The equation of the line into slope-intercept form is y = x/3 - 6
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to put the equation of a line into slope-intercept form?From the question, we have the following equation that can be used in our computation:
9y−3x= −54
Rewrite properly
This gives
9y - 3x = -54
Divide through the equation by 3
So, we have the following representation
9y/3 - 3x/3 = -54/3
Evaluate
3y - x = -18
To rewrite as slope-intercept form is to make y the subject
So, we have
3y = x - 18
Divide through the equation by 3
So, we have the following representation
y = x/3 - 6
Hence, the equation is y = x/3 - 6
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Lily plans to bring beverages for the school . she has 4 liters of apple juice . Also, she will bring 3 liters of grape juice for every 10 people. How many total liters of apple juice and grape juice does she need to bring for 40 people?
Answer: 12
Step-by-step explanation: multiply it all together then divide it by the product.
A(n)
O element
O subset
O component
O group
is a member of a set.
Answer:
B. Subset
Step-by-step explanation:
A(n) subset is a member of a set
21. At the gränd opening of a sporting goods store, the store is giving a free (-shirt to every 12th
person who attends. They give a $25 gift card to every 30th person. Which person will get both
a t-shirt and a gift card?
The person at the 300th number will get a t-shirt and a gift card both.
Given, at the grand opening of a sporting goods store, the store is giving a free shirt to every 12th person who attends.
They give a $25 gift card to every 30th person.
We have to find that which person will get both a t-shirt and a gift card.
To find the person who will get both, we have to find the LCM of 12 and 25.
As, the LCM of 12 and 25 is 300
So, the person at the 300th number will get a t-shirt and a gift card both.
Hence, the person at the 300th number will get a t-shirt and a gift card both.
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4. Kojo is given $1.20 to buy some peaches and apples. Peaches cost
20c each, apples 10c each. He is told to buy at least 6 individual
fruits, but he must not buy more apples than peaches.
Let x be the number of peaches Kojo buys.
Let y be the number of apples Kojo buys.
(a) Write down three inequalities which must be satisfied.
(b) Draw a linear programming graph and use it to list the
combinations of fruit that are open to Kojo.
Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)
Given,
Kojo is given $1.20 to buy some peaches and apples. Peaches cost 20c each, apples 10c each.
He is told to buy at least 6 individual fruits, but he must not buy more apples than peaches.
Let x be the number of peaches Kojo buys.
Let y be the number of apples Kojo buys.
(a)Since Kojo has $1.20 to buy peaches and apples; and each peach and apple costs 20c and 10c respectively.
We have the following inequalitites:
0.20x = 1.20
0.10y = 1.20
0.20x + 0.10y = 1.20
(b)Possible combinations of fruits are as follows:
x = 1.20/0.20 = 6
y = 1.20/0.10 = 12
x = 1,2,3,4,5 ; y = 10,8,6,4,2
Thus, Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)
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Your ending inventories this week for pasta were 35, 41, 32, 19, and 47 boxes. You par value is 120 and a supplier comes each night. If the cost of a box of pasta is $2. 64, then what will you be charged for pasta this week?.
The cost of a box of pasta is $2. 64, then what will you be charged for pasta this week is $1,125.
Define cost.The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function. The average cost function is defined as A(x)=C(x)x, where x > 0. The average cost per unit is calculated by dividing the total cost by the number of units produced.
Given,
Your ending inventories this week for pasta were 35, 41, 32, 19, and 47 boxes. You par value is 120 and a supplier comes each night.
Par level = [(120 - 35) + (120 - 41) + (120 - 32) + (120 - 19) + (120 - 47)]
Par level = [85 + 79 + 88 + 101 + 73]
Par level = 426 units.
Charges = par level × cost
Charges = 426 × 2.64
Charges = 1,124.64
Charges ≈ $1,125
The cost of a box of pasta is $2. 64, then what will you be charged for pasta this week is $1,125.
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help please..................................................................................................
Answer:
with what
Step-by-step explanation:
lol
where is the picture..................x1000000000000000000
Solve this system of 3 variables with elimination. Once you eliminate 1 variable to get down to only 2, you can use Desmos but show all work/steps first.
3x − 4y + z = 2
−9x + 12y − 3z = − 6
4x − 2y − z = -16
The solution of the system of the equations are; x = -2/3, y = -1/2 and z = 1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The system of equation is given by;
3x − 4y + z = 2 ---- (1)
−9x + 12y − 3z = − 6 -------(2)
4x − 2y − z = -16 -----(3)
Now we add equations 1 from equation 3;
(3x − 4y + z ) + (4x − 2y − z ) = 2 -16
7x - 6y = -14 -----(4)
Further we multiply equation 3 by 3 and subtract from equation 2;
3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6
12x - 6y - 3z + 9x - 12y + 3z = 42
21x - 18y = 42-----(5)
Now we multiply equation 4 by 3 and add it to equation 4
3(-3x + 3z) + (9x + 4z) = 5×3 - 2
-9x + 9z + 9x + 4z = 15 -2
13z = 13
z = 1
Now we put z = 1 in equation number 5
-3x + 3×1 = 5
-3x + 3 = 5
-3x = 5 - 3
-3x = 2
x = -2/3
y = -1/2
Therefore, the solution of the system of the equations are; x = -2/3, y = -1/2 and z = 1.
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If the interest for 4 years on rupees 350 be Rs 112,find the rate percent. In what time will rupees 800 amount to rupees 1120 at the same rate of interest?
Using Simple Interest formula ,
The rate percent on amount of Rs.300 is 5.5 .
At same rate, R = 5.5 the principle 800 will be Rs1120 in next 7 years .
In first case we have given that ,
principle = Rs.350
time = 4 years
Amount = Rs 1120
simple interest = 1120-350 = Rs.770
let rate of interest be R% .
Using the formul of simple interest
S.I = P×R×t /100
=> 770 = 350×4×R/100
=> R = 5.5 %
In Second case , rate of interest is same as in first case. So,
Amount = Rs. 1120
Principle = Rs. 800
rate of interest (R)= 5.5
Again simple interest formula Used:
Simple Interest = (P × R × T)/100
Simple interest = 1120 - 800 = Rs. 320
Simple Interest = (P × R × T)/100
⇒ 320 = 800×5.5 ×T/100
=> T = 7.27 ~ 7
∴ In the given principle Rs 800 with same rate of interest will be 1120 in 7 next years .
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Translate this sentence into an equation.
The product of 4 and Victor's savings is 60.
Use the variable v to represent Victor's savings. PLEASE THIS IS DUE TODAY!!!!
Answer:
4 × v = 60
= 15
Step-by-step explanation:
v represents Victor's savings
4 × v = 60
4v = 60
Divide both sides by 4v
v = 60/4
v = 15
The difference between a number and 5 is -11
Answer: n=-6
Step-by-step explanation:
1. Make your equation
n-5=-11
2. Solve for n by adding 5 to both sides
n=-6
Answer:
16
Step-by-step explanation:
1) Break down the question
We are told that the difference between a number a 5 is minus -11
As it is a minus we have to be careful we are using the correct operation required!
2) Figure out the number
As the difference is -11 we would need add 11 to 5 to get the final number
11 + 5 = 163) Check your answer makes sense
It is always best to double check your answer to make sure that your answer is 100% correct!
To do this we just have to work out way backwards.
16 - 11 = 5As we can see we have to minus 11 from 16 to get to 5 meaning our answer is correct and the number is 16!!!
Hope this helps, have a great day!
Henry compares the number of people in two cities. City A has a population of 863,400 people. City B has a population of 322,378 people. Estimate the number of people in each city as a single digit time a power of 10. How many times greater is the population of City A than the population of City B? Show your work
Answer:
I don't know I just got the app
Step-by-step explanation:
; /
39.7 consumers believe that cash will be obsolete in the next 20 years. assume that 6 consumers are randomly selected. find the probability that fewer than of the selected consumers believe that cash will be obsolete in the next 20 years.
The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;
Pr(C & fewer than 3) = 0.1985
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Here, we are required to find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.
Let Pr(C) be the number of consumers who believe that cash will be obsolete in the next 20 years.
Therefore, since 39.7% believe so,
Pr(C) = 39.7/100 = 0.397
If 6 consumers are selected randomly, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years will be;
Probability of 2 out 6 to believe so or Probability of 1 out of 6 to believe so.
Pr(2/6) + Pr (1/6)
Therefore the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is;
Pr (fewer than 3) = (2/6) + (1/6)
Pr (fewer than 3) = 3/6
Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;
Pr(C) × Pr (fewer than 3)
i.e 0.397 × (3/6) = 0.1985
Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;
Pr(C & fewer than 3) = 0.1985
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Morning knows that 15 pounds of hamburger meat will make 60 hamburgers. If Morgan needs to make 100 hamburgers for the picnic. How much hamburger meat does she need to buy?
?
Answer:
25 pounds of hamburger meat
Step-by-step explanation:
you need 15 pounds for 60 hamburgers.
We can turn this into a fraction.
15/60
now we need to make the denominator a power of ten.
15/60
=5/20
=25/100
She needs 25 pounds of hamburger meat
Marquis has a gross pay of $816. By how much will his gross pay be reduced if marquis has the following items withheld?federal tax of $92social security tax that is 6. 2% of his gross paymedicare tax that is 1. 45% of his gross paystate tax that is 22% of his federal taxa. $82. 66b. $129. 13c. $164. 01d. $174. 66.
As per the given tax percent deduction from Marquis gross pay of $816 , the gross pay is reduced by $174.66.
As given in the question,
Gross pay taken by Marquis is equal to $816
Items withheld from Marquis gross pay are as follow:
1. Federal tax = $92
2. Social security tax = 6.2% of gross pay
6.2% of 816
= (6.2/100) × 816
= $50.592
3. Medicare tax = 1.45% of gross pay
= 1.45% of 816
= (1.45/100) × 816
= $11.832
4. State tax = 22% of federal tax
= 22% of 92
= ( 22 /100) × 92
= $20.24
Total reduced tax amount from Marquis gross pay
= $ ( 92 + 50.592 + 11.832 +20.24 )
= $ 174.664
≈ $174.66
Therefore, for the given tax percent deduction from Marquis gross pay of $816 , the gross pay is reduced by $174.66.
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PLS HELP ASAP
Like AD is parallel to line HE. what is the value of x?
Answer:
Step-by-step explanation:
The value of x= 110 degrees as it is corresponding to the angle equal to 110 degrees.
a.
b.
Review &
Preview
The point (21, 32) is on a line with slope 1.5.
Find the equation of the line.
Find the coordinates of another point on the line.
The slope intercept form of equation of required line is
[tex]y = \frac{3}{2}x + \frac{1}{2}[/tex]
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Slope of the line = 1.5
The line passes through (21, 32)
Equation of required line =
[tex]y - 32 = 1.5(x - 21)\\y - 32 = \frac{3}{2}(x - 21)\\2y - 64 = 3x - 63\\2y = 3x - 63 + 64\\2y = 3x + 1\\y = \frac{3}{2}x + \frac{1}{2}[/tex]
Putting x = 1 on the line,
[tex]\frac{3}{2} \times 1 + \frac{1}{2}\\[/tex]
[tex]\frac{3 + 1}{2}\\\\\frac{4}{2}\\\\2[/tex]
(1, 2) is coordinate of another point on the line
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our text describes a trade-off that we must make as engineers between our confidence in the value of a parameter versus the precision with which we know the value of that parameter. that trade-off might be affected by whether we are looking at a two-sided or bounded (one-sided) interval. discuss your interpretation of the confidence-precision trade-off, and provide a few examples of how you might make a choice in one direction or the other in an engineering situation.
To boost the level of trust in the forecasted values, a balancing point must be attained.
The two phrases confidence interval and precision are intended to provide an accurate estimate of an object's measurability. We can compromise on the confidence level if the precision rises, but if the confidence level rises, the precision of the anticipated value likewise deteriorates.
Therefore, a balance point between these two variables must be reached in order to improve our confidence in the numbers being forecasted without compromising an accurate evaluation of accuracy. ensuring that accuracy and confidence are both upheld.
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help plss i need this done by 12
Answer:
oh no
Step-by-step explanation:
Find the measure of each angle indicated by the “?”. Also tell me what type of angle it is for example: alternate exterior.
Answer: ? = 50, same side interior angles
? = 84, alternate interior angles
Step-by-step explanation:
130 + x = 180
-130 = -130
x = 50
alternate interior angles are congruent
50° is the value of the missing angle.
Since u and v lines are parallel so the angle asked and the angle with the value of 130° are alternate interior angle.
Alternate interior angles have the following characteristics:
They are congruent: Alternate interior angles are equal in measure. If one angle measures x degrees, the other alternate interior angle will also measure x degrees.They are on opposite sides: Alternate interior angles are located on opposite sides of the transversal.They are inside the parallel lines: Alternate interior angles are positioned between the two parallel lines.Therefore,
x+130 = 180
x =180-130
x =50°
therefore, the missing angle is 50°.
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40 PIONTS ANSWER PLEZ IT IS NOW DUE!!!!!!
15. A triangle pattern is shown below.
Figure Perimeter
1 triangle 24
2 triangles 30
3 triangles 36
Which equation relates the number of triangles in the figure (n) to the perimeter of the figure (P)?
(1 point)
P = 6n + 18
P = 9n + 6
P = 6n + 9
P = 9n + 12
The equation that relates the number of triangles in the figure (n) to the perimeter of the figure (P) is P = 5n + 14.
We are given triangles. The triangles are arranged in a certain pattern. We need to find the relationship between the number of triangles and the perimeter of the figure. Let the perimeter of the figure having "n" number of triangles be represented by the variable "P(n)".
P(1) = 24
P(2) = 30
P(3) = 36
There is an increase of 6 units in the perimeter with every addition of a triangle. We can see and continue the pattern. The relationship between the perimeter and the number of triangles is given below.
P(n) = 18 + 6n
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what is the volume of a 1/5 by 2/5 by 3/5 rectangle?
Using the given information, the volume of the given rectangle is 6/125 cubic units
Calculating volume of rectangleFrom the question, we are to determine the volume of the given rectangle.
From the given information,
The dimension of the rectangle is 1/5 by 2/5 by 3/5
To determine the volume of the rectangle, we will determine the product of the length of the sides of the rectangle.
That is,
Volume of the rectangle = 1/5 × 2/5 × 3/5
Volume of the rectangle = 1 ×2×3 / 5×5×5
Volume of the rectangle = 6/125
Hence, the volume is 6/125 cubic units
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let the random variable x represent the profit made on a randomly selected day by a certain store. the distribution of x is approximately normal with a mean of $360 and a standard deviation of $50. what is the probability that the profit made by this store on a randomly selected day is greater than $400?
The number of standard deviations a score has from the population mean is measured by the z-score, also known as the standard score.
The range of the z-scores is from 3 to 3 on the normal distribution curve, and values outside of this range are called outliers. The z-score's formula is as follows:
Z=X-μ/σ
First, convert the given X value into a Z-score. Keep in mind that equals 50 and equals 360.As a result,
Z = 400-360/50 = 0.80
A measure of how dispersed the data are in relation to the mean is called the standard deviation (or ).Data with a low standard deviation are grouped around the mean, while data with a high standard deviation are more dispersed.
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What is the area of the obtuse triangle below?
Answer:
Step-by-step explanation:
1. Area for triangle. Base* Height/2
Here the base it 13 units and height is 11 units. Apply to the formula:
13*11/2=
71.5 sq units
2. Answer: 71.5 sq units
Q21.
A delivery company has a total of 160 cars and vans.
the number of cars: the number of vans = 3:7
Each car and each van uses electricity or diesel or petrol.
of the cars use electricity.
25% of the cars use diesel.
The rest of the cars use petrol.
Work out the number of cars that use petrol.
You must show all your working.
30 cars of the delivery company use petrol.
According to the question,
We have the following information:
A delivery company has a total of 160 cars and vans.
The number of cars: the number of vans = 3:7
1/8 of the cars use electricity.
25% of the cars use diesel and rest use petrol.
Let's take the number of cars to be 3x and the number of vans to be 7x.
3x+7x = 160
10x = 160
x = 160/10
x = 16
Number of cars = 3*16
Number of cars = 48
Now, cars that use electricity:
1*48/8
6 cars
Cars that use diesel:
25*48/100
12 cars
Cars that use petrol:
Total number of cars-(number of cars that use electricity and diesel)
48-(6+12)
48-18
30 cars
Hence, 30 cars of the delivery company use petrol.
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5. The half-life of a certain radioactive material is 78 hours. An initial amount of the material has
a mass of 790 kg. Write an exponential function that models the decay of this material. Find
how much radioactive material remains after 18 hours. Round your
answer to the nearest
thousandth.
Answer:
395 = 790e^(k*78)
Step-by-step explanation:
Dividing by 790 and taking the natural log
ln ( 395/790 ) = ( kx78 )
-0.6931 = 78k
-0.00888 = k
Now calculate how much is left after 18 hours:
Amount ( 18 )
= 790e^( -0.00888x18 )
Amount = 673.301 kg
A muic video webite receive 5,000 comment on a new ong they releae. The next day, the artit performed the ong on televiion and an additional 1,500 comment where made on the webite. What wa the percent of increae?
the 30% increase is 1,500 comments made on the website.
A music video website received 5,000 comments on a new song they released.
The next day, the artist performed the song on television and an additional 1,500 comments were made on the website.
As we know,
The percentage increase = [(increase value)/(old value)]x100
Divide the increase by the beginning number and multiply by 100 to determine the percentage increase between two numbers:
Increase value = 1500
old value =5000
Percent of increase = (1500/5000)x100
Percent of increase = 0.3x100
Percent of increase = 30%
30% if the next day, the artist performed.
In mathematics, a percentage is various or a ratio expressed as a fragment of one hundred. it is often denoted the use of the percent sign, "%", despite the fact that the abbreviations "pct.", "pct" and sometimes "laptop" is also used. A percent is a dimensionless wide variety; it has no unit of measurement. The calculation of chances is done and taught in special approaches relying on the stipulations and necessities. in this manner, the same old formulas can be acquired with proportions, which saves them from having to remember them. In so-referred to as intellectual arithmetic.
This unfastened percent calculator computes some of the values related to possibilities, consisting of the sharp distinction between two given values. percentages are essentially fractions where the denominator is 100. to reveal that a number is a percentage, we use the percent image (%) besides the range. as instance, if you purchased seventy-five questions proper out of a hundred on a check (seventy-five/100), you would have scored 75%.
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Which equation represents the line that is perpendicular to y=1/6 and passes through (-8,-2)?
Answer:
y = -6x - 50
Step-by-step explanation:
y = mx + b
Since it is perpendicular to y=1/6, the slope is -6. (Opposite reciprocal)
y = -6x + b.
Substitute to get: -2 = 48 + b
b = -50
y = -6x - 50
Grocery Giant is having a sale on Swiss cheese, 24 slices for $7.20.
How much would it cost to buy 5 slices of cheese at the same rate?
Answer:
$1.50
Step-by-step explanation:
first, find the unit rate which is 0.3 (7.2/24)
then multiply that by 5
he images on a computer screen are made up of more than 500 pixels,or dots,per square inch. How many pixels are on a computer screen that measures 108 square inches. Write answers in scientific notation
Answer:
Step-by-step explanation:
500(108)=54000 i may not be right
A rectangle with integer side length has perimeter 10. What is the greatest numbers of these rectangles that can be cut from a piece of paper with width 24 and length 60? A. 144 B. 180 C. 240 D. 360 E. 480
The greatest numbers of these rectangles that can be cut from a piece of paper with width 24 and length 60 is 360 which is option D.
Given:
A rectangle with integer side length has perimeter 10.
If the perimeter of rectangle 2(l+b) = 10
l+b = 10/2
l+b = 5.
Two choices:
1. 2 * 3 rectangle of area 6
2. 1 * 4 rectangle of area 4
The piece of paper has area 24×60 = 1440
This can be divided into rectangles with sides 2×3:
= 24/2 * 60/3
= 12*20
= 240
It can be divided into rectangles with sides 1×4:
= 24/1 * 60/4
= 24*15
= 360
Therefore the greatest numbers of these rectangles that can be cut from a piece of paper with width 24 and length 60 is 360 which is option D.
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