Answer: y=-5
Step-by-step explanation:
12-12=0
-18-12=-30
6y=-30
y=-5
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]Bo rolls a fair 6-sided number cube then chooses one card from a deck of four cards numbered 1through 4. What is the probability that the number cube and the card have the same number?
the probability is 1 whole number 1 over 2
in a sale normal prices are reduced by 15%. The sale price of a CD player is £102. work out the normal price of the CD player
The normal price for the CD player is $117.30
How to calculate the value?Since the normal prices are reduced by 15%, the percentage for the normal price will be:
= 100% + 15%
= 115%
Also, the sale price of a CD player is £102.
Therefore, the normal price will be:
= Percentage for normal price × Price
= 115% × $102
= 1.15 × $102
= $117.30
The price is $117.30.
Learn more about percentages on;
brainly.com/question/24304697
#SPJ1
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 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.
NAMEDATEPERIOD21. Clare has a 1/2 liter bottle full of water. A cone-shaped paper cup has diameter 10 cmand slant height 13 cm as shown. Can she pour all the water into one paper cup, or willit overflow? Explain your reasoning. (3 pts.)(The volume of a cone ismerhand liter = 500 cubic centimeters)10cm13 cm
We have the following:
The first thing is to calculate the volume of the cone
[tex]\begin{gathered} V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h \\ \end{gathered}[/tex]where r is the radius and h is the height
the radius is half the diameter, like this
[tex]r=\frac{d}{2}=\frac{10}{2}=5[/tex]The radius is 5 cm.
Now, for the height, we calculate it by means of the Pythagorean theorem that says the following
[tex]\begin{gathered} c^2=a^2+b^2 \\ c=13 \\ a=5 \\ b=h \\ \text{replacing:} \\ 13^2=5^2+h^2 \\ h^2=13^2-5^2 \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144}=12 \end{gathered}[/tex]The height is 12 cm
The volume is:
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot5^2\cdot12 \\ V=314 \end{gathered}[/tex]The water bottle has a total of 500 cubic centimeters, while the cone is 314 cubic centimeters, therefore it cannot pour out all the water and it would overflow
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.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
simplify 3p x 5q x 2
30pq=3p×5q=15pq×2=30pq
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]Larry is measuring the volume of a pitcher. He uses a measuring cup that holds 2 cups and fills the measuring cup 7.5 times to fill the entire pitcher. How much does the pitcher hold?
Given,
The amount of liquid hold by measuring cup is 2 cups.
The number of times measuring cup used to fill the pitcher.
Required:
The amount of liquid pitcher hold.
The amount of liquid hold by the pitcher is,
[tex]Amount\text{ of liquid = number of times measuring cups used}\times amount\text{ of liquid hold by measuring cup}[/tex]Substituting the values.
[tex]\begin{gathered} Amount\text{ of liquid =7.5}\times2\text{ cups} \\ =15\text{ cups} \end{gathered}[/tex]Hence, the pitcher can hold 15 cups.
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.
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
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.
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
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
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
HELPPPPAbigail buys 3 gallons of milk a week. How many pints of milk does she buy?
Answer:
She buys 24 pints of milk
Step-by-step explanation:
The conversion rule for a pint to the gallon is represented:
[tex]\text{ 1 pint=0.125 gallons}[/tex]Then, we can make a proportional relationship to determine how many pints of milk she buys:
[tex]\begin{gathered} \frac{1}{0.125}=\frac{x}{3} \\ x=\frac{3}{0.125} \\ x=24\text{ pints} \end{gathered}[/tex]......................
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
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
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
Learn more about about slope intercept form here
brainly.com/question/9682526
#SPJ1
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]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
Z A I + 5 4x - 3 3r-1 2x + 1 What value of x makes ASTW - AXYZ? s 3 + 1 T 4r-5 x = 2 X = 3 X=4 X=1
Here, we have two congruent triangles.
Given:
ST = 3x - 1 XY = 4x - 5
SW = 3x + 1 XZ = 4x - 3
TW = 2x + 1 YZ = x + 5
Since triangle STW and triangle XYZ are congruent, they have exactly the same corresponding sides.
To find the value of x, equate the corresponding sides and evaluate.
ST = XY
SW = XZ
TW = YZ
Take one of the corresponding sides.
We have:
ST = XY
3x - 1 = 4x - 5
Subtract 4x from both sides:
3x - 4x - 1 = 4x - 4x - 5
-x - 1 = -5
Add 1 to both sides:
-x - 1 + 1 = -5 + 1
-x = -4
Divide both sides by -1:
[tex]\begin{gathered} \frac{-x}{-1}=\frac{-4}{-1} \\ \\ x=4 \end{gathered}[/tex]Therefore, the value of x that makes ΔSTW ≅ ΔXYZ is 4
ANSWER:
x = 4
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.
2/3 divided 17/28 equals what?
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:
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.
An accountant finds that the gross income, in thousands of dollars, of a small business can be modeled by the polynomial −0.3t 2 + 8t + 198, where t is the number of years after 2010. The yearly expenses of the business, in thousands of dollars, can be modeled by the polynomial −0.2t 2 + 2t + 131.a. Find a polynomial that predicts the net profit of the business after t years. b. Assuming that the models continue to hold, how much net profit can the business expect to make in the year 2016?I know that the equation is -0.1t^2+6t+67, but i don't know how to find part b.
ANSWER:
STEP-BY-STEP EXPLANATION:
a.
We know that the net profit is equal to the incomes minus the expenses, therefore, the final equation would be:
[tex]\begin{gathered} \text{profit = income - expense} \\ \text{replacing} \\ p=-0.3t^2+8t+198-(-0.2t^2+2t+131) \\ p=-0.3t^2+8t+198+0.2t^2-2t-131 \\ p=-0.1t^2+6t+67 \end{gathered}[/tex]b. t is the number of the years after 2010. Therefore, for the year 2016, x is equal to 6 (2016 - 2010), we replace:
[tex]undefined[/tex]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
The sum of three
numbers is 18. The largest
is 5 times the smallest,
while the sum of the
smallest and twice the
largest is 22. Write a
system of equations to find
the numbers, then solve.
The required system of equation is x+y+z=18, z=5x, x+2z=22 and the required values of x=2, y=6 and z=10 by using the substitution method of solving equations and according to given conditions: The sum of three numbers is 18. The largest is 5 times the smallest, while the sum of the smallest and twice the largest is 22. .
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the other equation in this method, as the name implies.
x+y+z=18
z=5x
x+2z=22
x+10x=22
x=2
y=6
z=10
The required system of equations is x+y+z=18, z=5x, x+2z=22, with the required values of x=2, y=6, and z=10 when solving equations using the substitution method under the conditions stated: Three numbers added together equal 18. The sum of the smallest and twice-largest numbers is 22, while the largest is five times the smallest.
To know more about system of equation,
https://brainly.com/question/10413253?referrer=searchResults
#SPJ13