Let y be the number of female customers in the restaurant. Since we know that 3 out of 4 customers are females and that x is the total number of customers, this means that:
[tex]y=\frac{3}{4}x[/tex]Question 9, on which interval is the graph negative ?
The intervals where the graph is negative are those where it goes below the x-axis. With the figure we can easily identify the following negative portion of the graph:
As you can see, these negative values are located for all the points within (-5, -1), this is equivalent to the interval -5 < x < -1. Then option B is the correct answer
hello I am having difficulty on this problem please help thank you
we have a system of inequalities
Inequality A
[tex]-4x+3y<6[/tex]Isolate the variable y
[tex]\begin{gathered} 3y\lt6+4x \\ y<\frac{4}{3}x+\frac{6}{3} \\ y\lt\frac{4}{3}x+2 \end{gathered}[/tex]The solution to the first inequality is the shaded area below the dashed line y=(4/3)x+2
Inequality B
[tex]4x+7y\leq-7[/tex]Isolate the variable y
[tex]\begin{gathered} 7y\leqslant-7-4x \\ y\leqslant\frac{-7}{7}-\frac{4x}{7} \\ \\ y\leqslant-\frac{4}{7}x-1 \end{gathered}[/tex]The solution to the second inequality is the shaded area below the solid line y=-(4/7)x-1
therefore
The solution to the system of inequalities is the shaded area below the dashed line y=(4/3)x+2 and below the solid line y=-(4/7)x-1
Using a graphing tool
see the attached figure below
Remember that
If an ordered pair is a solution to the system of inequalities
then
the ordered pair must lie in the shaded region of the solution
so
the point (-2,-2) is a solution to the system of inequalities
see the figure below
6. Sheila simplified an expression using the following steps. Which property justifies Step 3?
The distributive property of multiplication is represented by the following expression:
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]Notice that Sheila uses distributive property to simplify the expression:
[tex]\begin{gathered} 5x+4(3+2x) \\ =5x+4\cdot3+4\cdot2x \\ =5x+12+8x \\ =13x+12 \end{gathered}[/tex]A group of friends wants to go to the amusement park. They have no more than $225to spend on parking and admission. Parking is $5, and tickets cost $20 per person,including tax. Write and solve an inequality which can be used to determine p, thenumber of people who can go to the amusement park.3Inequality:рSubmit AnswerPrivacy Policy Terms of Service
Answer:
Inequality: 5 + 20p ≤ 225
p ≤ 11
Explanation:
The total cost can be calculated as the sum of the parking and ticket costs. So, we can calculate the total cost as:
5 + 20p
Because 20p represents the total ticket cost for p people.
Then, this total cost should be less than or equal to 225. It means that the inequality that represents the situation is:
5 + 20p ≤ 225
Finally, we can solve the inequality by subtracting 5 from both sides as:
5 + 20p - 5 ≤ 225 - 5
20p ≤ 220
Then, divide both sides by 20, to get:
20p/20 ≤ 220/20
p ≤ 11
So, the number of people who can go to the amusement park is less than or equal to 11.
Therefore, the answers are:
Inequality: 5 + 20p ≤ 225
p ≤ 11
The following data are the distances from the workplace (in miles) for the 5 employees of a small business.
1. Given that the population data is : 15,5,8,2,5
• number of sample in data , ,n = 5
,• Mean = sum of sample in the data / number of sample
= (15+5+8+2+5)/5
= 35/5
Therefore mean = 7
2. Calculate varience as in the box below:
[tex]\begin{gathered} _{}\text{Varience = }\frac{1}{n}\mleft\lbrace(x_i-\vec{x}\mright)^2 \\ \text{ = }\frac{1}{5}\mleft\lbrace(7-15)^2+(7-5)^2+(7-8)^2+(7-2)^2+(7-5)^2\mright\rbrace \\ \text{ = }\frac{1}{5}\mleft\lbrace(-8^2\mright)+(-2)^2+(-1^2)+(5^2)+(2^2)\} \\ \text{ =}\frac{1}{5}\mleft\lbrace64\text{ + 4+ 1 +25+4}\mright\rbrace \\ \text{ = }\frac{1}{5}(98) \\ \text{ = }\frac{98}{5} \\ \therefore S\tan dard\text{ deviation = }\sqrt[]{varience\text{ }} \\ \text{ = }\sqrt[]{\frac{98}{5}}\text{ } \\ \text{ =4.427} \end{gathered}[/tex]• This means that Standard deviation = 4.43
Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval. x2 + 2x + 2 x2 The area is 54 (Type an integer or a simplified fraction.)
To find this area, it is necessary to solve an integral, actually the sum of 2 integrals
[tex]\int (x^2+2x+2)dx+\int (3x+4)dx[/tex]The first one must be evaluated from -3 to 2 and the second one from 2 to 3
[tex]\begin{gathered} \int (x^2+2x+2)dx+\int (3x+4)dx \\ (\frac{x^3}{3}+x^2+2x)+(\frac{3x^2}{2}+4x) \\ \end{gathered}[/tex]Evaluate the first integral
[tex]\begin{gathered} \frac{x^3}{3}+x^2+2x\text{ (From -3 to 2)} \\ (\frac{2^3}{3}+2^2+2\cdot2)-(\frac{(-3)^3}{3}+(-3)^2+(2\cdot-3)) \\ \frac{8}{3}+4+4-(-\frac{27}{3}+9-6) \\ \frac{35}{3}+5=\frac{50}{3} \end{gathered}[/tex]Evaluate the second integral
[tex]\begin{gathered} \frac{3x^2}{2}+4x\text{ (From 2 to 3)} \\ (\frac{3\cdot(3^2)}{2}+4\cdot3)-(\frac{3\cdot(2^2)}{2}+4\cdot2) \\ (\frac{27}{2}+12)-(\frac{12}{2}+8) \\ \frac{15}{2}+4=\frac{23}{2} \end{gathered}[/tex]Now, solve the sum
[tex]\begin{gathered} \frac{50}{3}+\frac{23}{2} \\ \frac{100+69}{6}=\frac{169}{6} \end{gathered}[/tex]The area is 169/6
[tex] {x}^{2} - [/tex]which could be the missing term in the expression if a factor of the expression is x-2ya) 2xyb) -2yc) [tex] {4y}^{2} [/tex]d)4y
This is a difference of two squares.
If one factor is
[tex]x+2y[/tex]An the other is
[tex]x-2y[/tex]We have that the expression is:
[tex](x+2y)\cdot(x-2y)=x^2-4y^2[/tex]So the missing term is 4y², option c
Convert: 3 days = minutes
ANSWER
4320 minutes
EXPLANATION
To convert from days to minutes, first, we have to convert from days to hours. It is known that 1 day has 24 hours, so 3 days have,
[tex]3\text{ }days\cdot\frac{24\text{ }hours}{1\text{ }day}=72\text{ }hours[/tex]Then, we convert from hours to minutes. If 1 hour has 60 minutes,
[tex]72\text{ }hours\cdot\frac{60\text{ }minutes}{1\text{ }hour}=4320\text{ }minutes[/tex]Hence, there are 4320 minutes in 3 days.
Alex is 12 years older than George, Carl is three times older than Alex, The sum of their ages is 68. Find the ratio of George's age to Carl's age to Alex's age.
Firstly, let x represent Alex's age, y represent George's age and z represent Carl's age.
from the question;
Alex is 12 years older than George, So;
[tex]x=y+12\ldots\ldots\ldots\ldots.1[/tex]Carl is three times older than Alex, So;
[tex]z=3x\ldots\ldots\ldots..2[/tex]The sum of their ages is 68, So;
[tex]x+y+z=68\ldots\ldots\ldots\ldots\ldots3[/tex]Now we have three equations and three unknowns, so it is solvable.
Let us substitute equation 2 into equation 3; that is replace z with 3x in equation 3.
[tex]\begin{gathered} x+y+3x=68 \\ 4x+y=68\ldots\ldots\ldots\ldots\ldots\ldots4 \end{gathered}[/tex]Next, let us substitute equation 1 into equation 4. that is replace x with y+12 in equation 4.
[tex]\begin{gathered} 4(y+12)+y=68 \\ 4y+48+y=68 \\ 5y+48=68\ldots\ldots\ldots.5 \end{gathered}[/tex]we can now solve for the value of y from equation 5.
[tex]\begin{gathered} 5y+48=68\ldots\ldots\ldots.5 \\ \text{subtract 48 from both sides.} \\ 5y+48-48=68-48 \\ 5y=20 \\ y=\frac{20}{5} \\ y=4 \end{gathered}[/tex]let us now replace y with 4 in equation 1 to get the value of x. since y = 4;
[tex]\begin{gathered} x=y+12\ldots\ldots\ldots\ldots.1 \\ x=4+12 \\ x=16 \end{gathered}[/tex]then, since x =16 let us replace x with 16 in equation 2 to get z.
[tex]\begin{gathered} z=3x\ldots\ldots\ldots..2 \\ z=3(16) \\ z=\text{ 48} \end{gathered}[/tex]so we have;
[tex]\begin{gathered} \text{Alex's age = x = 4 years} \\ George^{\prime}sage_{}=y=16\text{ years} \\ Carl^{\prime}sage=z=48\text{ years} \\ \end{gathered}[/tex]We now need to find the ratio of George, Carl and Alex's age.
[tex]\begin{gathered} 16\colon48\colon4 \\ \text{dividing through by 4 we have;} \\ 4\colon12\colon1 \end{gathered}[/tex]So the ratio of their ages are;
[tex]4\colon12\colon1[/tex]Example(-9, -2) (1,3)Find the slopeWrite in point slopeWrite in slope intercept formComplete the same three steps for 50extra points using the points(-6,7)(-3,6)
The slope, m, of a line passing therough the points (x₁, y₁ ) and (x₂, y₂) can be calculated using the formula
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]For the points (-9, -2) and (1, 3):
x₁ = -9, y₁ = -2, x₂ = 1, y₂ = 3
Substituting these points into the slope formula given above
[tex]\begin{gathered} m\text{ = }\frac{3-(-2)}{1-(-9)} \\ m\text{ = }\frac{5}{10} \\ m\text{ = }\frac{1}{2} \end{gathered}[/tex]The slope, m = 1/2
The point-slope form of the equation of a line passing through the points (x₁, y₁ ) and (x₂, y₂) can be calculated using the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - (-2) = }\frac{1}{2}(x\text{ - (-9))} \\ y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \end{gathered}[/tex]The slope-intercept form of the equation will be of the form y = mx + c
Reduce the point-slope form written above to the intercept-slope form
[tex]\begin{gathered} y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \\ y\text{ + 2 = }\frac{x}{2}+\text{ }\frac{9}{2} \\ y\text{ = }\frac{x}{2}+\frac{9}{2}-2 \\ y\text{ = }\frac{1}{2}x\text{ +}\frac{5}{2} \end{gathered}[/tex]According to the histogram, what is the least number of broken light bulbs received in a shipment?
Responses
A 0
B 1
C 10
D 50
I GIVE YOU BRAINEST PLEASE ANWER UNDER 30 MIN
Round to the nearest hundredth.1.9541
In order to round to the neares hundreth 1.9541, consider that hundreths are the second number after the decimal point, moreover, take into account that the value of such a number depends of the value of the next number (that is, third number after decimal point).
If next number is lower than 5, then, the second number remains the same, if next number is 5 or greater, second number is increased 1 unit.
In this case, the next number is 4, then, second number or hundreths remain the same.
Hence, you have:
[tex]1.9541\approx1.95[/tex]If f(x) = x2 + x, find f(-3).-123O6
To find f(-3) we have to substitute x = -3 in the equation.
[tex]\begin{gathered} f(-3)=(-3)^2+(-3) \\ f(-3)=9-3 \\ f(-3)=6 \end{gathered}[/tex]A segment has endpoints A and C. What are two names for the segment? Choose the correct answer below O AC and CA OAC and CA O AC and CA O AC and CA
Given that endpoints of a segment: A and C
The two names for the sgment will be:
AC and CA
ANSWER:
AC and CA
how do I find the central angle for turn b?
We will to use the formula to a sector areaa, which is given for:
[tex]A=r^2\theta/2[/tex]Where r is the radius and θ is the central angle.
We can rewrite the formula to obtain the central angle like this:
[tex]\theta=\frac{2A}{r^2}[/tex]We replace with the values of the track:
[tex]\theta=\frac{2\ast51\pi}{20\ast3^2}=\frac{17\pi}{30}[/tex]Then we change radians to degrees:
[tex]\frac{17\pi}{30}\ast\frac{180}{\pi}=102\text{ \degree}[/tex]Then the correct answer is 102°.
Consider the rectangle. IT 4 x+1 Which two expressions represent the area of the rectangle?
sides of the rectangle:
4
x+1
Area of the rectangle = product of the sides
4 (x+1 )
Apply distributive property:
4(x)+4(1)
4x+4
So, the correct options are:
C. 4x+1
E.4x+4
What is the quotient in simpilest form? 3/4÷5/16
the given expression is
[tex]\frac{\frac{3}{4}}{\frac{5}{16}}[/tex][tex]\frac{3\times16}{5\times4}=\frac{12}{5}=2.4[/tex]so the quotient will be 2.4
- Gross pay: $38,550; married,
2 dependents; state income tax rate:
3 percent.
Answer:
Step-by-step explanation:
This is 0% of your total income of $0. 0% would also be your average tax rate. Your income puts you in the 0% tax bracket. At higher incomes, exemptions, many deductions and many credits are phased out. This increases your tax bill and your marginal tax rate. With these phase outs, adding $1,000 to your income would result in a 0% marginal tax rate.
Cara has 42.5 pounds of coffee. If she splits the coffee into 2.5 pound bags, how many bags will she need?A)17B)19C)21D)23
choose the expression that is represented by the following phrase:"the square of Y decreased by the quotient of 8 and y"
Find a quadratic function with the given vertex ans passing through the given point vertex forn E Vertex (4,5): passes through (1, 2)
The quadratic function forms a parabola. The vertex form of the equation is expressed as
y = a(x - h)^2 + k
Where
h and k are the x and y coordinates of the parabola's vertex. Given that the vertex is (4, 5),
h = 4, k = 5
Substituting these values into the above equation, it becomes
y = a(x - 4)^2 + 5
Given that the parabola passes through the point, (1, 2), we would substitute x = 1 and y = 2 into y = a(x - 4)^2 + 5. It becomes
2 = a(1 - 4)^2 + 5
2 = a * 9 + 5
2 = 9a + 5
9a = 2 -5
9a = - 3
a = - 3/9 = - 1/3
Substituting a = - 1/3 into y = a(x - 4)^2 + 5, the equation would be
[tex]y\text{ = -}\frac{1}{3}(x-4)^2\text{ + 5}[/tex]could i have a fast answer please? if not it’s ok
Given:
Strip diagrams are given.
Option D represents the 175% .
Option D is the correct answer.
what is 10•(-1/2)= ??
For this problem, we are given a product between an integer and a fraction.
The expression is shown below:
[tex]10\cdot(\frac{-1}{2})[/tex]To solve this problem, we need to multiply the two numerators and denominators, then simplify the fraction:
[tex]\frac{-10}{2}=-5[/tex]The result is -5.
What is the intersection of the sets C = {5, 7, 10, 13, 19) and D = {3, 9, 14, 15}?O null setO (5, 7, 9, 10, 13, 14, 15, 19}O {5, 9, 14)O {3, 19)
We are given the following two sets C and D
C = {5, 7, 10, 13, 19}
5/6 year = how many months
We will solve as follows:
We multiply the value we want to know (5/6) times the number of months that are in a year(12 months) and divide it by the number of years 12 months represent:
[tex]m=\frac{(\frac{5}{6})\cdot(12)}{1}\Rightarrow m=10[/tex]So, 5/6 of a year are 10 months.
The graph of y = –2/x lies in ____.A. Quadrant I and IIIB. Quadrant I and IIC. Quadrant II and IVD. Quadrant III and IV
In order to find the quadrants of y = -2/x, let's choose a positive and a negative value of x, then we calculate the corresponding values of y and check the quadrants:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{2}{-2}=1 \\ \\ x=2\colon \\ y=-\frac{2}{2}=-1 \end{gathered}[/tex]The point (-2, 1) is in quadrant II (negative x and positive y) and the point (2, -1) is in quadrant IV (positive x and negative y).
Therefore the correct option is C.
.............................
step 1
Find out the expected value
In this game, the total possible outcomes are 12
The probability of a win is P=1/12
The probability of loss is P=11/12
so
EV=(1/12)*(30-20)-(11/12)*30
EV=(1/12)*(10)-(11/12)*30
EV=(10/12)-(330/12)
EV=-320/12
EV=-26.67p ----> is negative because is a loss for the players
If 60 people play the game
26.67*60=1,600
therefore
The school expect to raise for charity 1,600p
Divide by 100
1,600p/100=$16a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
the equation is equal to
Multiply the number of tanks by 24
so
24c
the answer is 24cPart 2
1/13 is the reciprocal of 13
because
(13)(1/13)=1
a number multiplied by its reciprocal is equal to 1
what is the area of a sector bounded by a 114 arc
Step1: Write out the given parameter
Θ=114°,r= 6ft
Step2; Write out the formula
The area of a sector is given as
[tex]\frac{\theta}{360}\times\pi r^2[/tex]Step3: substitute the parameters into the formula
[tex]\frac{114}{360}\times\pi\times6^2[/tex][tex]\begin{gathered} \frac{114}{10}\pi \\ \frac{57}{5}\pi \end{gathered}[/tex]Hence the area of the sector is (57/5)π interms o
The amount of money Jeremy makes varies directly with the number of hours he works. Ifhe earns $195 for 3 days of work, how much will he earn if he works 12 days?
Given:
a.) Jeremy earns $195 for 3 days of work.
To be able to determine how much will he earn if he works 12 days, we will be using ratios and proportions.
Let,
x = his earnings if he works for 12 days.
[tex]\text{ 195 : 3 = x : 12}[/tex][tex]\text{ 195 : 3 = x : 12 }\rightarrow\text{ }\frac{\text{ 195}}{3}\text{ = }\frac{\text{ x}}{12}[/tex][tex]\frac{\text{ 195}}{3}\text{ = }\frac{\text{ x}}{12}[/tex][tex]\text{ (195)(12) = (x)(3)}[/tex][tex]\text{ 2,340 = 3x}[/tex][tex]\text{ }\frac{\text{2,340}}{3}\text{ = }\frac{\text{3x }}{3}[/tex][tex]\text{ 780 = x}[/tex]Therefore, he'll earn $780 for working 12 days.