The minimum that could be earned is $150. The required inequalities are solved below:
What is an inequality?
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: The symbol a b indicates that an is smaller than b. The symbol a > b indicates that an is more than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed.
(a) The minimum that could be earned is $150.
(b) The required inequality is given as 150+20x≥630
or, 20x≥630-150
or, x≥480/20
or, x≥24
(c) The required inequality is given as 150+20x≥750
or, 20x≥750-150
or, x≥600/20
or, x≥30
(d) The required inequality is given as 150+20x≤950
or, 20x≤950-150
or, x≤800/20
or, x≤40
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I understand the answer to simplifying it, i want a mathematical expression of the method of simplifying to know how to show my work
Answer:
This is how I would approach it
Step-by-step explanation:
Ruth is a costume designer for the local children's theater company. Yesterday, she sewed 1 female costume and 5 male costumes, which used 52 yards of fabric. Today, she sewed 5 female costumes and 2 male costumes, which used a total of 76 yards. How many yards of fabric does each type of costume require? yards of fabric, and every male costume requires Each female costume requires yards.
Given:
Yesterday:
1 female and 5 male = 52 yards
Today:
5 female and 2 male = 76 yards
Let's find the number of yards of fabric each type of costume requires.
Let F represent the number if yards for each female customer use.
Let M represent the number of yards each male customer uses.
From this situation, we have the system of equations:
1F + 5M = 52
5F + 2M = 76
Now, let's solve the system of equations simultaneously using substitution method.
Rewrite equation 1 for F:
F = 52 - 5M
Substitute 52 - 5M for F in equation 2:
[tex]\begin{gathered} 5F+2M=76 \\ \\ 5(52-5M)+2M=76 \\ \\ 5(52)+5(-5M)+2M=76 \\ \\ 260-25M+2M=76 \\ \\ 260-23M=76 \end{gathered}[/tex]Subtract 260 from both sides:
[tex]\begin{gathered} 260-260-23M=76-260 \\ \\ -23M=-184 \end{gathered}[/tex]Divide both sides by -23:
[tex]\begin{gathered} \frac{-23M}{-23}=\frac{-184}{-23} \\ \\ M=8 \end{gathered}[/tex]Substitute 8 for M in either of the equations:
F = 52 - 5M
F = 52 - 5(8)
F = 52 - 40
F = 12
Therefore, we have the solution:
F = 12, M = 8
Each male customer requires 8 yards while each female customer requires 12 yards.
ANSWER:
• Male customer = 8 yards
,• Female customer = 12 yards
Venus has a mean distance from the sun of 67,240,000 miles while mars has a mean distance from the sun of 4,213,000,000 miles. how much farther is mars from the sun than venus? a. 4,145,760,000 miles b. 4,146,260,000 miles c. 4,245,760,000 miles d. 4,280,240,000 miles
The Mean distance is 4,145,760,000 miles
The correct option is (a)
Given,
The mean distance from Venus to the sun is 67,240,000 miles.
The mean distance from Mars to the sun is 4,213,000,000 miles.
Now, According to the question
Subtract the distance of Mars to the sun from Venus to the sun :
Let's Calculate the mean distance:
= 4,213,000,000 - 67,240,000
= 4,145,760,000 miles
Hence, The Mean distance is 4,145,760,000 miles.
The correct option is (a)
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El precio de los boletos para un partido de fútbol es de $19 pesos. Si en total caben 26,472 personas en el estadio, calcula la cantidad aproximada de dinero que se obtiene de la venta de los boletos.
La ganancia aproximada del estadio por concepto de la venta de boletos para un partido de fútbol es $ 502,968.
¿Cuál es la ganancia neta aproximada por la venta de boletos?
En esta pregunta se nos solicita determinar la ganancia aproximada por la venta de boletos para un partido de fútbol en un estadio. La ganancia aproximada es igual al producto del aforo del estadio y el costo de cada boleto. Entonces,
c = ($ 19) · (26,472)
c = $ 502,968
La ganancia aproximada por el partido de fútbol es $ 502,968.
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Translate this sentence into an equation.68 is the product of Diane's score and 4.Use the variable d to represent Diane's score.
68 = Diane's score x 4
Equation
68= 4d
___________________
Can you see the updates?
_________________
Diane's score
4d= 68
d= 17
A population grows according to an exponential growth model. The initial population is P0=9, and the growth rate isr=0.4.Then:P1 = P2 = Find an explicit formula for Pn. Your formula should involve NPn = Use your formula to find P9=Give all answers accurate to at least one decimal place
Answer:
From the question,
[tex]\begin{gathered} P_0=9 \\ r=0.4 \end{gathered}[/tex]The formula for the growth rate will be calculated using the formula below
[tex]\begin{gathered} F=P(1+r)^n \\ F=\text{future value} \\ P=present\text{ value} \\ r=\text{growth rate} \\ n=nu\text{mber of times per period} \end{gathered}[/tex]In,
[tex]\begin{gathered} P_0,n=0 \\ P_1,n=1 \\ P_2,n=2 \\ P_9,n=9 \end{gathered}[/tex]Given that
[tex]\begin{gathered} P_0=9 \\ F=P(1+r)^n \\ P_0=9(1+0.4)^0 \\ P_0=9\times1 \\ P_0=9 \end{gathered}[/tex][tex]\begin{gathered} F=P(1+r)^n \\ P_1=9(1+0.4)^1 \\ P_1=9\times1.4 \\ P_1=12.6 \end{gathered}[/tex]Hence,
P1 = 12.6
Also, we will have P2 to be
[tex]\begin{gathered} F=P(1+r)^n \\ P_2=9(1+0.4)^2 \\ P_2=9\times1.4^2 \\ P_2=17.64 \\ P_2\approx1\text{ decimal place} \\ P_2=17.6 \end{gathered}[/tex]Hence,
P2 = 17.6
Therefore,
The formula for Pn will be represented below as
[tex]\begin{gathered} P_n=9(1+0.4)^n \\ P_n=9(1.4)^n \end{gathered}[/tex]The explicit formula for Pn will be
[tex]P_n=9(1.4)^n[/tex]To figure out the values of P9. we will substitute the value of n=9 in the equation below
[tex]\begin{gathered} P_n=9(1.4)^n \\ P_9=9(1.4)^9 \\ P_9=185.9 \end{gathered}[/tex]Hence,
P9 = 185.9
Given the slope of a line is -2 and it passes through the point (4,-5), write the equationof the line in standard form.
Answer:
The equation of the line is;
[tex]y=-2x+3[/tex]Explanation:
Given that
the slope of a line is -2 and it passes through the point (4,-5).
Applying the slope-intercept form of equation;
[tex]y-y_1=m(x-x_1)[/tex]Substituting the values of the slope and coordinates;
[tex]\begin{gathered} y-(-5)=-2(x-4) \\ y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]Therefore, the equation of the line is;
[tex]y=-2x+3[/tex]Answer:
2x + y = 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (4, - 5 ) into the partial equation
- 5 = - 8 + c ⇒ c = - 5 + 8 = 3
y = - 2x + 3 ← in slope- intercept form
add 2x to both sides
2x + y = 3 ← equation in standard form
3. a sociologist wishes to estimate the percentage of u.s. citizens living in poverty. what sample size should be obtained if she wishes the estimate to be within 2% points (the error) with 99% confidence if she uses the year 2000 estimate of 11.8% poverty obtained from the census?
The sample size is 1727 points for given data . Sample size is defined as the number of observations used to determine estimates for a given population. Sample size was drawn from the population .
In this question we want to find the sample size and so let's, look at the formula that is given by, the value at over 2, divided by a margin of error, whole squared times p into 1 minus p.
N= ( Z ₐ / E)² p (1-p)
In this case , Z --> Z-Score
E --> error value
P --> estimated proportion or if given standard deviations
Given that, estimate error is 2% that is margin (E) = 2% = 2/100 =0.02
Now, what we have is our confidence level and our made error, so our estimate has been given us 2 percent or confidence level is 99 percent. Now, let's get our Z values, so we use alpha(a) to find out. For alpha value 1 minus 0.99 , we get 0.01. now we are going to be 0.01 divide by 2 and get 0.005 . So, the corresponding value of Z ₀.₀₀₅ is 2.576 . The only value of p is 11.8% (year 2000 estimate ) of what is required for getting an answer
= 118/1000= 0.118
Finally, we put all these values into formula of sample size , i.e.,
N= ( 2.576 / 0.02)² (0.118 )(1- 0.118) = 1726.56 1727
Our sample size is , 1727 point.
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Line m passes through points (9, 9) and (6, 1). Line n passes through points (10, 7) and (1, 15). Are line m and line n parallel or perpendicular?
Answer:
Step-by-step explanation:
Slopes of parallel lines are the same. ( [tex]m_{1}[/tex] = [tex]m_{2}[/tex] )
Slopes of two perpendicular lines are opposite reciprocals. ( [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = - 1 )
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
~~~~~~~~~~~~~
(9, 9)
(6, 1)
[tex]m_{m}[/tex] = [tex]\frac{1-9}{6-9}[/tex] = [tex]\frac{8}{3}[/tex]
(10, 7)
(1, 15)
[tex]m_{n}[/tex] = [tex]\frac{15-7}{1-10}[/tex] = - [tex]\frac{8}{9}[/tex]
Lines m and n neither parallel, nor perpendicular.
I need to know what system of inequalities is graphed below
SOLUTION:
For inequalities, the solution to is usually where the two regions meet.
The graphs here are:
[tex]\begin{gathered} x-3y\leq6\text{ (thick lines)} \\ \text{Here, checks the graph testing points (3,-1) and (0,-2)} \\ 2x\text{ }+\text{ y }>2.\text{ (broken lines)} \\ \text{Here, the checks the graph testing points (}0,2)\text{ and (1,0)} \end{gathered}[/tex]Final answer:
The final answer here is Option (B)
I need help with these asap
1) What is the equation of the line through the points (1,1), (5,4), (9,7), and (13,10)
A) y = 4/3 x + 1/3
B) y = 4/3 x - 1/3
C) y = 3/4 x + 1/4
D) y = 3/4 x - 1/4
2) Image
1st question (the image):
y= -5/4x + 3/2
how to solve:
y=mx+b
b: where the line meets the y axis
3/2 is 1.5 which matches up perfectly with the graph
m: the direction of the slope
If you look where the line matches with a point and you go down -5 and go right 4 it matches up and thats why m = -5/4
2nd question (the text):
C) y = 3/4 x + 1/4
how to solve
draw a graph (up above)
y:mx+b
to find m: rise/run
find the first point (1,1) you have to go 3 points up and 4 points right to get to the next point
(5,4) and thats why m=3/4
b: where the link hits the y axis compare the answers and the graph and find the most resonable one... which is 1/4
What is the volume of the diagram below?
Answer: 11 units^2
Step-by-step explanation: count the blocks
3y=x-6 in standard form
Answer: x-3y=6
Step-by-step explanation:
so first subtract x to get -x+3y = -6 because standford is ax+by = c
and then multiply by -1 since x has to be positive
x-3y = 6 That is your answer
Evaluate the given expression.
10 C4 4C2
a.
1,260
C.
1,275
b.
1,278
d.
1,270
The value of an expression using combinations ¹⁰C₄ ⁴C₂ is 1260.
What is the combination?The combination is a mathematical method for counting the number of potential configurations in a set of elements when the order of the selection is irrelevant.The formula for finding the combination of any given expression is given:
ⁿCr =(n!)/(r!(n*r)!)So,
¹⁰C₄ ⁴C₂¹⁰C₄ = 10! /(4!(10-4)!)¹⁰C₄ = 10! /(4!)*6!¹⁰C₄ = (10*9*8*7*6*5*4*3*2*1)/(4*3*2*1*6*5*4*3*2*1)¹⁰C₄ = 210Then,
4C2 = 4! /(2!(4-2)!)4C2 = 4*3*2*1) /(2*1*2*1)4C2 = 6¹⁰C₄ ⁴C₂ = 210*6 ¹⁰C₄ ⁴C₂ =1260Therefore, the value of an expression using combinations ¹⁰C₄ ⁴C₂ is 1260.
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10. Which of the following is equivalent to thisexpression?72.7-4Tutor
To answer this question we need to remember that:
[tex]a^ma^n=a^{m+n}[/tex]then:
[tex]\begin{gathered} 7^2\cdot7^{-4}=7^{2-4} \\ =7^{-2} \end{gathered}[/tex]now we need to remember that:
[tex]a^{-n}=\frac{1}{a^n}[/tex]hence:
[tex]7^{-2}=\frac{1}{7^2}[/tex]Therefore:
[tex]7^{-4}\cdot7^2=\frac{1}{7^2}[/tex]and the asnwer is A.
5.What is the area of the triangle?Include the unit of measurein your answer.:::::
Answer: Area = 126 square inches
Explanation:
The formula for calculating the area of a triangle is expressed as
Area = 1/2 x base x height
From the information in the diagram,
base = 18
height = 14
Thus,
Area = 1/2 x 18 x 14
Area = 1/2 x 252 = 252/2
Area = 126 square inches
help please ill give brainlest !!
Answer:
-31, 9, 1, 5, 37
Step-by-step explanation:
f(x) = -2(-2)^2 + 1
f(x) = 4^2 + 1
f(x) = 8+1
f(x) = 9
f(x) = -2(0)^2 +1
f(x) = 0^2 + 1
f(x) = 0 + 1
f(x) = 1
f(x) = -2(1)^2 + 1
f(x) = -2^2 + 1
f(x) = 4+1
f(x) = 5
f(x) = -2(3)^2 + 1
f(x) = -6^2 + 1
f(x) = 36+1
f(x) = 37
the length and width of a rectangle are consecutive integers. the area of the rectangle is 210 square meters. find the length and width of the rectangle
The length and the width of the rectangle are 14 and 15 meters, respectively
How to determine the dimension of the rectangle?From the question, the statement is given as
Length and width are consecutive integers
Where
Area = 210 square feet
Represent the dimensions with x and y
Where Length = x and Width = y
And also, we have
y = x + 1
The area of a rectangle is
Area = Length x width
Mathematically, this can be represented as
Area = x * y
So, we have
x * y = 210
Substitute y = x + 1 in x * y = 210
x * (x + 1) = 210
Express 210 as 14 * 15
x * (x + 1) = 14 * 15
This means that
x = 14
Substitute x = 14 in y = x + 1
y = 14 + 1
Evaluate
y = 15
So, we have
x = 14 and y = 15
Hence, the length and the width are 14 and 15 meters
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An online furniture store sells chairs and tables. Each day, the store can ship no more than 19 pieces of furniture. Write an inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint.
An inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint is (c + t) ≤ 19
In this question, we have been given the online furniture store can ship not more than 19 pieces of chairs and tables each day.
If the possible number of chairs they can ship each day is represented by c and the possible number of tables they can ship each day is represented by t, then the inequality equation can be written as
(c + t) ≤ 19
Therefore, an inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint is (c + t) ≤ 19
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A ball is thrown straight down from the top of a 300-ft building with an initial velocity of -12 ft per second.
The position function is s(t) = -16t² +vot+so. What is the velocity of the ball after 4 seconds?
Answer:
Below in bold.
Step-by-step explanation:
s(t) = -16t² - 12t + 300
v(t) = ds/ dt = -32t - 12
At time t:
velocity = -32(4) - 12 = -140 ft/s.
For a diving event, the highest and the lowest of seven scores are discarded. Next, the total of the remaining scores is multiplied by the degree of difficulty of the dive. That value is then multiplied by 0.6 to determine the final score. Find the final score for the dive.
A drawing of a score board of the event, 3-meter springboard. It shows the scores of the 7 judges as Judge 1, 80; judge 2, 75; judge 3, 90; judge 4, 70; judge 5, 80; judge 6, 85; judge 7, 75. The difficulty level is marked as 3.1.
Answer: 734.7
Step-by-step explanation:
We get rid of 90 and 70 since they are the highest and lowest scores.
80+75+80+85+75 = 395
395 * 3.1 = 1224.5
1224.5*0.6 = 734.7
A way to write a fraction as an equivalent fraction that contains no common factors is _________ form.
Answer:
simplest form.
Step-by-step explanation:
The sides of an equilibrium triangle are 9.4cm,correct to the nearest milimetre. Work out the upper bound of the perimeter of this triangle.
The perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.
What are the upper and lower bounds of an approximation?The numerical value that is rounded up to represent the supplied value's next value serves as its upper bound.
The numerical number that is rounded off for the previous value or the predicted value of the provided value is the lower bound for the supplied value.
The sides of an equilateral triangle are 9.4 cm
The perimeter of an equilateral triangle = 3 × length of the side
The perimeter of an equilateral triangle = 3 × 9.4
The perimeter of an equilateral triangle = 28.2 cm
Hence, the perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.
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Anjelah took a hike.She finished in 2 hours and 47 minutes.If she started at 10:15 A.M.,what time did she finish?
Anjelah finished at 1:02 P.M. if she started at 10:15 A.M. and she took 2 hours and 47 minutes to complete it.
According to the question,
We have the following information:
Anjelah finished in 2 hours and 47 minutes.
She started at 10:15 A.M.
Now, we know that there are 60 minutes in an hour (more to know: there are 60 seconds in a minute).
So, we will add 2 hours to 10:15 A.M.:
10:15 + 2:00
12:15 P.M.
(Note that the digits before the colon gives us time in hours and the digits after the colon gives us minutes.)
Now, we will add 47 minutes to it:
12:15 + 0:47
(Now, we know that only 45 minutes can be added to 15 minutes because then it will make an hour. So, 2 more minutes will be added to the next hour.)
So, we have the following expression:
1:02 P.M.
Hence, the time when Anjelah will finish is 1:02 P.M.
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There are 4,000 books in the town's library. of these, 2600 are fiction. write a percent equation that you can use to find the percentage of books that are fiction. then solve your equation.
The percent equation is = 2600/ 4000 × 100/1
The percentage of books that are fiction is 65%
What is percentage?Percentage can be described as the ratio, quotient or number that is being expressed as a fraction of 100.
It is also described as the given part or amount in every hundred.
It is expressed as a fraction with 100 as the denominator of the fraction
It is represented with the symbol "%".
Given the information ;
Total number = 4000 books
Fiction books = 2600
The percentage is represented as;
= 2600/ 4000 × 100/1
Find the ratio
= 0. 65 × 100/1
Multiply through
= 65%
Hence, the value is 65%
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Write the expression as a monomial in standard form. -0.01a^4*(-10a^5)^3
The monomial -0.01a^4*(-10a^5)^3 as a single expression is 10a^19
How to rewrite the expression?The expression is given as
-0.01a^4*(-10a^5)^3
Evaluate the expression in the bracket
So, we have the following equation
-0.01a^4*(-10a^5)^3 = -0.01a^4 * (-1000a^15)
Next, we remove the bracket
So, we have the following equation
-0.01a^4*(-10a^5)^3 = 0.01a^4 * 1000a^15
Evaluate the products in the above equation
So, we have
-0.01a^4*(-10a^5)^3 = 10a^19
Hence, the equivalent expression is 10a^19
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A public storage company charges new customers an initial fee of $35.00. Each month of storage costs $18.75. The company uses the formula T = 35.00 + 18.75m to calculate the total charges, where T is the total charges, and m is the number of months of storage. How many months of storage would cost a new customer $260.00?
Answer:
12 months
Explanation:
Given the function that models the total chacrge of a company as T = 35.00 + 18.75m where;
T is the total charges,
m is the number of months of storage
Given
T = $260.00
we are to find the value of m
Substitute
260 = 35 + 18.75m
18.75m = 260 - 35
18.75m = 225
m = 225/18.75
m = 12
Hence it will take 12 months to cost a new custimer $260.00
A ball, dropped vertically falls d metres in t seconds
d is directly proportional to the square of t
The ball drops 125 metres in the first 5 seconds
How far does the ball drop in nthe next 9 seconds?
The distance covered in the next 9 seconds is 405 meters
How to determine the distance coveredThe variation statement is given as
d is directly proportional to the square of t
This means that
d = kt²
Where k represents the constant of variation
Using the parameters in the question, we have
When d = 125, t = 5
Substitute d = 125, t = 5 in d = kt²
This gives
125 = k x 5²
Evaluate
k = 5
So, we have
d = 5t²
After 9 seconds, we have
t = 9
Substitute t = 9 in d = 5t²
Here, we have
d = 5 x 9²
This gives
d = 405
Hence, the distance is 405 meters
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the vertex of the function shown below is located at?
Given the graph of the parabola
AS shown in the figure
The coordinate of the vertex is the point (2.5, 2.25)
so, the answer will be:
the vertex of the function shown below is located at (2.5, 2.25)
Given f(x) = -x - 2, find f(-6).
Answer:
f( -6) = 4
Step-by-step explanation:
f(x) = -x -2 You will replace x with -6
f(-6) - -(-6) -2
f(-6) = 6 - 2
f(-6) = 4