Answer:
7 days
Step-by-step explanation:
Given: Ms. Ache is paid $1250 per week but it's fined $100 each day she is late to work.
To Find: maximum number of days she can be late to work and still reach her goal of making at least $3000?
Solution:
per week payment of Ms. Ache =[tex]\$[/tex] [tex]1250[/tex]
Fine for getting late a day = [tex]\$[/tex] [tex]100[/tex]
let number of days Ms. Ache gets late = [tex]\text{x}[/tex]
Amount Ms. Ache wants to make in three weeks = [tex]\$[/tex] [tex]3000[/tex]
maximum earning potential of Ms. Ache in 3 weeks = [tex]1250\times3[/tex]= [tex]\$[/tex] [tex]3750[/tex]
Net earning = maximum earning potential of Ms. Ache in 3 weeks - total fine
=[tex]\$ 3750 - 100\text{x}[/tex]
To reach a goal of [tex]\$[/tex] [tex]3000[/tex]
[tex]\$ 3750 - 100\text{x}[/tex] ≥ [tex]3000[/tex]
[tex]100\text{x}[/tex]≤[tex]750[/tex]
[tex]\text{x}\leq 7[/tex]
Maximum number of days she can be late to work and still reach her goal of making at least $3000 is [tex]7[/tex] [tex]\text{days}[/tex]
a rectangle has a length of 2 1/5 yards and a width of 4 9/20 what is the perimeter of the rectangle? express your answer in mixed number form and reduce if possible
What are the input variable and the output variable?
number of rowers in a rowboat and the speed of the rowboat
input: number of rowers in the rowboat; output: speed of the rowboat
input: speed of the rowboat; output: number of rowers in the rowboat
input: number of rowboats; output: speed of the rowboat
input: number of rowers in the rowboat; output: the number of rowboats
Answer:
input: number of rowers in the rowboat; output: speed of the rowboat
Step-by-step explanation:
took the test and this was correct
A 30-gallon tank initially contains 15 gallons of salt water containing 6 pounds of salt. suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. how much salt is in the tank when the tank is full
Final answer:
Calculate the amount of salt in a tank given rates of inflow and outflow, and determine the final salt quantity when the tank is full.
Explanation:
A 30-gallon tank initially contains 15 gallons of salt water containing 6 pounds of salt.
Find the initial amount of salt per gallon in the tank: 6 pounds / 15 gallons = 0.4 pounds per gallon.
Calculate the rate of salt being added and leaving the tank: In: 1 pound per gallon × 2 gallons per minute = 2 pounds per minute; Out: 0.4 pounds per gallon × 1 gallon per minute = 0.4 pounds per minute.
Subtract the rate of salt leaving from the rate of salt coming in to find the net rate of salt accumulation: 2 pounds per minute - 0.4 pounds per minute = 1.6 pounds per minute.
How much salt is in the tank when it is full?
Using the net rate of salt accumulation, calculate the time needed to fill the tank: 30 gallons / 2 gallons per minute = 15 minutes.
Finally, calculate the total amount of salt in the tank when full: 15 minutes × 1.6 pounds per minute = 24 pounds of salt.
If four times a certain number, increased by 6 is equal to 94, what is the number?
If x represents the number, then which of the following equations could be used to solve the problem?
4x + 6 = 94
4(x + 6) = 94
x + 6 = 4(94)
At Avery Middle School, 273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be a new school mascot. Four times as many students chose Tiger. Twice as many students chose Lion as chose Tiger. How many students chose Lion?
A) 39 students
B) 78 students
C) 156 students
D) 273 students
Answer with Step-by-step explanation:
273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be a new school mascot.
Let t students chose tiger
b students chose bulldog
and l students chose lion
then, t+b+l=273
Four times as many students chose Bulldog as chose Tiger.
i.e. b=4t
Twice as many students chose Lion as chose Tiger.
i.e. l=2t
So, t+4t+2t=273
i.e. 7t=273
Dividing both sides by 7, we get
t=39
Number of students who chose lion=2t
= 2×39
= 78
Hence, Correct option is:
B) 78 students
Math please help!!!!
Write an equation for a linear function whose graph has the given characteristics.
Passes through (42,0), perpendicular to the graph of g(x)=6x+2
f(x)=
pls help 7th grade math
48.24 total
divide this by 12 to get the monthly average
48.24 / 12 = 4.02 inches per month
y+y+2=18 please help me 8 th grade 45POINTS
A rectangular plot of land has an area of 1/8 square mile. Its width is 3/20 mile.What is the length of the plot of land?
Write forty and eight tenths as a decimal. 48.1 40.8 40.08 40.008
The correct representation of forty and eight tenths as a decimal is 40.8.
Here's an explanation for each option:
48.1: This representation is incorrect because it implies forty-eight and one tenth, not forty and eight tenths.
40.8: This is the correct representation. It means forty whole units (40) and eight tenths (0.8).
40.08: This representation is incorrect because it implies forty whole units (40), eight hundredths (0.08), and no tenths.
40.008: This representation is incorrect because it implies forty whole units (40), eight thousandths (0.008), and no tenths.
Therefore, the correct representation of "forty and eight tenths" as a decimal is 40.8.
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Ritz can eat 8 apples in 15 minutes. How long does it take to eat 16 apples at same rate?
Final answer:
To determine how long it takes to eat 16 apples at the same rate as 8 apples in 15 minutes, set up a proportion and solve for the time.
Explanation:
This question demands basic understanding of ratio and proportion in general.
To find out how long it takes to eat 16 apples at the same rate Ritz eats 8 apples in 15 minutes, you can set up a proportion:
8 apples / 15 minutes = 16 apples / x minutes
8/15 × 1/16 = 1/x
1/15 × 1/2 = 1/x
1/x = 1/30
X = 30
Order pairs (x,y) that is the solution to the equation.
5x-y=4
(x,y) =
Is m=1/2 a solution of the equation 6m-8= -5
write the quadratic equation whose roots are -1 and 3 and whose leading coefficient is 1
The quadratic equation with roots -1 and 3 and a leading coefficient of 1 is: [tex]f(x) = x^2 - 2x - 3[/tex]
To write a quadratic equation with roots -1 and 3, we can use the factored form of a quadratic equation:
A quadratic equation in factored form looks like this:
[tex]f(x) = a(x - r1)(x - r2)[/tex]
where:
f(x) is the quadratic function,
a is the leading coefficient,
r1 and r2 are the roots of the quadratic equation.
Given the roots -1 and 3, the factored form of the quadratic equation is:
[tex]f(x) = a(x - (-1))(x - 3)[/tex]
Now, you mentioned that the leading coefficient (a) is 1. So we can rewrite the equation as:
[tex]f(x) = 1(x + 1)(x - 3)[/tex]
Now, we can expand the equation to its standard form:
[tex]f(x) = (x + 1)(x - 3)[/tex]
Using the FOIL method (First, Outer, Inner, Last):
[tex]f(x) = x^2 - 3x + x - 3[/tex]
Simplify:
[tex]f(x) = x^2 - 2x - 3[/tex]
So, the quadratic equation with roots -1 and 3 and a leading coefficient of 1 is: [tex]f(x) = x^2 - 2x - 3[/tex]
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Which of the following statements is true? 0.74 < 0.80 0.61 > 0.93 0.83 < 0.94 1.548 < 0.698
Among the given statements, the only true statements are
0.74 < 0.80 and 0.83 < 0.94.
How is this so?In both cases, the number on the left is less than the one on the right. Which makes the expression and or use of the less than symbol correct.
The greater than symbol (>) and the less than symbol (<) are used to compare two numbers or expressions to determine their relationship.
The greater than symbol (>) represents "greater than" and indicates that the number on the left side is larger than the number on the right side.
The less than symbol (<) represents "less than" and indicates that the number on the left side is smaller than the number on the right side.
For example, 5 > 3 means "5 is greater than 3," and 2 < 7 means "2 is less than 7."
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What is 10000 times 20000000
is a whole number with 4 digits always greater than or less than a whole number with 3 digits explain
A whole number with 4 digits is always greater than a whole number with 3 digits because each position to the left in a decimal number is ten times greater than the one to the right, making the smallest 4-digit number, 1000, larger than the largest 3-digit number, 999.
A whole number with 4 digits is always greater than a whole number with 3 digits. This is because the value of a digit in a number is determined by its position or place value. In our decimal number system, each digit to the left is ten times greater than the one to its immediate right.
For example, the smallest 4-digit number is 1000. The largest 3-digit number is 999. Clearly, 1000 (which has the smallest possible value for a 4-digit number) is greater than 999 (which has the largest possible value for a 3-digit number), hence a 4-digit number is always greater than a 3-digit number.
When considering significant figures, such as those that arise in measurements, certain digits are known exactly, while others may be more uncertain due to rounding or measurement limitations. However, this does not affect the overall rule that more digits in a whole number represent a greater value.
Nia is three years older than half Jordans age , if Jordan is eight years old , how old is Nia?
Answer:
7
Step-by-step explanation:
solve th inequality y/-6 > 10
what is the value of each of these digits in 654321
Solve the inequalities for x, and match each solution to its number line graph.Two less than 3/2 of a number (x) is no more than 5 1/2 . The sum of two times a number (x) and -2 is at least 8. Seven subtracted from 4 times a number (x) is more than 13. Four added to 3 times a number (x) is less than 19. Pairs Number Line Graph Inequality
Answer:
(i) [tex]x\leq 5[/tex]
(ii) [tex]x\geq 5[/tex]
(iii) [tex]x>5[/tex]
(iv) [tex]x<5[/tex]
Step-by-step explanation:
(i) Two less than [tex]\frac{3}{2}[/tex] of a number (x) is no more than [tex]5\frac{1}{2}[/tex],
⇒ Two less than [tex]\frac{3}{2}[/tex] of x is less than equal to [tex]5\frac{1}{2}[/tex],
[tex]\implies \frac{3}{2}x-2\leq 5\frac{1}{2}[/tex]
[tex]\frac{3x-4}{2}\leq \frac{11}{2}[/tex]
[tex]3x-4\leq 11[/tex]
[tex]3x\leq 15[/tex]
[tex]\implies x\leq 5[/tex]
(ii) The sum of two times a number (x) and -2 is at least 8,
[tex]\implies 2x+(-2) \geq 8[/tex]
[tex]2x-2\geq 8[/tex]
[tex]2x\geq 10[/tex]
[tex]x\geq 5[/tex]
(iii) Seven subtracted from 4 times a number (x) is more than 13,
[tex]\implies 4x-7>13[/tex]
[tex]4x>20[/tex]
[tex]\implies x>5[/tex]
(iv) Four added to 3 times a number (x) is less than 19.
[tex]3x+4<19[/tex]
[tex]3x<15[/tex]
[tex]\implies x<5[/tex]
3(a + b + c)2 for a = 2, b = 3, and c = 4.
3(a+b+b)^2 =
3(2+3+4)^2 =
3(9)^2=
3*81 =243
What is 0.17 as an equivalent fraction
Enter a formula in cell d5 to calculate b5/b4 rounded to 4 decimal places.
Excel formulas are expressions used to perform computation.
The Excel formula to enter in cell D5 is = ROUND(B5/B4, 4)
From the question, we have:
The formula in cell D5 is the quotient of cells B5 and B4The result is to be approximated to 4 decimal placesThe quotient of cells B5 and B4 is represented as:
B5/B4
To round the quotient, we make use of the ROUND function
So, we have:
ROUND(B5/B4, 4)
Excel formulas begin with the "=" sign
This gives
= ROUND(B5/B4, 4)
Hence, the Excel formula to enter in cell D5 is = ROUND(B5/B4, 4)
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solve for x −1/2(x+2)+11/2x=3
A machine produces 240 bolts in 25 minutes. At the same rate how many bolts would be produced in 45 minutes
Jess observed that 60% of the people at the mall on a particular day shopped for clothes 2500 people at the mall did not shop for clothes that day was ? (Only put numeric values, no symbols
Final answer:
To find the total number of people at the mall, we calculate that 2500 represents 40% of the total. Dividing 2500 by 0.40 gives us the total number of people, which is 6250.
Explanation:
Jess observed that 60% of the people at the mall on a particular day shopped for clothes. If 2500 people at the mall did not shop for clothes that day, we can calculate the total number of people who were at the mall. Since 60% is the percentage that shopped for clothes, then 40% represents the percentage that did not shop for clothes. This means that the 2500 people constitute 40% of the total number of people at the mall.
To find the total number of people, we can set up the equation: 40% of total people = 2500. Translating percentages into decimals (40% = 0.40), the equation becomes 0.40 × total people = 2500. To solve for the total number of people, we divide 2500 by 0.40:
Total people = 2500 ÷ 0.40
Total people = 6250
Therefore, the total number of people at the mall that day was 6250.
How long will it take you to ski a distance of 36 miles at a speed of 3 miles per 30 minutes?
Gretchen lives in Florida, for the current temperature 69°F and rising at a rate of 2°F per hour. She's talking on the phone to her friend in Indiana where the temperature is now 84°F and falling at a rate of 3°F per hour.
A.) If the temperature continue changing at the same rates, how many hours would Gretchen and her friend have to talk before the temperature become equal?
B.) What will the temperature be?
Answer:
A) Gretchen and her friend have to talk 3 hours before the temperature become equal.
B) The temperature after 3 hours will be 75°F.
Step-by-step explanation:
Current temperature in Florida = 69°F
Rate at which temperature is rising = 2°F per hour
Current temperature in Indiana = 84°F
Rate at which temperature is falling= 3°F per hour
A) Suppose in x hours both places have same temperature:
[tex] 69^oF +2F^o\times x=84^oF-3^oF\times x[/tex]
[tex]5x=84^oF-69^oF[/tex]
x = 3 hours
Gretchen and her friend have to talk 3 hours before the temperature become equal.
B) The temperature after 3 hours:
x = 75°F
[tex]69^oF +2F^o\times x=69^oF +2F^o\times 3=75^oF[/tex]