
m=-30/6
m=-5
step 2
Find the equation in point slope form
y-y1=m(x-x1)
substitute the given values
we have
m=-6
(x1,y1)=(4,-8)
substitute
y+8=-6(x-4)find the area of the semicircle round to the nearest tenth use 3.14 for pi do not include units with your answer 12 in
226.08
1) Since the area of the semicircle is half the circle area, then we can write:
[tex]S=\frac{1}{2}\cdot\pi\cdot r^2[/tex]2) So we can plug into that the size of that radius:
[tex]\begin{gathered} S=\frac{1}{2}\cdot\pi\cdot(12)^2 \\ S=\frac{1}{2}\cdot\pi\cdot144 \\ S=72\pi\Rightarrow S=72\times3.14\Rightarrow S=226.08 \end{gathered}[/tex]3) Hence, the area of that semicircle is 226.08 in²
(a) How high is the javelin when it was thrown? How do you know?(b) How far from the thrower does the javelin strike the ground?
The height of the javelin is given by
[tex]h(x)=-\frac{1}{20}x^2+8x+6[/tex]Here, x is the horizontal distance from the point at which the javelin is thrown.
a)
When the javelin is thrown, the horizontal distance from the point at which the javelin is thrown is zero. So, put x = 0 to find the height of the javelin when thrown. So, the distance:
[tex]\begin{gathered} h(0)=-\frac{1}{20}(0)^2+8(0)+6 \\ =0+0+6 \\ =6 \end{gathered}[/tex]Thus, the height of the javelin when it was thrown is 6 ft.
b)
When the javelin strikes the ground the value of h(x) is zero.
Find the value of x when h(x) is zero.
[tex]\begin{gathered} h(x)=0 \\ -\frac{1}{20}x^2+8x+6=0 \\ -x^2+160x+120=0 \\ x^2-160x-120=0 \end{gathered}[/tex]Now, the roots of the equation are x = 160.74 and x = -0.74.
The distance cannot be negative. So, the javelin is 160.74 ft far from the thrower when it strikes the ground.
A cashier has 24 bills, all of which are $10 or $20 bills. The total value of the money is $410. How many of each type of bill does the cashier have?
The cashier has 7 bills of $10 and 17 bills of $20 (found using linear equation).
According to the question,
We have the following information:
A cashier has 24 bills, all of which are $10 or $20 bills. The total value of the money is $410.
Now, let's take the number of $10 bills to be x and the number of $20 bills to be y.
So, we have the following expression:
x+y = 24
x = 24-y .... (1)
10x+20y = 410
Taking 10 as a common factor from the terms on the left hand side:
10(x+2y) = 410
x+2y = 410/10
x+2y = 41
Now, putting the value of x from equation 1:
24-y+2y = 41
24+y = 41
y = 41-24
y = 17
Now, putting this value of y in equation 1:
x = 24-y
x = 24-17
x = 7
Hence, the cashier has 7 bills of $10 and 17 bills of $20 when the total value of the money is $410.
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Question 2(Multiple Choice Worth 2 points)
(03.01 LC)
Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 8 10 16
Total Pages 25 38 85 76 180
Which data display would you use to represent this data?
O Histogram
Scatter plot
O Line graph
O Line plot
To represent the data, histogram would have been used.
Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 8 10 16
Total Pages 25 38 85 76 180
In a histogram, a graphical representation of the distribution of data is done. The histogram is represented by a set of rectangles, adjacent to each other and each bar represent a kind of data.
Here the number of chapters can be kept in x axis and the total number of pages can be kept in the y axis.
Therefore, histogram would be used to display the data.
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How do I solve this and what is the answer
Answer:
157.5°
Explanation:
To convert from radians to degrees, multiply the angle in radians by 180/π.
Therefore, 7π/8 radians in degrees will be:
[tex]\begin{gathered} \frac{7\pi}{8}\text{ radians=}\frac{7\pi}{8}\times\frac{180}{\pi} \\ =\frac{7}{8}\times180 \\ =157.5\degree \end{gathered}[/tex]