Choose the correct translation for the following statement.It must exceed seven.Ox<7Ox57Ox>7Ox27
Solution:
Given that a value or quantity must not exceed ten, let x represent the value or quantity.
Since it must not exceed 10, this implies that
[tex]x\leq10[/tex]The second option is the correct answer.
Nicholas and Jack volunteer to fill gift boxes for soldiers serving overseas. Both work at a constant rate. They work together for 6 hours and fill 126 boxes. Nicholas fills 9 boxes every hour. How many boxes does Jack fill every hour?
Firstly, we need to know the number of boxes they both filled per hour.
From the question, we are told that 126 boxes were filled in six hours; thus in an hour, the number of boxes filled will be 126/26 = 21 boxes
Now in an hour, Nicholas filled 9 boxes; the number of boxes that will be filled is clearly the remainder of the 21 boxes.
The number of boxes filled by Jack is thus; 21 - 9 = 12 boxes
Jack fills 12 boxes in an hour
Help please.
We have the equation negative 9 minus this whole expression, 9x minus 6—this whole thing is being subtracted from negative 9—is equal to 3 times this whole expression, 4x plus 6.
Solve the Equation
The value of x in the equation given is x = -4/7.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The information given will be illustrated as:
9 - (9x - 6) - 9 = 3(4x + 6)
9 - 9x + 6 - 9 = 12x + 18
Collect like terms
-9x + 6 = 12x + 18
-9x - 12x = 18 - 6
-21x = 12
Divide
x = 12/-21
x = -4/7
This illustrates the concept of equations.
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Your family decides to go out to dinner to celebrate your brothers graduationfrom high school. The family's meal cost $75. Your waitress did a great job andyour parents decide to leave her a 20% tip. How much tip money should yourparents leave her if they leave her 20%? And what is the total cost of the meal? *
$75 -----> 100%
x ---------> 20%
[tex]\begin{gathered} x\times100=75\times20 \\ 100x=1500 \\ \frac{100x}{100}=\frac{1500}{100} \\ x=15 \end{gathered}[/tex]asnwer 1: they leave her $ 15
answer 2: the total cost of the meal is
[tex]75+15=90[/tex]$ 90
Erica paid a self employment tax last year. she calculated the self-employment tax for different amounts of net earnings and recorded them in a table shown . Which function describes the relationship between X ,amount of net earrings and y ,the self- employment.
Answer:
[tex]y=\frac{153}{1,000}x[/tex]Step by step explanation:
Linear functions represent situations that have a constant rate of change, and they are represented by:
[tex]\begin{gathered} y=kx \\ \text{where,} \\ k\text{ is the constant rate of change} \end{gathered}[/tex]We can calculate the constant rate of change with the following formula:
[tex]\begin{gathered} k=\frac{\Delta y}{\Delta x} \\ k=\frac{2,295}{15,000} \\ k=\frac{153}{1,000} \end{gathered}[/tex]Then, the function that describes the relationship between x, the number of net earnings, and y, the self-employment tax would be:
[tex]y=\frac{153}{1,000}x[/tex]Solve each system of equations "-x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3
show your work please so i can understand how to do it!
x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given three equations are
-x+y+2z=-5.....(1)
5x+4y-4z=4....(2)
x-3y-2z=3....(3)
Add equations (1) and (3)
-x+y+2z+x-3y-2z=-5+3
Add the like terms
-2y=-2
y=1
Now put value of y in equations (1) and (2)
-x+2z=-6..(4)
5x-4z=0...(5)
Multiply with 5 on equation 4 and add with equation 5
-5x+10z+5x-4z=-30
6z=-30
z=-5
Now put y and z values in equation (1)
-x+1+2(-5)=-5
-x+1-10=-5
-x-9=-5
-x=4
x=-4
Hence x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3
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32. Recall the pattern that you found in the diamond problems from Ready, Set, Go #2. Use the pattern you discoveredto complete each diamond below.8-121-724ISet
Answer:
Step-by-step explanation:
Help please and thank you
If f(x) is a linear function and gives f(3) = 3 and f(9) = -2
Part a
The slope of the line = -5/6
Part b
The y-intercept = 11/2
Part c
f(x) = (-5/6)x + 11/2
The values of
f(3) = 3
f(9) = -2
The points are (3,3) and (9,-2)
Part a
The slope of the line is the change in y coordinate with respect to the change in x coordinate.
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{-2-3}{9-3}[/tex]
=-5/6
Part b
The slope intercept form of the line
y = mx+b
b is the y intercept
Substitute the values in the equation
3 = (-5/6)×3 + b
3= -5/2 + b
b = 11/2
Part c
Then the linear function f(x) = (-5/6)x + 11/2
Hence, if f(x) is a linear function and gives f(3) = 3 and f(9) = -2
Part a
The slope of the line = -5/6
Part b
The y-intercept = 11/2
Part c
f(x) = (-5/6)x + 11/2
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Elsa drove 14 laps on a race track. Each lap was the same length. If she drove atotal of 30.8 mi what was the length of each lap? Write your answer in yards.Use the table of conversion facts as necessary, and do not round your answer.Conversion facts for length12 inches (in) = 1 foot (ft)3 feet (ft) = 1 yard (yd)36 inches (in) = 1 yard (yd)5280 feet (ft) = 1 mile (mi)1760 yards (yd) = 1 mile (mi)|0ydGХ?
Givens.
• The total number of laps is 14.
,• The total distance is 30.8 miles.
First, divide the total distance by the number of laps.
[tex]\frac{30.8mi}{14}=2.2mi[/tex]Each lap length is 2.2 miles.
Let's transform it to yards using the conversion factor 1 mile = 1760 yards.
[tex]2.2mi\cdot\frac{1760yd}{1mi}=3872yd[/tex]Therefore, each lap length is 3872 yards.
You roll a six-sided die twice. What is the probability of rolling an even number and then an odd number?A)1B)1/3 큼C)nilaD)
Let's begin by listing out the given information:
A fair dice has 6 sides
The dice has its sides numbered from 1-6
The number of sides with even numbers (2, 4 & 6) equals 3
The number of sides with odd numbers (1, 3 & 5) equals 3
The probability of rolling an even number is given as shown below:
[tex]\begin{gathered} P=\frac{Number\text{ of Possible Outcome}}{Total\text{ Number of Outcome}} \\ P\mleft(even\mright)=\frac{3}{6}=\frac{1}{2} \\ P(even)=\frac{1}{2} \end{gathered}[/tex]The probability of rolling an odd number is given as shown below:
[tex]\begin{gathered} P=\frac{Number\text{ of Possible Outcome}}{Total\text{ Number of Outcome}} \\ P(odd)=\frac{3}{6}=\frac{1}{2} \\ P(odd)=\frac{1}{2} \end{gathered}[/tex]The probability of rolling an even number followed by an odd number is obtained by the product of the probabilities above. We have:
[tex]\begin{gathered} P(even,odd)=P(even)\times P(odd) \\ P(even,odd)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \\ P(even,odd)=\frac{1}{4} \end{gathered}[/tex]Therefore, the probability of rolling an even number and then an odd number is 1/4
Conver 10 feet per second to inches per second
Answer:120 inches per second
Step-by-step explanation:120 inches per second this is because 1 ft= 12 inches so you can multiply 10 x 12 which is 120 inches.
the perimeter of a rectangle is a rational number. the length of a rectangle is 6 units. the width of a rectangle must be a/an rational/irrational (circle one) number.
A rational number
Explanations:The perimeter of a rectangle is given by the formula:
Perimeter = 2(Length + Width)
The Length = 6 units
Perimeter = 2 (6 + Width)
Perimeter = 12 - 2 Width
2 Width = 12 - Perimeter
Width = (12 - Perimeter)/2
Note that a rational number is a number that can be written as a fraction of two integers.
Since the perimeter is said to be a rational number, any rational number substituted into the formula equation for the width above will give a rational number.
The width of the rectangle is therefore a rational number
The equation for the line of best fit is shown below.What does the y-intercept represent? A. the cost to upload an unlimited amount of files B. the cost to enroll in the file sharing service C. the cost per file uploaded D. the cost per Mb uploaded
Answer:
B. the cost to enroll in the file-sharing service
Explanation:
The y-intercept is the cost when x = 0. It means that it is the cost of the service when the customer uploads 0 Mb, so it should represent the cost to enroll in the file-sharing service.
simplify 3p x 5q x 2
30pq=3p×5q=15pq×2=30pq
identify the equation
SOLUTION
We want to identify the equation that represents the data in the table.
Let's put the first values for x and y from the table, that is x = -2 and y = 11 and see if it works for the first option
[tex]y=x+5[/tex]This becomes
[tex]\begin{gathered} y=x+5 \\ y=-2+5 \\ y=3 \end{gathered}[/tex]Since we didn't get y = 11, but we got y = 3, then the first option is wrong.
Let's try the next one
[tex]y=-3x+5[/tex]This becomes
[tex]\begin{gathered} y=-3x+5 \\ y=-3(-2)+5 \\ y=6+5 \\ y=11 \end{gathered}[/tex]So, we got y = 11, this option should be the correct answer, but let us confirm with the next values of x and y which are (0, 5).
So we will put x = 0, if we get y = 5, then the option is correct, so
[tex]\begin{gathered} y=-3x+5 \\ y=-3(0)+5 \\ y=0+5 \\ y=5 \end{gathered}[/tex]Since we got y = 5, this option is correct.
Hence, the answer is the 2nd option.
[tex]y=-3x+5[/tex]Identify the domain, vertical asymptotes and horizontal asymptotes of the following rational function: f(x)= \frac{3x-4}{x^3-16x} Domain is all real numbers except x\neq Answer , Answer and AnswerVertical asymptote at x= Answer , Answer and AnswerHorizontal asymptote at y= Answer
Answer
Domain is all real numbers except x ≠ 0, -4, and 4
Vertical asymptote at x = 0, -4, and 4
Explanation
Given function:
[tex]f(x)=\frac{3x-4}{x^3-16x}[/tex]Note: The domain of a function is a set of input or argument values for which the function is real and defined.
For the function to be real; the denominator must not be equal zero, i.e.
[tex]\begin{gathered} x^3-16x\ne0 \\ x(x^2-16)\ne0 \\ x(x-4)(x+4)\ne0 \\ x\ne0,x-4\ne0,\text{ and }x+4\ne0 \\ \therefore x\ne0,x\ne4,\text{ and }x\ne-4 \end{gathered}[/tex]Hence, the domain is all real numbers except x ≠ 0, -4, and 4.
Note: A vertical asymptote with a rational function occurs when there is division by zero.
Hence, the vertical asymptote at x = 0, -4, and 4
Find the value of z such that 0.03 or f the area lies to the right of z Round your answer tom2 decimal places
ANSWER
z = 1.88
EXPLANATION
We have to find z such that the area under the normal curve to the right of that value is 0.03,
This is the same as finding z such that the area to the left of that value is 1 minus 0.03,
[tex]1-0.03=0.97[/tex]These are the values that z-score tables show. So, we have to find a z-score where the value in the table is 0.97,
The z-score whose area to its left is closest to 0.97 is z = 1.88.
Hence, for z = 1.88, the area under the curve to its right is 0.03.
The area of the triangle is 330 square feet.The height of the triangle is ___
Answer:
22 feet
Explanation:
The area of a triangle can be calculated using the following equation:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the base and h is the height.
We know that the area is 330 square feet and the base is 30 ft, so we can replace these values to get:
[tex]330=\frac{30\times h}{2}[/tex]Now, we can solve the equation for h. First, multiply both sides by 2:
[tex]\begin{gathered} 2\times330=2\times\frac{30\times h}{2} \\ 660=30\times h \end{gathered}[/tex]Then, divide both sides by 30:
[tex]\begin{gathered} \frac{660}{30}=\frac{30\times h}{30} \\ 22=h \end{gathered}[/tex]Therefore, the height of the triangle is 22 feet.
use the following graph to find the mean, median, and mode
Given:
A graph
To determine the Mean, Median, and Mode based on the given graph, we first get the data set as shown below:
2,5,5,5,5,6,9,11,12,13,14,15,18,20
Next, we find the Mean by getting the average:
[tex]\begin{gathered} Mean=\frac{2+5+5+5+5+6+9+11+12+13+14+15+18+20}{14} \\ Simplify \\ Mean=\frac{140}{14} \\ Mean=10 \end{gathered}[/tex]Then, we get the Median by getting the average of the two middle values since there is an even number of data values:
[tex]\begin{gathered} Median=\frac{9+11}{2} \\ Simplify \\ Median=10 \end{gathered}[/tex]Now, we get the Mode by finding the number that appears most frequently. Hence, the Mode is 5.
Therefore, the answer is:
Mean:10, Median:10, Mode:5
......................
Answer: x 0 1 2 3
p(x) 0.011 0.170 0.279 0.539
Given that the values of x =
Television 0 1 2 3
Household 30 443 727 1401
Let television be = x
Household = frequency = distribution
Firstly, we need to find the interval of x
The interval of x = Range between two numbers
1 - 0 = 1
2 -1 = 1
3 - 2 = 1
Hence, the interval is 1
[tex]p(x)\text{ = }\frac{frequency\text{ for x interval}}{N\text{ x w}}[/tex]Where N = total frequency
w = interval
Total frequency = 30 + 443 + 727 + 1401
Total frequency = 2601
[tex]\begin{gathered} \text{when x = 0} \\ p(x)\text{ = }\frac{30}{2601\text{ x 1}} \\ p(x)\text{ = }\frac{30}{2601} \\ p(x)\text{ = }0.011 \end{gathered}[/tex]when x = 1
[tex]\begin{gathered} p(x)\text{ = }\frac{443}{2601\text{ x 1}} \\ p(x)\text{ = }\frac{443}{2601} \\ p(x)\text{ = 0}.170 \end{gathered}[/tex]When x = 2
[tex]\begin{gathered} p(x)\text{ = }\frac{727}{2601\text{ x 1}} \\ p(x)\text{ = }\frac{727}{2601} \\ p(x)\text{ = 0.279} \end{gathered}[/tex]when x = 3
[tex]\begin{gathered} p(x)\text{ = }\frac{1401}{1\text{ x 2601}} \\ p(x)\text{ = }\frac{1401}{2601} \\ p(x)\text{ = 0.539} \end{gathered}[/tex]Therefore,
x 0 1 2 3
p(x) 0.011 0.170 0.279 0.539
Deck PlanOutside* EdgeWall A10 feetDoorway13 feet-10 feetWall BThe deck will have the shape of one fourthof a circle. What is the best estimate of thearea (A) of this deck?(Area of circle = tr2)πr)(Use 3.14 for it.)
18) the best estimate will be 75 square feet (option G)
Explanation:18) radius = 10ft
let π = 3.14
We are told the deck will have 1/4 the area of a circle. We need to first find the area of a circle.
Area of circle = πr²
[tex]\begin{gathered} Area\text{ of circle = 3.14 }\times\text{ 10}^2 \\ Area\text{ of circle = 314 ft}^2 \end{gathered}[/tex]Next, we will divide the area by 4:
[tex]\begin{gathered} Area\text{ of the deck = }\frac{area\text{ of circle}}{4} \\ Area\text{ of the deck = }\frac{314}{4} \\ \\ Area\text{ of the deck = 78.5 ft}^2 \end{gathered}[/tex]From the options, the one close to the result we got is 75 square feet
Hence, the best estimate will be 75 square feet (option G)
In gym class, a student can do 30 sit-ups in 60 seconds and 90 sit-ups in 180 seconds.
Graph the proportional relationship.
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 120 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 50
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30
A graph of the proportional relationship is given by: D. graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30.
What is a graph?A graph can be defined as a type of chart that's commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.
Mathematically, a proportional relationship can be modeled by the following linear equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.Furthermore, the graph of any proportional relationship is characterized by a straight line with data points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) decreases or increases, the values on the y-coordinate (y-axis) decreases or increases simultaneously.
In this context, we can reasonably infer and logically deduce that the relationship between the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of this graph is proportional and given by this equation:
y = 3x
Where:
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Answer:
A graph of the proportional relationship is given by: D. graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30.
Step-by-step explanation:
third time asking, please help.
In a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the
smallest angle. Find the measure of all three angles. Hint: The angles of a triangle add up to 180°
Answer:
The 3 angles are 22.5, 67.5 and 90 degrees.
Step-by-step explanation:
Let the smallest angle be x degrees.
Then the other angles = 3x and 2x + 45.
x + 3x + 2x + 45 = 180
6x = 180 - 45
6x = 135
x = 135/6 = 22.5 degrees
3x = 67.5 degrees
2x+45 = 90 degrees.
if 3x +6 = 18 what is 10x -2
38
1) Starting from the first equation
3x +6 = 18 Subtract 6 from both sides
3x = 18 -6
3x = 12 Divide both sides by 3
x =4
2) Since x =4, let's plug that into the second expression 10x -2 to find out "what is 10x -2"
10x -2 Replace x, by 4
10(4) -2 Effectuate the multiplication
40 -2
38
Hence, the answer is 38
pls help????? –2x = –20y + 18
Answer:
y = 1/10x + 9/10
Step-by-step explanation:
Find slope intercept form: –2x = –20y + 18
slope intercept form: y = mx + b
_______________________________
–2x = –20y + 18
add 20y to both sides:
–2x + 20y = –20y + 18 + 20y
–2x + 20y = 18
add 2x to both sides:
–2x + 20y + 2x = 18 + 2x
20y = 18 + 2x
divide all terms by 20:
20y/20 = 18/20 + 2x/20
y = 9/10 + 1/10x
reorder terms for slope intercept form:
y = 1/10x + 9/10
Answer:
[tex]y=\dfrac{1}{10}x+\dfrac{9}{10}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]-2x=-20y+18[/tex]
To write the given equation in slope-intercept form, make y the subject.
Add 20y to both sides:
[tex]\implies 20y-2x=-20y+18+20y[/tex]
[tex]\implies 20y-2x=18[/tex]
Add 2x to both sides:
[tex]\implies 20y-2x+2x=2x+18[/tex]
[tex]\implies 20y=2x+18[/tex]
Divide both sides by 20:
[tex]\implies \dfrac{20y}{20}=\dfrac{2x+18}{20}[/tex]
[tex]\implies \dfrac{20y}{20}=\dfrac{2x}{20}+\dfrac{18}{20}[/tex]
[tex]\implies y=\dfrac{1}{10}x+\dfrac{9}{10}[/tex]
Therefore, the given equation in slope-intercept form is:
[tex]\boxed{y=\dfrac{1}{10}x+\dfrac{9}{10}}[/tex]
food cost for your restaurant is about $.38 on the dollar. that means for every dollar in sales, you spend 38 cents in food cost.figure out the food cost for the following days’ sales:monday:$3,459.00tuesday:$2,976.81wednesday:$3,185.32thursday:$3,562.91friday:$4,582.13saturday:$4,820.36
The Solution.
Monday's sales is $3459.00
The food cost for Monday is
[tex]\text{ Food cost = 0.38}\times3459=\text{ \$1314.42}[/tex]Tuesday's sales is $2976.81
The food cost for Tuesday is
[tex]\text{Food cost = 0.38}\times2976.81=\text{ \$}1131.19[/tex]Wednesday's sales is $3185.32
The food cost for Wednesday is
[tex]\text{ Food cost = 0.38}\times3185.32=\text{ \$}1210.42[/tex]Thursday's sales is $3562.91
The food cost for Thursday is
[tex]\text{Food cost = 0.38}\times3562.91=\text{ \$}1353.91[/tex]Friday's sales is $4582.13
The food cost for Friday is
[tex]\text{Food cost = 0.38}\times4582.13=\text{ \$}1741.21[/tex]Saturday's sales is $4820.36
The food cost for Saturday is
[tex]\text{Food cost = 0.38}\times4820.36=\text{ \$}1831.74[/tex]Determine which point is the solution to the given system. y= -7/2 x + 32 y= 4/5 x -11
Answer:
(10, -3)
Step-by-step explanation:
[tex]-\frac{7}{2}x+32=\frac{4}{5}x-11 \\ \\ -35x+320=8x-110 \\ \\ -43x=-430 \\ \\ x=10 \\ \\ \therefore y=-\frac{7}{2}(10)+32=-3[/tex]
2/3 divided 17/28 equals what?
Factor the following polynomials completely.(x + y)³ + 1 =
Given the equation (x + y)³ + 1 , we can assume we have two terms here. These are (x + y)³ and 1. Since both terms are perfect cubes, we can use the sum of cubes formula which is:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]where a = (x+y) and b = 1.
Therefore, the factors of (x + y)³ + 1 is:
[tex]\begin{gathered} \mleft(x+y\mright)^3+1=(x+y+1)\lbrack(x+y)^2-(x+y)(1)+1^2) \\ (x+y)^3+1=(x+y+1)(x^2+2xy+y^2-x-y+1) \end{gathered}[/tex]The factor of (x + y)³ + 1 is (x + y + 1)(x² + 2xy + y² - x - y +1).
what is the slope of the line shown graohed belowzero5undefined-5
Answer: undefined
The slope of this graph is undefined because it does not run on the horizontal
Since, slope = y2 - y1 / x2 - x1
Therefore, x2 - x1 = 0
Slope = y2 - y1 / 0 = undefined