Jacob and Sarah are saving money to go on a trip. They need at least $1850 in order
to go. Jacob mows lawns and Sarah walks dogs to raise money. Jacob charges $15
each time he mows a lawn and Sarah charges $10 each time she walks a dog. The
number of dog walks that Sarah has scheduled is no more than five times the
number of lawns Jacob has scheduled to mow. Sarah will walk at least 65 dogs.
Answers
Answer:
[tex]\textsf{Constraint 1}: \quad 15x+10y\geq 1850[/tex]
[tex]\textsf{Constraint 2}: \quad y \leq 5x[/tex]
[tex]\textsf{Constraint 3}: \quad y \geq 65[/tex]
Step-by-step explanation:
Inequality signs:
< Less than.≤ Less than or equal to.> More than.≥ More than or equal to.Given variables:
x = Number of lawns mowed.y = Number of dogs walked.Constraint 1Given information:
$15 = Charge for mowing a lawn.$10 = Charge for walking a dog.$1850 = Minimum amount needed for the trip.Therefore, the amount earned from mowing the lawns and walking dogs should be more than or equal to $1850:
[tex]\boxed{15x+10y\geq 1850}[/tex]
Constraint 2Given information:
The number of dog walks that Sarah has scheduled is no more than 5 times the number of lawns Jacob has scheduled to mow:Therefore, Sarah will walk less than or equal to 5 times the number of lawns mowed:
[tex]\boxed{y \leq 5x}[/tex]
Constraint 3Given information:
Sarah will walk at least 65 dogs.Therefore, Sarah will walk more than or equal to 65 dogs:
[tex]\boxed{y \geq 65}[/tex]
Related Questions
Find the perimeter of abc with vertices (1,-6) (1,-3) (-4,-6)
Answers
Answer:
8+√34
Step-by-step explanation:
use distance formula d =√(x2-x1)² +(y2-y1)² to find the sides
√ (1 -1)²+( -6+3)² = √9 = 3
√ (1+4)²+( -6+6)² = √25 =5
√ (1+4)² + (-3+6)² = √25+9 =√34
Perimeter is P = 3+5+√34 = 8+√34
I NEED HELP ASAP PLEASE AND THANKS.
Answers
Answer:
b=320; slope=-30
Step-by-step explanation:
if you look along the y-axis find the spot that the line intercepts and then that's b
now for the slope
find two points on the line, i chose(8 , 120) and (4 , 240)
use the slope formula: y2-y1 over x2-x1
240-120=120 and 4-8= -4
so the slope is 120/-4 and that can be simplified to 30/-1 or -30
There are 234 pieces of candy in 9 bags of candy. If there are the same amount of pieces of candy in each bag, how many total pieces of candy are in 5 bags?
Answers
Answer:
130 pieces of candy in 5 bags
Step-by-step explanation:
234/9 equals 26, that means there would be 26 pieces of candy in 9 bags, therefore 26x5 equals 130, and just to make sure, divide 130/26 to check if its wrong, but it should be 130. :) hope this helps you out!
PLZ ANSWER ASAP!!!
A parallelogram ABCD , with I as the middle point of AC and EF is a line that goes through I. Show that IE=IF.
Answers
Answer:
IE = IF (By CPCT)
Step-by-step explanation:
Given:
ABCD is a parallelogram
So,
LINE AC || DC
Computation:
IN ΔAIE and ΔCIF
∠AIE = ∠CIF (Vertical opposite angle)
AI = IC (I is midpoint of line AC)
∠IAE = ∠ICF (Alternate angle)
So,
ΔAIE ≅ ΔCIF
So,
IE = IF (By CPCT)
Use the graph to find the slope.
Answers
Ok ok ok ok ok ok ok ok ok ok
Answers
Answer:
53%
Step-by-step explanation:
dont mind this it’s for the character limit
A nurse assesses a 66 - year - old client who is attempting to quit smoking . The client states , " I started smoking at age 16 , and smoked one pack each day until 10 years ago . Then I decreased to a half of a pack per day . " How many pack - years should the nurse document for this client ?
Answers
The nurse should document for this client as 45 pack years.
Pack year is determined by dividing the quantity of packs smoked daily by the number of years the smoker has smoked.
total years of smoking = current age of the client - the year he started smoking
= 66 - 16
50 years of smoking
For 40 years he smoked 1 pack per day but then he reduced it to a half pf a pack per day
= 40 x 1 + 10 x 0.5
= 45 pack- years
The nurse should document for this client as 45 pack years as the client has started smoking at age 16 , and smoked one pack each day until 10 years ago then he had decreased to a half of a pack per day.
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PLEASE HELP
Find the unit rate.
12 slices from 2 cakes =
Answers
Answer:
1 cake 6 slice
Step-by-step explanation:
just divide
12/2=6
How many laps would 50 miles be on a 1/2 mile track?
Answers
Answer:
100
Step-by-step explanation:
Multiply 50 by 2
What ratio is equivalent to the ratio 14:7 A 1:7 B2:7 C2:1
Answers
Answer:
c 2:1
Step-by-step explanation:
If you simplify 14:7 it is 2:1 (divide by 7)
Answer:
14:7 is the same as 2:1 because 7 can go into 14 two times and into 7 once
so your answer would be C
What is the Volume of this Cube?
Answers
Answer:
1 cubic cent
Step-by-step explanation:
Cause the volume of a cube is V^3. So, 1x1x1 = 1
Answer:
The answer is 1 cubic centimeter.
Step-by-step explanation:
Help 66 points show your work and I’m giving brainliest
Answers
Based on the calculations on the given expressions, the correct answers are as follows:
Expression = -5.Quotient = 60/12.x = 48.Expression = 13/20.Prime factorization of 64 = 2⁶.Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, and 100.The graph of x = 3.5 is shown in the image attached below.Number of bags = 5 bags.Expression = 100.What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
How to evaluate the given expression?When x = 6, we have:
Expression = 9 + x + 5 - 20
Expression = 9 + 6 + 5 - 20
Expression = 15 - 20
Expression = -5.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.
How to interpret and simplify the word problem?The quotient of 60 and 12:
Quotient = 60/12
How to solve the given equation?x/12 = 4
Cross-multiplying, we have:
x = 12 × 4
x = 48.
How to evaluate the given expression?1/20 + 3/5 =
Lowest common multiple (LCM) = 20;
(1 + 12)/20 = 13/20.
How to write the prime factorization of 64?Factors of 64 = 1, 2, 4, 6, 8, 16, and 32
Prime factorization of 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶.
What are factors?Factors can be defined as the fundamental building blocks of a number. This ultimately implies that, factors refers to numbers which can be multiplied together to get another number.
List of all the factors of 100.Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, and 100.
How to calculate the number of boxes?In order to calculate the number of boxes that Doritos can buy, we would apply direct proportion:
1 box = $8
X box = $40
Cross-multiplying, we have:
8X = 40
X = 40/8
X = 5 bags.
Number of bags = 5 bags.
How to simplify the given expression?In order to simplify this expression, we would apply the PEMDAS rule, where operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the operations of addition or subtraction would be performed from left to right.
Expression = 100 + 2(25 - 5²)
Expression = 100 + 2(25 - 25)
Expression = 100 + 2(0)
Expression = 100.
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Answer this question please
Answers
Answer:
See below
Step-by-step explanation:
This means
x < 3 or
-x < 3 <==== multiply both sides by -1 <=== this reverses the <
x > -3
so combining the two underlined
-3 < x < 3
Answer:
Step-by-step explanation:
we can expand the inequality to x>-3 or x<3 meaning x should be between -3 and 3 mathematically we can say -3<x<3
hope this helps
5 over 7 converted into a decimal
Answers
Answer: 5/7=0.(714285)
Step-by-step explanation:
[tex]\displaystyle\\\frac{5}{7}=0.(714285)[/tex]
.
If each 10 x 10 unit square represents one whole, then what
percent is represented by the shaded region?
. In the model above, 25% represents a quantity of 10
students. How many students does the shaded region
represent?
Answers
Answer: 125% and 50 students.
2(4)-5=
i dont know what the answer is but i need help now bc it is a timed test someone pls help pls
Answers
Answer:
3
Step-by-step explanation:
write 7x7x7 as a base and an exponent (2ps possilbe)
Answers
Answer:
[tex]7^{3}[/tex]
Step-by-step explanation:
7 is being multiplied by itself 3 times meaning it's to the power of 3 so the base is 7 while the exponent is 3.
2^5 is equal to 2•5.
Group of answer choices
Answers
Answer:
32≠10
False
Step-by-step explanation:
José put $1,500 into a savings account. He earns 3% interest every year. How much simple interest will he earn at the end of 3 years?
Answers
He would have a total of: $1639.09
In intrest alone he would've made 1639.09
Step-by-step explanation:
3%= 0.03
The first thing you do is multiply $1,500 by the %3 (0.03).When your done multiplying, you should get 45.Add 45 to 1500Now you have 1545Then you repeat the process over, two more times. However the numbers will change.If x varies directly as y and z and inversely as the square
of r, and x = 16 when y = 3, z = 12 and r = 3, find
x when y = 5, z = 30, and r
r =10
Answers
Answer:
x = 6
Step-by-step explanation:
Take the statement x varies directly as y and z
This means value of x is directly proportional to the value of y and z represented as x ∝ yz which can be represented as x = k.y.z where k is a constant known as the constant of proportionality
If x varies inversely as the square of r we represent this as x ∝ 1/r² or in equation form x = k/r²
Since the value of x is dependent on the values of y, z and jointly we have a single equation of proportionality:
[tex]\bold{x= k\cdot\frac{yz}{r^{2}}}[/tex]
Given the values for x, y, z and r we can compute the proportionality constant and determine the value of x for any value of y, z or r
x = 16 when y = 3, z = 12 and r = 3
[tex]16 = k\cdot \frac{3\cdot 12}{3^2} \\\\16 = k\cdot \frac{3\cdot 12}{9}\\\\16 = k\cdot4\\\\k = 16/4 = 4\\[/tex]
So the constant of proportionality is k = 4. Us this value in the proportionality equation along with y, z and r to get the value of x
[tex]x = 4\cdot \frac{5\cdot 30}{10 \cdot 10}\\\\x = 4\cdot\frac{150}{100}\\\\x = \frac{600}{100} = 6\\\\[/tex]
So x = 6 is the answer
Shep Company’s records show the following information for the current year:
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Determine net income (loss) for each of the following separate situations. (For all requirements, losses should be entered with a minus sign.)
a. Additional common stock of $4,600 was issued, and dividends of $8,600 were paid during the current year.
b. Additional common stock of $15,400 was issued, and no dividends were paid during the current year.
c. No additional common stock was issued, and dividends of $13,600 were paid during the current year.
.
Answers
The determination of the net income for each of the following separate situations is as follows:
Situation A Situation B Situation C
Net income $21,800 $2,400 $31,400
Data and Calculations:Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Situation A:
Common Stock issued = $4,600
Dividend paid = $8,600
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 4,600
Dividend paid (8,600)
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$21,800 ($47,400 - $29,600 - 4,600 + 8,600)
Situation B:Common Stock issued = $15,400
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 15,400
Dividend paid
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$2,400 ($47,400 - $29,600 - 15,400)
Situation C:Dividends paid = $13,600
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued
Dividend paid $13,600
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$31,400 ($47,400 - $29,600 + 13,600)
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Please help see the attached photo above
Answers
Combine like terms
4x -16 = 180
Add 16
4x = 196
Divide by 4
X = 49
Which shows two products that both result in positive values?
(0.5)(-0.4) and (1,2)(-0,8)
(-0,5)(-0.4) and (1,2)(-0,8)
(0,5)(0.4) and (-1,2)(-0,8)
(0,5)(-0,4) and (1,2)(0,8)
Answers
Answer: A is the answer
Step-by-step explanation:
_1. Which of the following is equivalent to 3x - 4y = 6?
Answers
Kelly makes fruit juice each morning. She uses 2 1/3 pints of strawberries and 1 2/5 pins of grapes in her juice how many more pints of strawberries than pints of grapes does she use?
Answers
A rectangular garden has a walkway around it. The area of the garden is 6(3.5x+1.5). The combined area of the garden and the walkway is 7.5(6x+5). Find the area of the walkway around the garden as the sum of two terms.
Answers
Answer:
[tex]A_w=24x+28.5[/tex]
Step-by-step explanation:
The rectangular garden is surrounded by a walkway.
The combined area of both is 7.5(6x+5) and the area of the garden alone is 6(3.5x+1.5).
The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:
[tex]A_w=7.5(6x+5) -(6(3.5x+1.5))[/tex]
Removing parentheses:
[tex]A_w=45x+37.5 -21x-9[/tex]
Simplifying:
[tex]\mathbf{A_w=24x+28.5}[/tex]
what is 4320 divided by 27
Answers
Answer:
160
Step-by-step explanation:
Answer:
160
Step-by-step explanation:
In a sample of 80 Americans, 55% wished that they were rich. In a sample of 90
Europeans, 45% wished that they were rich.
a) At a = 0.01, is there difference in the proportions?
b) Find the 99% confidence interval for the differences of the two proportions
Answers
Answer:
hjgkulihjoj;l
Step-by-step explanation:
No Com
A certain shade of paint is made by mixing 5 parts blue paint with 2 parts white paint. To get
the correct shade, how many quarts of white paint should be mixed with 8.5 quarts of blue
paint?
Answers
Answer:
5.5
Step-by-step explanation:
8.5-5=3.5
so you need to add 3.5 to the amount of white paint.
2+3.5 is 5.5
The answer is 5.5
What is the slope of the line shown below?
A. -1/4 B.1/4
C. 4
D.-4
I
Answers
Answer:
D -4
Step-by-step explanation:
rise over run rise=-12 run= 3 - 12/3 simplified is -4
Answer:
4
Step by step
you move 12 spots to get to 8 from -4 and 3 to get from -1 to 2 then you do 12/3