Answer:
f(-5)=-11
Explanation:
Given the piecewise function:
[tex]f(x)=\begin{cases}{-3x+1,\text{ when }x>1} \\ {-2x,\text{ when }x=1} \\ {2x-1,\text{ when }x<1}\end{cases}[/tex]We want to find the value of f(-5).
When x=-5:
[tex]\begin{gathered} -5<1\implies f(x)=2x-1 \\ \text{ Therefore:} \\ f(-5)=2(-5)-1 \\ =-10-1 \\ =-11 \end{gathered}[/tex]The value of f(-5) is -11.
Michelle can wash dry and fold 5 loads of laundry in 3 1/2 hours. what is the average amount of time it takes Michelle to do one load of laundry
Blackgrass black graph is the of y=f(x) chose the equation for the red graph
The Solution:
The correct answer is [option A]
Given:
Required:
To determine the equation of the red graph if the black graph function is y = f(x).
The correctb
The profit of a cell-phone manufacturer is found by the function y= -2x2 + 108x + 75 , where x is the cost of the cell phone. At what price should the manufacturer sell the phone tomaximize its profits? What will the maximum profit be?
Hello!
First, let's rewrite the function:
[tex]y=-2x^2+108x+75[/tex]Now, let's find each coefficient of it:
• a = -2
,• b = 108
,• c = 75
As we have a < 0, the concavity of the parabola will face downwards.
So, it will have a maximum point.
To find this maximum point, we must obtain the coordinates of the vertex, using the formulas below:
[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ Y_V=-\frac{\Delta}{4\cdot a} \end{gathered}[/tex]First, let's calculate the coordinate X by replacing the values of the coefficients:[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ X_V=-\frac{108}{2\cdot(-2)}=-\frac{108}{-4}=\frac{108}{4}=\frac{54}{2}=27 \end{gathered}[/tex]So, the coordinate x = 27.
Now, let's find the y coordinate:[tex]\begin{gathered} Y_V=-\frac{\Delta}{4\cdot a} \\ \\ Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \\ \\ Y_V=-\frac{108^2-4\cdot(-2)\cdot75}{4\cdot(-2)} \\ \\ Y_V=-\frac{11664+600}{-8}=\frac{12264}{8}=1533 \end{gathered}[/tex]The coordinate y = 1533.
Answer:
The maximum profit will be 1533 (value of y) when x = 27.
Can you tell me if im right or wrong
I will begin typing in the answer tab. It will take me approximately _
Please help asap will give Brainly!!!
The following completes the proof: D. The Alternate Interior Angles Theorem shows that the angles BAC and DCA are congruent.
The Alternate Interior Angles Theorem: What is it?
According to the alternate interior angles theorem, when a transversal cuts over two (2) parallel lines, the alternate interior angles that are created are congruent.
We can infer and logically derive from the Alternate Interior Angles Theorem that the sentence that correctly concludes the proof is that angle BAC and angle DCA are congruent.
Segment AB is parallel to segment DC, while segment BC is parallel to segment AD, according to the information provided. Create the diagonals A and C using a straight edge. By virtue of the Reflexive Property of Equality, it is congruent to itself.
to learn more about Alternate Interior Angles refer to:
https://brainly.com/question/1807741
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use the information provided to write the equation of each circle. center: (12,-13)point on circle: (18, -13)
Answer:
[tex](x-12)^2+(y+13)^2=36[/tex]Explanation:
Given:
• Center: (12,-13)
,• Point on circle: (18, -13)
First, we find the length of the radius.
[tex]\begin{gathered} r=\sqrt[]{(18-12)^2+(-13-(-13)_{})^2} \\ =\sqrt[]{(6)^2} \\ r=6\text{ units} \end{gathered}[/tex]The general equation of a circle is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substituting the centre, (h,k)=(12,-13) and r=6, we have:
[tex]\begin{gathered} (x-12)^2+(y-(-13))^2=6^2 \\ (x-12)^2+(y+13)^2=36 \end{gathered}[/tex]The equation of the circle is:
[tex](x-12)^2+(y+13)^2=36[/tex]i have to find is they similar or not. help im lost
First we have to find the missing angle on each case.
In the first triangle we have
180°-(28°+80°)=72°
In the second triangle we have
180°-(28°+71°)=81°
Since the values of the angles are not the same for both triangles they are not similar.
find the slope of the line that passes through (10,2) and (2,10)
Number of adult tickets sold = Number of child tickets sold =
Given:
Total ticket = 321
Total collection = $3535
Adult ticket price = $15
Child ticket price = $5
Find-:
(1)
Number of adult tickets sold
(2)
Number of child tickets sold
Explanation-:
Let the number of adult tickets = x
Let the number of child tickets = y
If the total ticket is 321 then,
[tex]x+y=321........................(1)[/tex]Price for adult ticket is:
[tex]=15x[/tex]The price for child ticket is:
[tex]=5y[/tex]total price is $3535 then,
[tex]15x+5y=3535...................(2)[/tex]From eq(1)
[tex]\begin{gathered} x+y=321 \\ \\ 5x+5y=1605..............(3) \end{gathered}[/tex]So eq(2) - eq(3) is:
[tex]\begin{gathered} (15x+5y)-(5x+5y)=3535-1605 \\ \\ 15x-5x+5y-5y=1930 \\ \\ 15x-5x=1930 \\ \\ 10x=1930 \\ \\ x=\frac{1930}{10} \\ \\ x=193 \end{gathered}[/tex]Put the value in eq(1) then,
[tex]\begin{gathered} x+y=321 \\ \\ 193+y=321 \\ \\ y=321-193 \\ \\ y=128 \end{gathered}[/tex]So,
Number of adult tickets = 193
Number of child tickets = 128
Which of the following is equivalent to - sin ¹1?A. sin ¹111OB. - sin(-11)OC. sin(-11)D. sinReset Selection
The correct option is C.
What is the image point of (1,−3) after a translation right 2 units and up 2 units?
For this problem we have the following point given:
[tex]P=(1,-3)[/tex]And we want to determine the image point after a translation of 2 units to the right and upward. So then we just need to do the following:
[tex]I=(1+2,-3+2)[/tex]And after do the math we got:
[tex]I=(3,-1)[/tex]And the final answer for this case would be I=(3,-1)
Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find AU (BNC).{
Solution:
Given that;
[tex]\begin{gathered} A=\left\{0,2,4,6\right\} \\ B=\left\{1,2,3,4,5\right\} \\ C=\left\{1,3,5,7\right\} \end{gathered}[/tex]For B∩C, i.e . common elements between bot sets
[tex]B\cap C=\lbrace1,3,5\rbrace[/tex]Then, A∪(B∪C), i.e. all the elements in A and B∩C
[tex]A∪\left(B∪C\right)=\lbrace0,1,2,3,4,5,6\rbrace[/tex]Hence, A∪(B∪C) is
[tex]\begin{equation*} \lbrace0,1,2,3,4,5,6\rbrace \end{equation*}[/tex]Determine if the following statement uses inductive reasoning and explain in complete sentences. Find a counterexample, if possible.Statement: If the Charleston Chiefs score two touchdowns each quarter, then they must have won the game
Answer:
Explanation:
The given statement is
Statement: If the Charleston Chiefs score two touchdowns each quarter, then they must have won the game
It is an inductive statement
The counterexample would be
If the Charleston team won the game, they must have scored two touchdowns each quarter
A set of 12 data points is given above. Which of thefollowing is true of these data?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\lbrace14.9,21.1,21.2,8.4,14.5,5.9,7.6,10.0,4.8,3.2,28.7,29.5\rbrace[/tex]STEP 2: Find the mean ofthe data
[tex]\begin{gathered} The\:arithemtic\:mean\:\left(average\right)\:is\:the\:sum\:of\:the\:values\:in\:the\:set\:divided\:by\:the\:number\:of\:elements\:in\:that\:set. \\ \mathrm{If\:our\:data\:set\:contains\:the\:values\:}a_1,\:\ldots \:,\:a_n\mathrm{\:\left(n\:elements\right)\:then\:the\:average}=\frac{1}{n}\sum _{i=1}^na_i\: \\ Sum=169.8 \\ n=12 \\ mean=\frac{169.8}{12} \\ mean=14.15 \end{gathered}[/tex]STEP 3: Find the median
[tex]\begin{gathered} \mathrm{The\:median\:is\:the\:value\:separating\:the\:higher\:half\:of\:the\:data\:set,\:from\:the\:lower\:half.} \\ \:the\:number\:of\:terms\:is\:odd,\:then\:the\:median\:is\:the\:middle\:element\:of\:the\:sorted\:set \\ If\:the\:number\:of\:terms\:\:is\:even,\:then\:the\:median\:is\:the\:arithmetic\:mean\:of\:the\:two\:middle\:elements\:of\:the\:sorted\:set \\ \\ \mathrm{Arrange\:the\:terms\:in\:ascending\:order} \\ 3.2,\:4.8,\:5.9,\:7.6,\:8.4,\:10,\:14.5,\:14.9,\:21.1,\:21.2,\:28.7,\:29.5 \\ median=12.25 \end{gathered}[/tex]Hence, it can be seen here that the mean is larger than median.
STEP 4: Find the Interquartile range
[tex]\begin{gathered} The\:interquartile\:range\:is\:the\:difference\:of\:the\:first\:and\:third\:quartiles \\ First\text{ Quartile}=6.75 \\ Third\text{ quartile}=21.15 \\ IQR=14.4 \end{gathered}[/tex]STEP 5: Find the standard deviation
[tex]\begin{gathered} \mathrm{The\:standard\:deviation,\:}\sigma \left(X\right)\mathrm{,\:is\:the\:square\:root\:of\:the\:variance:\quad }\sigma \left(X\right)=\sqrt{\frac{\sum _{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1}} \\ Standard\text{ deviation}=9.11836 \end{gathered}[/tex]Hence, it can be seen from above that the interquartile range is larger than the standard deviation.
STEP 6: Find the range
[tex]\begin{gathered} \mathrm{The\:range\:of\:the\:data\:is\:the\:difference\:between\:the\:maximum\:and\:the\:minimum\:of\:the\:data\:set} \\ Minimum=3.2 \\ Maximum=29.5 \\ Range=26.3 \end{gathered}[/tex]STEP 7: Fnd the variance
[tex]\begin{gathered} \mathrm{The\:sample\:variance\:measures\:how\:much\:the\:data\:is\:spread\:out\:in\:the\:sample.} \\ \mathrm{For\:a\:data\:set\:}x_1,\:\ldots \:,\:x_n\mathrm{\:\left(n\:elements\right)\:with\:an\:average}\:\bar{x}\mathrm{,\:}Var\left(X\right)=\sum _{i=1}^n\frac{\left(x_i-\bar{x}\right)^2}{n-1} \\ Variance=83.14454 \end{gathered}[/tex]Hence, it can be seen that the range is not larger than the variance.
Therefore, the answer is I and II only.
You have a bag full of 4 green marbles and 1 blue marble. You pick a marble out at random. If it's blue, you stopbecause you win 20 points. If not, you get another chance. Without replacing the green marble, you pick again. It'sblue, you win 10 points, otherwise you lose 20 points. Let X be the number of points you eam in this game. If you playedthis game 100 times, how many points can you expect to win (or lose)?
As per given by the question,
There are given that, 4 green marbles and 1 blue marble contains in a box and pick a marble at randomly.
Now,
Here pick a marble out at random, so first pick a marble for blue;
Then,
Total number of green marbles is 4, and the total number of blue marble is 1, and;
The total numbers of marbles in a bag is, 4+1=5.
So,
For pick the blue marble from 5 marble,
Now,
[tex]\begin{gathered} 5_{C_1}=\frac{5!}{1!\times(5-1)!} \\ =\frac{5!}{1!\times4!} \\ =\frac{5\times4!}{1!\times4!} \\ =5 \end{gathered}[/tex]Now, for pick the green marble from 5 marbles.
Here, total green marble is 4.
So,
[tex]\begin{gathered} 5_{C_4}=\frac{5!}{4!\times(5-4)!} \\ =\frac{5\times4!}{4!\times1!} \\ =5 \end{gathered}[/tex]Now,
From the question, there are clearly mention that if pick a blue, then stop because you won 20 points.
So,
Probability of the blue marble that won the 20 points.
then,
[tex]\begin{gathered} P(x=20)=\frac{total\text{ number of blue marble}}{\text{total number of marble}} \\ P(x=20)=\frac{1}{5} \end{gathered}[/tex]Now,
There are also mention that, pick a green marbles without replacing and if its blue then win the 10 points,
So,
probability of the blue marbles that won 10 pointss is,
[tex]P(x=10)=\frac{1}{4}[/tex]Now,
Here, find the probability that no points for the first green ball is,
[tex]P(x=0)=\frac{4}{5}[/tex]Now,
If you played this game 100 time, then the probability is,
[tex]\begin{gathered} P(x=0)+_{}P(x=10)+P(x=20)=\frac{4}{5}+\frac{1}{4}+\frac{1}{5} \\ =1.25 \end{gathered}[/tex]now,
For 100 times,
[tex]1.25\times100=125\text{ points.}[/tex]Hence, 125 points can you expect to win.
Assume that a sample is used to estimate a population proportion p. Find the 80% confidence interval for a sample of size 362 with 54 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.
We have to find the 80% confidence interval for a population proportion.
The sample size is n = 362 and the number of successes is X = 54.
Then, the sample proportion is p = 0.149171.
[tex]p=\frac{X}{n}=\frac{54}{362}\approx0.149171[/tex]The standard error of the proportion is:
[tex]\begin{gathered} \sigma_s=\sqrt{\frac{p(1-p)}{n}} \\ \sigma_s=\sqrt{\frac{0.149171*0.850829}{362}} \\ \sigma_s=\sqrt{0.000351} \\ \sigma_s=0.018724 \end{gathered}[/tex]The critical z-value for a 80% confidence interval is z = 1.281552.
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z\cdot\sigma_s=0.149171-1.281552\cdot0.018724\approx0.1492-0.0240=0.1252[/tex][tex]UL=p+z\cdot\sigma_s=0.1492+0.0240=0.1732[/tex]As the we need to express it as a trilinear inequality, we can write the 80% confidence interval for the population proportion (π) as:
[tex]0.125<\pi<0.173[/tex]Answer: 0.125 < π < 0.173
Can anyone help me with this I’m stuck and this is pretty difficult.
Answer:
x=-1
Explanation:
Given the equation:
[tex]$$ 24=4(x-7)+8(1-6 x) $$[/tex]First, expand the brackets:
[tex]24=4x-28+8-48x[/tex]Next, collect like terms and simplify:
[tex]\begin{gathered} 24=4x-48x-28+8 \\ 24=-20-44x \\ \text{ Add 20 to both sides} \\ 24+20=-44x \\ 44=-44x \\ \text{ Divide both sides by -44} \\ \frac{44}{-44}=\frac{-44x}{-44} \\ x=-1 \end{gathered}[/tex]The solution to the equation is -1.
Part I: Domain and Range-identify the domain and range of each graph. Problem / Work Answe 2+ 6+ 2+ 1. Week 15 Homework Packet pdf 2003
Domain is the set of input values,
In the graph x axis show the domain
Where the x values is lies at -2,-1,0,1,2
Sothe domain will be :
[tex]\text{Domain =-2}\leq x\leq2[/tex]Range is the set of output values,
In the graph the value of function at y axis is : 0,2,4,6,8-2,-4.....
So, the range will be :
[tex]\text{Range = -}\infty\leq y\leq\infty[/tex]what is the correct base and coefficient for the function:
The general form of a logarithmic function is:
[tex]y=a\cdot\log _b(x)[/tex]Where a is the coefficient and b is the base. In the given picture, we can see that the coefficient is equal to 1, while the base is equal to 2.
Determine the required value of a missing probability to make the distribution a discrete probability distribution… p(4) =
The table given showed the discrete probability distribution for random variables 3 to 6 and their corresponding probability except for the probability of 4
It should be noted that for a probability distribution, the cummulative probabibility (that is the sum of all the probability) must be equal to one.
This means that
[tex]P(3)+P(4)+P(5)+P(6)=1[/tex]From the given table, it can be seen that
[tex]\begin{gathered} P(3)=0.32 \\ P(4)=\text{?} \\ P(5)=0.17 \\ P(6)=0.26 \end{gathered}[/tex]Then, p(4) is calculated below
[tex]\begin{gathered} P(3)+P(4)+P(5)+P(6)=1 \\ 0.32+P(4)+0.17+0.26=1 \\ P(4)+0.32+0.17+0.26=1_{} \\ P(4)+0.75=1 \\ P(4)=1-0.75 \\ P(4)=0.25 \end{gathered}[/tex]Hence, P(4) is 0.25
Jodie is an event planner who believeseach person requires 3.75 feet ofpersonal space at her events. Her nextevent will be at a venue that measures40 feet by 75 feet. How many peopleshould she include on the guest list?
The venue measures 40 ft by 75 ft . This means the venue has the shape of a rectangle. A rectangle
determine how many vertices and how many edges the graph has
in the given figure,
there are 4 vertices
and there are 3 edges.
thus, the answer is,
vertiev
What is the probability of drawing a jack from a standard deck of cards, replacing it,shuffling, then drawing an ace?
- We have 52 cards in a deck of cards.
- We have 4 cards of the same number (4 jack, 4 aces...).
Probability of drawing a jack = 4/52
Probability of drawing a jack followed by an ace =(4/52)*(4/52)=0.00592
Evaluate the expression shown below and write your answer as a fraction in
simplest form.
-3/8+(-9/10)
Answer:
-1 11/40
Step-by-step explanation:
-51/40 this is simplest form.
Step-by-step explanation:
This is Calculus 1 Linear Optimization Problem! MUST SHOW ALL THE JUSTIFICATION!!!
Given:
Required:
We need to find the value of AB
Explanation:
Here ABC is the right anglr triangle
so
[tex]\begin{gathered} AB^2=BC^2+AC^2=36+36=72 \\ AB=6\sqrt{2} \end{gathered}[/tex]Final answer:
The minimum length of crease is
[tex]6\sqrt{2}[/tex]Translate and solve: The difference of a and 7 is 11
Answer:
(B)a=18
Explanation:
The difference of a and 7 translated as an expression is:
[tex]a-7[/tex]Thus, the equation is:
[tex]a-7=11[/tex]To solve for a, add 7 to both sides of the equation:
[tex]\begin{gathered} a-7+7=11+7 \\ a=18 \end{gathered}[/tex]The correct choice is B.
Karen is planning to drive 870 miles on a road trip. If she wants to complete the trip in 6 days, how many miles will she need to drive each day??
Answer:
145 miles
Step-by-step explanation:
870 ÷ 6 = 145
Cost of a CD: $14.50Markup: 30%
Given:
Cost of a CD = $14.50
Markup =30%
If markup 30% then:
[tex]\begin{gathered} =\frac{130}{100} \\ =1.3 \end{gathered}[/tex]So the cost is:
[tex]\begin{gathered} =1.3\times14.50 \\ =18.85 \end{gathered}[/tex]markup cost is 18.85
How do we determine the number of hours each family used the sprinklers?
Given:
The output rate of Martinez family's sprinkler is 25L per hour and Green family's sprinkler is 35L per hour. The combined usage of sprinkler is 40 hours. The resulting water output is 1250L.
To find:
The number of hours each family used the sprinkler.
Solution:
Let Martinez family used sprinkler for x hours and Green family used sprinkler for y hours.
Since the combined usage of sprinklers is 40 hours. So,
[tex]x+y=40...\left(i\right)[/tex]The output rate of Martinez family's sprinkler is 25L per hour and Green family's sprinkler is 35L per hour. The resulting water output is 1250L. So,
[tex]\begin{gathered} 25x+35y=1250 \\ 5x+7y=250...\left(ii\right) \end{gathered}[/tex]Multiply (i) by 7 and subtract from (ii), to get:
[tex]\begin{gathered} 5x+7y-7\left(x+y\right)=250-7\left(40\right) \\ 5x+7y-7x-7y=250-280 \\ -2x=-30 \\ x=\frac{-30}{-2} \\ x=15 \end{gathered}[/tex]Now, we get x = 15, Put x = 15 in the equation (i):
[tex]\begin{gathered} 15+y=40 \\ y=40-15 \\ y=25 \end{gathered}[/tex]Thus, x = 15, y = 25.
The width of a 2-by-4 piece of wood is actually 34 inches. Find the total width of 28 2-by-4s laid side-by-side. Simplify youranswer.o 126 inchesO 98 inches0784 inches844 inches
The of one 2-by-4 piece of wood is 3.5 inches
To find the width of 28 pcs of wood, just multiply the number of wood to the actual width which is 3.5 inches
So we have :
[tex]28\times3.5=98[/tex]The answer is 98 inches
