Answers
According to the direct variation model, the value of the variable y is the mixed number [tex]3 \frac {1}{5}[/tex]. (Correct choice: C)
What is the value of a variable according to a direct variation model?If a variable y varies directly with the variable x, then we can derive the following relationship to find the missing value:
y₁ / x₁ = y₂ / x₂
Where:
x₁, x₂ - Value of the variable x.y₁, y₂ - Value of the variable y.If we know that x₁ = 3 / 5, y₁ = [tex]2 \frac{2}{5}[/tex] and x₂ = 4 / 5, then the value of y₂ is:
y₁ = 2 + 2 / 5 = 12 / 5
y₂ = (y₁ / x₁) · x₂
y₂ = [(12 / 5) / (3 / 5)] · (4 / 5)
y₂ = (12 / 3) · (4 / 5)
y₂ = 4 · (4 / 5)
y₂ = 16 / 5
y₂ = 15 / 5 + 1 / 5
y₂ = 3 + 1 / 5
y₂ = [tex]3 \frac{1}{5}[/tex]
The value of the missing variable is the mixed number [tex]3 \frac{1}{5}[/tex].
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Related Questions
A bank tellers’ hourly wage will increase from $24 to $27.60. What percent increase does this represent? An employee’s salary for Alar Services is $37,500. Next year, she will get an 8% increase in salary. How much is her new salary?
Answers
(a).A bank tellers’ hourly wage will increase from $24 to $27.60.
The increament n wage is
[tex](27.60-24)=3.6[/tex]Therefore, the percent of increament is
[tex]\frac{3.6}{24}\times100=15[/tex]Therefore, it represents 15% increament.
(b). An employee’s salary for Alar Services is $37,500. Next year, she will get an 8% increase in salary.
So, new salary is
[tex]37500+(37500\times\frac{8}{100})=40500[/tex]Therefore, new salary is $40500.
The function shown can be used to determine the amount of money, indollars, in a savings account after m months. If no money is added orwithdrawn, which of the following is closest to the amount of money inthe account after 30 months?f(m) = 1500(1.003)^m
Answers
Given data:
The given function of amount of mmoney after m months is f(m)=1500(1.003)^m.
Substitute 30 for m in the given expression.
f(30)=1500(1.003)^(30)
=1500(1.094)
=1641
Thus, the total amount of money after 30 monnths is 1641.
Which equation represents the relationship shown in
the graph?
Answers
Answer:
[tex]y\le-\frac{1}{4}x^{2}+\frac{1}{2}x+12[/tex]
Step-by-step explanation:
It has to have a y-int of +12 so that eliminates the first 2.
It needs to be contained inside the parabola therefore the x^2 value needs to be negative.
It needs to be shifted 1/2 to the right, therefore it needs a pos x value.
Hope that helps
Which of the following represents a linear function? these are the options a, c or b How do you know?these are the options it creates a simple shapeit passes the vertical line testit is a straight line
Answers
We want to identify the linear function.
Of course,
a linear function is going to be a line
The vertical line test is for understanding whether it is a function or not.
By vertical line test,
Picture 1 [passes]
Picture 2 [passes]
Picture 3 [fails]
Now, we can clearly see that Option B is the a straight line, hence a linear function.
find the acute angle between the lines 2y+x=1 and x+3y=6
Answers
Given the equations of the lines:
[tex]\begin{gathered} 2y+x=1 \\ x+3y=6 \end{gathered}[/tex]the given equations written in standard form, we will rewrite in in the slope-intercept form
So,
[tex]\begin{gathered} y=-\frac{1}{2}x+\frac{1}{2} \\ y=-\frac{1}{3}x+\frac{6}{3} \end{gathered}[/tex]So, the slopes of the lines are { -1/2, -1/3 }
The acute angle between the lines of slopes m1 and m2 is given by the formula:
[tex]\text{tan}\theta=|\frac{m_{1_{}}-m_2}{1+m_1m_2}|[/tex]Substitute with slopes of the lines
So,
[tex]\tan \theta=|\frac{-\frac{1}{2}-(-\frac{1}{3})}{1+(-\frac{1}{2})(-\frac{1}{3})}|=|\frac{-\frac{1}{6}}{1+\frac{1}{6}}|=\frac{1}{7}[/tex]so, the angle will be:
[tex]\theta=\tan ^{-1}(\frac{1}{7})=8.13\degree[/tex]So, the answer will be the acute angle = 8.13°
What type of correlation is shown in this scatterplot 1. Perfect positive 2. Perfect Negavite 3. Low positive 4.High Negavite
Answers
SOLUTION
A Scatter Plot has points that show the relationship between two sets of data.
When the line shows a negative slope, the correlation is a negative correlation
Consider the image below
This shows a perfect Negative correlation between the set of data.
Hence
The Second option is Right(2)
help me please
thank you
Answers
Answer:
Domain: [1, 7], Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
What is 201 divided by 12
Answers
Answer: 16.75
Step-by-step explanation:
201/12
Try Again3Graph the line with slopepassing through the point (-4,5)
Answers
A force of 250 newtons stretches a spring 30 centimeters . Please find how much work is done in stretching the spring from 20 centimeters to 50 centimeters.
Answers
Camille attended a music store's banjo sale. She counted the types of banjos and made note of their discounts. 4 strings 5 strings 6 strings 25% off 4 4 8 50% off 6 8 3 What is the probability that a randomly selected banjo has 6 strings or 5 strings? Simplify any fractions.
Answers
number of banjos with 6 or 5 strings: 4 + 8 + 8 + 3 = 23
total number of banjos: 4 + 6 + 4 + 8 + 8 + 3 = 33
The probability that a randomly selected banjo has 6 strings or 5 strings is:
[tex]p=\frac{23}{33}[/tex]THE RECTANGLE BELOW IS DILATED BY A SCALE FACTOR OF 3.6 TO CREATE A NEW RECTANGLE. WHICH OF THE FOLLOWING COILD BE THE DIMENSIONS OF THE NEW RECTANGLE? A: 14.4 CM x 5.4 B: 5.4 cm x C: 7.2 cm x 1.8 cm D: 14.4 cm x 7.2 cm.
Answers
ANSWER:
A: 14.4 CM x 5.4
STEP-BY-STEP EXPLANATION:
We must multiply the value of the scale factor by the original measures of the rectangle, like this:
[tex]\begin{gathered} AB=3.6\cdot1\frac{1}{2}=5.4 \\ BC=3.6\cdot4=14.4 \end{gathered}[/tex]Which set of numbers are integers but not whole numbers or natural numbers?{V1, –4, V=5}IO{*}O {V2, , V3}O {0,1,2,3}O {-2, -3, - 4}
Answers
The set of whole numbers or natural numbers are the ones that appear naturally, which would go from 0 and beyond. While the set of integers are the numbers that don't have any decimal point, which would include negative numbers. Therefore the correct answer is the last option.
It takes a sheet metal worker 2/3 of an hour to fabricate a fitting, How many fittings can a sheet metal worker
make in an 8 hour day?
Answers
12 fittings can a sheet metal worker make in 8 hours.
What is ratio calculator?
Ratio Calculator is a formula used to solve ratio problems to express two or three numbers ratio to its simplest form.
2/3 hours taken to fabricate = 1 sheet
8 hours taken to fabricate = 8/2/3
= 4(3)
= 12
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Wesley has just been hired for a new job and wants to work out his budget for each month. The healthinsurance plan he selected has an average monthly premium of $294. The average monthly cost of hiselectric bill is $199 and the phone/internet/cable package he wants costs an average of $110 eachmonth. If his monthly salary is $1900, estimate the amount of money he will have after paying thesebills each month.
Answers
Answer:
$1297
Explanation:
First, let's add all the costs that Wesley has each month, so
$294 + $199 + $110 = $603
Because the health insurance cost $294, the electric bill is $199 and the phone/internet/cable cost $110.
Then, To find the amount of money that he will have after paying these bills, we need to subtract $603 from his salary, so
$1900 - $603 = $1297
Therefore, the answer is $1297
1. 3y=-3x+6
Slope_
y-intercept
Answers
Answer:
Slope = -1
y-intercept = 2
Step-by-step explanation:
Equation of a line in slope-intercept form is
y = mx + b
where m = slope and b =y-intercept
Here we have
3y = -3x + 6
Dividing by 3 on both sides:
y = -1x + 2
So slope m = -1, y-intercept b = 2
Hannah reads at a constant rate of
3pages every 8minutes.
Write an equation that shows the relationship between
p, the number of pages she reads, and
m
mm, the number of minutes she spends reading.
Answers
The relationship between p, the number of pages she reads, and m, the number of minutes she spends reading is 8p = 3m.
It is given in the question that Hannah reads at a constant rate of 3 pages every 8 minutes.
We have to write an equation that represents the relationship between p, the number of pages she reads, and m, the number of minutes she spends reading.
If she reads 3 pages every 8 minutes, then
She reads 1 page every 8/3 minutes.
If she reads p pages , she will take 8p/3 minutes
If m represents the number of minutes she she spends reading p pages.
Then, we can write,
8p/3 = m
8p = 3m
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Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene’s car had 6.5 gallons in the 15-gallon tank on the coldest day of the year. Irene filled the tank with gas that cos $3.70 per gallon.
How much did Irene spend on gas?
Answers
After doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.
What are mathematical operations?An operation is a mathematical function that converts zero or more input values into an output value with a known value.The number of operands affects how complex the operation is.The order of operations refers to the rules that define the sequence in which multiple operations should be performed to solve an expression.PEMDAS is an abbreviation for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, the amount Irene spends on gas:
The gas in the tank is 6.5 gallons.The gas amount per gallon is $3.70.Then, the amount of 6.5 gallons of gas:
6.5 × 3.70 = $24.05Therefore, after doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.
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Determine whether the coordinate plane shows a reflection in the x-axis, y-axis, or neither.O neitherO X-axisy-axis
Answers
1) To determine a reflection across the x-axis, the rule to be followed is
Pre-Image Image
(x,y) --------------------> (x, -y)
A reflection across the y-axis follows this one:
Pre-Image Image
(x,y) --------------------> (-x, y)
2) Let's pick one point from the pre-image and the image on the graph
Since A (-2,0) and F (1,-3) then we cannot state that there was a reflection across the x-axis or y-axis.
3) The answer is neither
Find the solution(s) for x in the equation below. 12 + 10.1 + 21 = 0 O A. I = -3; I = -7 OB. I = -3; 1 -3; r = 7 O c. 3; 1 = -7 3; D = 7 OD..I
Answers
Answer:
Choice A: x = -3, x = -7
Explanation:
To solve the equation for x, we use the quadratic formula which says that if you have an equation
hello I'm a 7th grader can you please help me with my math summer package and explain it in a way that a 7th grader can understand it.....I need help with number 1 ...
Answers
Suppose that both Brian and Kristen pay $18.42 in order to diminish their checkbook balance. Then, after the payment, their current balances would be
[tex]\begin{gathered} Brian:-23.45+18.42=-5.03 \\ Kristen:18.42-18.42=0 \end{gathered}[/tex]Therefore, after paying the same amount ($18.42), Kristen's debt has reduced to zero while Brian still owes $5.03.
Thus, Brian owes more money than Kristen.solve the system of equations for each variable x, y, and z. please show your work 2xy=z 4x+z=4y y=x+1
Answers
The solution of the system of equations 2xy = z, 4x + z = 4y, y = x + 1 are:
x = 1, y = 2, z = 4 and;
x = - 2, y = - 1, z = 4.
Consider the system of equations,
2xy = z ------------(1)
4x + z = 4y ------------(2)
y = x + 1 -------------(3)
Substituting equation (3) in equation (2),
4x + z = 4y
4x + z = 4( x + 1)
4x + z = 4x + 4
z = 4
Substituting equation (3) in equation (1),
2xy = z
2x( x + 1 ) = z
2x² + 2x = 4
x² + x = 2
Hence, x = 1, - 2
Therefore,
When x = 1,
y = x + 1 = 2
When x = - 2, y = x + 1 = - 1
So, the solution for the system of the equations are x = 1, y = 2, x = 4 and x = - 2, y = - 1, z = 4.
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Hana is organizing a 3/4 mile fun run. There will be a water station every 1/4 of a mile after the start. How many water station will there be?
Answers
There will be 3 water stations along the fun run using the mathematical operation of division.
What is a mathematical operation?A mathematical operation uses addition, subtraction, division, or multiplication to reach a result after combining variables, numbers, and mathematical operands.
In this situation, we only use division to get the quotient, which is the number of water stations along the fun run.
The total distance for a fun run = 3/5 miles (0.75 miles)
The spread of the water station along a mile = every 1/4 mile (0.25 miles)
The number of water stations along the run = 3 (0.75/0.25)
Thus, Hana needs to station 3 water stations along the run by dividing the total distance by the expected spread.
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Help pleasee i want it today
Answers
Answer:
Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example. Polynomials are used in engineering, computer and math based jobs, in management, business and even in farming. In all careers requiring knowledge of polynomials, variables and constants are used to create expressions defining quantities which are known and unknown.
Step-by-step explanation:
hope this helps you
state the value of as a 5/7 recurring decimal
Answers
Answer:
The value of 5/7 recurring numbers is 714285
Explanation:
The given fraction 5/7 is the equivalent of
0.7142857142857142857142857142857142857142857142857142857142857142...
Notice that the recurring numbers are:
714285
more help need 50 points
Answers
9p+25 is the answer.
Answer:
9p-25
Step-by-step explanation:
always do parentheses first
-5(-10p + 8p -5)-p
multiply negative with negative gives positive
-5(-2p-5)-p
variable always has a 1 in front
10p-1p-25
9p-25
Whoever helps me first with this gets a free gift card. Comment on the problem with my email. after that you can claim your reward plus a bonus of 30+ points
Answers
The table of 3 × 3 such that the sum of any row, column, or even diagonal is 30.3 has been created below.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Subtraction = Minus of any two or more numbers.
The third grid in first raw will be → 39.3 - (14.9 + 10.7) = 13.7
The third grid in second raw will be→ 39.3 - (13.7 + 11.3) = 14.3
The 2nd grid of 2nd raw will be → 39.3 - (17.9 + 11.3) = 13.1
The 1st grid in 2nd column will be→ 39.3 - (13.1+14.3) = 11.9
The 1st grid of 3rd raw will be → 39.3 - (14.9+11.9) = 12.5
The 2nd grid of 3rd raw will be → 39.3 - (12.5 + 11.3) = 15.5
Hence "The table of 3 × 3 such that the sum of any row, column, or even diagonal is 30.3 has been created below".
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3. David’s watch broke. He decides to get it fixed instead of replacing it. Since David is a loyal customer, he received a coupon in the mail for a discount. The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair. Explain what each part of the expression represents in the context of the problem.
Please show work :)
Answers
What each part of the expression represents in the context of the problem include the following:
r represents the original cost of the repair.0.07r represents the tax.(r – 20) represents the discount.What is an algebraic expression?An algebraic expression is a mathematical equation that can be used for showing the relationship which exist between two or more variables, numerical quantities, as well as in conjunction with different mathematical operations.
What is a coefficient?In Mathematics, a coefficient simply refers to a constant numerical value (number or numeral) that written before the variable in any algebraic expression.
Given the following algebraic expression:
0.07r + (r – 20)
In the context of fixing David’s broken watch, the variable r represents the original cost of the repair while 0.07r most likely represents the amount of money charged as tax. Lastly the expression (r – 20) represents the discount on fixing David’s broken watch.
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(Real-World Proportional Problems MC)
Three students are participating in a walkathon. The data for each student is shown.
Student A: The equation y = 14x represents the amount of money raised (y) for walking (x) miles.
Student B: $42 is raised after walking 3 miles.
Student C:
Miles Walked 6 9
Money Raised $72 $108
Determine which student raised the least amount of money after walking 8 miles.
Student A
Student B
Student C
All three students raised the same amount of money after walking 8 miles.
Answers
Student C raised the least amount of money after walking 8 miles.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
Given that;
Condition for A;
The equation y = 14x represents the amount of money raised (y) for walking (x) miles.
Condition for B;
$42 is raised after walking 3 miles.
Condition for C;
Miles Walked = 6 9
Money Raised = $72 $108
Now, For student A;
The amount of money raised for walking 8 miles will be;
⇒ y = 14x
⇒ y = 14 × 8
⇒ y = $112
So, The amount of money raised for walking 8 miles = $112
For student B;
The amount of money raised for walking 1 miles will be;
= $42 / 3
= $14 per mile
Hence, The amount of money raised for walking 8 miles will be;
= $14 x 8
= $112
So, The amount of money raised for walking 8 miles = $112
For student C;
The amount of money raised for walking 1 miles will be;
= $72 / 6
= $12 per mile
Hence, The amount of money raised for walking 8 miles will be;
= $12 x 8
= $96
So, The amount of money raised for walking 8 miles = $96
Therefore,
Student C raised the least amount of money after walking 8 miles.
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The value of c must be greater than 0 1 3 7
Answers
The true statement about the triangle is the value of c must be greater than 3.
How to complete the statementThe figure that completes the question is added as an attachment
From the figure, we have the following parameters
The length of segment AB is 12 units.The length of segment AC is 15 units.The length of segment of BC is represented by the variable c
By the triangle inequality theorem, we have:
The sum of any two sides length is greater than the third length
This means that
12 + 15 > c
c < 27
Also, we have
15 + c > 12
c >-3
Lastly, we have
12 + c > 15
c >3
Using the list of options as a guide, we have x > 3 to be true
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