The width of the rectangular strip of land is 2/3 miles whose the width of the rectangular strip of land is 2/3 miles.
To find the width of the rectangular strip of land, we can use the formula for the area of a rectangle, which is:
Area = Length × Width
Given that the length of the rectangular strip of land is 3/4 miles and the area is 1/2 square mile, we can plug these values into the formula and solve for the width (W):
Area = 1/2 square mile
Length = 3/4 miles
1/2 = (3/4) × Width
To solve for the width (W), divide both sides by 3/4:
Width = (1/2) ÷ (3/4)
When dividing by a fraction, you can multiply by its reciprocal:
Width = (1/2) × (4/3)
Now, multiply the numerators and denominators:
Width = 4/6
The fraction 4/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:
Width = 2/3
So, the width of the rectangular strip of land is 2/3 miles.
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Please Help ASAP!! 98 Points to Brainliest!!
Answer:
all the lines are correct but for x<= 2 there need to be a closed circle, and vica versa for all the others.
Step-by-step explanation:
The lines are correct but for x<= 2
A regular pentagon with a perimeter of 18 centimeters is dilated by a scale factor of 3/2 to create a new pentagon?
Answer:
if that is all it says you can do simple cross multiplication
Step-by-step explanation:
18*3/2=x
x will give you the nre number. If you dont know how to do that math go to desmos and type it in. the answer should be 27 if i did it correctly in my head but please check my work.
A student helping a student
The new pentagon has a perimeter of 27 centimeters.
Explanation:To find the perimeter of a regular pentagon, we multiply the length of one side by the number of sides. In this case, the perimeter is 18 centimeters, so each side of the pentagon is 18/5 = 3.6 centimeters long.
When this pentagon is dilated by a scale factor of 3/2, each side of the new pentagon will be 3/2 x 3.6 = 5.4 centimeters long.
Therefore, the new pentagon has a perimeter of 5.4 x 5 = 27 centimeters.
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Sammy bought 3 T-shirts for $15.75 each and pairs of jeans for $28.79 each. If the sales tax on his purchases totaled $5.24, how much money did Sammy spend in all?
Answer:
Sammy, after picking out her clothes, bringing them to the counter and ringing them up. owes in total: $49.78
Step-by-step explanation:
Final answer:
This answer explains how to calculate the total amount of money Sammy spent on T-shirts and jeans including sales tax.
Explanation:
To find out how much Sammy spent in total:
Calculate the total cost of the 3 T-shirts: $15.75 x 3 = $47.25
Calculate the total cost of the pairs of jeans: $28.79 x 2 = $57.58
Add the total costs of the T-shirts and jeans: $47.25 + $57.58 = $104.83
Add the sales tax to get the final amount: $104.83 + $5.24 = $110.07
Therefore, Sammy spent $110.07 in all.
The population of at a town has grown 2% each year. In 1998, the population of the town was about 10,000 people. What was the population in 1999?
Answer:
10200
Step-by-step explanation:
The population in 1999 was 10200.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the population of at a town has grown 2% each year. In 1998, the population of the town was about 10,000 people.
Let the population be in 1999 be {x}. Then, we can write -
{x} = 10000 + {2% of 10000}
{x} = 10000 + {2/100 x 10000}
{x} = 10000 + 200
{x} = 10200
Therefore, the population in 1999 was 10200.
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Kendyl is memorizing a piece of saxophone music to perform at a local festival. She currently has the first eight bars memorized and plans to memorize two more bars everyday until she has the whole piece memorized. Write a recursive formula to model Kendyl's progress.
Answer:
The recursive formula to model Kendyl's progress is:
Fourth option: an=an-1 + 2, a1=8
Step-by-step explanation:
She currently has the first eight bars memorized: The first value is 8:
a1=8
She plans to memorize two more bars everyday until she has the whole piece memorized:
The number of bars memorized is two more than the last day:
an=an-1 + 2
Then, the recursive formula is:
an=an-1 + 2, a1=8
Answer:
The correct choice is D hope that helps
Rita spends 52% of her pocket money on magazines and 23% on movies. If her pocket money was RS.144 what amount of her pocket money is left
Answer:
The amount of Rita's pocket money left is Rs. 36.
Step-by-step explanation:
Pocket money that Rita had before = 144
Money spent for magazines = 52% of 144
= [tex]\frac{52}{100} (144)[/tex]
= 0.52(144)
= 74.88
Money spent for movies = 23% of 144
= [tex]\frac{23}{100} (144)[/tex]
= 0.23(144)
= 33.12
Money left with Rita = 144 - (74.88 + 33.12)
= 144 - 108
= 36
Hence, Rita left with Rs. 36.
Aliter:
Total money spent = (52 + 23)% = 75%
So, money left with Rita = 100 - 75 = 25%
25% of 144 = 0.25(144) = 36.
A patient is given a 100-milligram dosage of a drug that decays exponentially at a rate of 11% per hour. The doctor wants to know when 15 milligrams of the drug remains.
Write an equation that models the situation. Explain each aspect of your equation.
Answer:
16.3 hours.
Step-by-step explanation:
"Decays exponentially at a rate of 11% per hour" translates into
(1 - 0.11)^h, where h is the number of hours during which the drug decays.
The negative sign comes from "decay."
The complete formula applicable here is
d(h) = (100 mg)(1 - 0.11)^h, where h is the number of hours.
We want to know how many hours it will be until all but 15 mg remain. The appropriate formula for this is
15 mg = (100 mg)()^h. Dividing both sides by 100 mg, we get:
15 mg
------------- = 0.89^h, or 0.15 = 1.11^h
100 mg
Apply properties of logs to solve this. Take the natural log of both sides of the above equation. We get:
ln 0.15 = h(ln 0.89). Dividing both sides by ln 0.89, we get:
h = 16.3
The original 100 mg dosage would decay to 15 mg after 16.3 hours.
The measurement, y, varies directly with regard to another value, x. If y = 9 and x = 24, find x for y = 25.
Answer:
x=66.667
Step-by-step explanation:
Basically, if y varies directly with a value x, you get an equation of the form y=kx, where k is a constant. To answer the question, first substitute 9 into y, and 24 into x.
9=24k
k=0.375
k is 0.375, so to get x, substitute 0.375 into k and 25 into y
25=0.375x
x=66.667
And we got it!
Final answer:
To find x when y = 25 in a direct variation where y = 9 when x = 24, first find the constant of proportionality (k = 3/8), then use this constant to solve the equation 25 = (3/8)x which yields x ≈ 66.67.
Explanation:
The student's question concerns direct variation, which is a concept where one variable changes in proportion to another variable. In this particular problem, the measure y varies directly with x. Given that y = 9 when x = 24, we can use this information to establish the constant of proportionality k where y = kx.
First, we solve for k using the initial condition:
9 = k * 24
k = 9/24
k = 3/8
Now that we have the constant of proportionality, we can find x when y = 25 by setting up the equation:
25 = (3/8)x
x = 25 * (8/3)
x = 200/3
x ≈ 66.67
Therefore, when y = 25, the value of x is approximately 66.67.
unction f is an exponential function
X -2 | 0 | 2 | 4| 6
F(x) 1/8 | ½| 2 |8 | 32
By what factor does the output value increase as each
input value increases by 1?
Answer:
4
Step-by-step explanation:
As each x value increases by 1, the output values increase by a factor of 4. This means that each y value can be multiplied by 4 to get the next y value.
1/2(4)=2
2(4)=8
8(4)=32
4 is the factor.
If you break up the number under the radical in the square root of 36 into two factors that are perfect squares, what are the two factors?
Answer: 4 and 9
Step-by-step explanation:
9 x 4 = 36
The square root of 9 is 3, so 9 is a perfect square.
The square root of 4 is 2, so 4 is a perfect square.
Answer:
9 x 4 = 36
Step-by-step explanation:
you should be able to mark him brainliest now =) =) =)
Write a solution in Interval Notation - (you don't have to help me on all, 1 or 2 is fine c: )
1) | m | -2 > 0
2) | x - 4 | - 3 > 5
3) | 6 + 9x | ≤ 24
4) | 1 - 5a | > 29
QUESTION 1
The given inequality is
[tex]|m|-2>0[/tex]
We group like terms to get,
[tex]|m|>2[/tex]
This implies that,
[tex]-m>2[/tex] or [tex]m>2[/tex].
We simplify the inequality to get,
[tex]m<-2[/tex] or [tex]m>2[/tex].
We can write this interval notation to get,
[tex](-\infty,-2)\cup (2,+\infty)[/tex].
QUESTION 2
[tex]|x-4|-3\:>\:5[/tex].
We group like terms to get,
[tex]|x-4|\:>\:5+3[/tex].
[tex]|x-4|\:>\:8[/tex]
We split the absolute value sign to get,
[tex]-(x-4)\:>\:8[/tex] or [tex]x-4\:>\:8[/tex]
This implies that,
[tex]x-4\:<\:-8[/tex] or [tex]x-4\:>\:8[/tex]
[tex]x\:<\:-8+4[/tex] or [tex]x\:>\:8+4[/tex]
[tex]x\:<\:-4[/tex] or [tex]x\:>\:12[/tex]
We can write this interval notation to get,
[tex](-\infty,-4)\cup (12,+\infty)[/tex].
QUESTION 3
The given inequality is
[tex]|6+9x|\leq 24[/tex]
We split the absolute value sign to obtain,
[tex]-(6+9x)\leq 24[/tex] or [tex](6+9x)\leq 24[/tex]
This simplifies to
[tex]6+9x\ge -24[/tex] and [tex]6+9x\leq 24[/tex]
[tex]9x\ge -24-6[/tex] and [tex]9x\leq 24-6[/tex]
[tex]9x\ge -30[/tex] and [tex]9x\leq 18[/tex]
[tex]x\ge -\frac{10}{3}[/tex] and [tex]x\leq 2[/tex]
[tex]-\frac{10}{3}\leq x\leq2[/tex]
We write this in interval form to get,
[tex][-\frac{10}{3},2][/tex]
QUESTION 4
The given inequality is
[tex]|1-5a|>29[/tex]
We split the absolute value sign to get,
[tex]-(1-5a)>29[/tex] or [tex]1-5a>29[/tex]
This simplifies to,
[tex]1-5a\:<\:-29[/tex] or [tex]1-5a\:>\:29[/tex]
This implies that,
[tex]-5a\:<\:-29-1[/tex] or [tex]-5a\:>\:29-1[/tex]
[tex]-5a\:<\:-30[/tex] or [tex]-5a\:>\:28[/tex]
[tex]a\:>\:6[/tex] or [tex]a\:<\:-\frac{28}{5}[/tex]
We write this in interval notation to get,
[tex](-\infty,-\frac{28}{5})\cup (6,+\infty)[/tex]
A jogger runs 91 yd in 10.00 seconds. What would be his time for a 449 m run at the same rate? Answer in units of s.
Answer:
4,910 seconds
Step-by-step explanation:
A building's basement is 15 feet below ground. The building is square shaped with side lengths of 60 feet. If the height of the building is 55 feet, what is the length of the building from basement to roof? A) 40 feet B) 45 feet Eliminate C) 70 feet D) 75 feet
Tax returns filed manually have a 20% chance of containing errors, while tax returns filed electronically have a 0.05% chance of containing the same. If 2.7 million tax returns are filed each way, how many more erroneous manually filed returns will there be than erroneous electronically filed returns? a. 270,675 b. 538,650 c. 541,350 d. 269,325
Answer:
B) 538, 650
Step-by-step explanation:
Given:
Errors on tax returns filed manually = 20%
Errors on tax returns filed electronically = 0.05%
Tax return filled in each way = 2.7 million
Manual filing:
2,700,000 x 20% = 2,700,000*0.2 = 540,000
Electronic filing:
2,700,000 x 0.05% = 2, 700,000*0.0005 = 1,350
Error difference = 540,000 - 1,350 = 538,650
There will be 538,650 more erroneous tax returns filed manually than there are filed electronically.
Thank you.
The difference between manually filed return and the electronically filed return is [tex]\boxed{538650}[/tex]. Option (b) is correct.
Further Explanation:
Explanation:
The total tax return is 2.7 million.
The errors on the tax return for electronic filling are [tex]0.05\%.[/tex]
The errors on the tax return for manual filling are [tex]20\%.[/tex]
Number of errors in filing tax return manually can be calculated as follows,
[tex]\begin{aligned}{\text{Errors in manual filling}} &= 2700000 \times 20\%\\ &= 2700000 \times \frac{{20}}{{100}} \\&= 540000\\\end{alignd}[/tex]
Number of errors in filing tax return electronically can be calculated as follows,
[tex]\begin{aligned}{\text{Errors in electronically filling}} &= 2700000 \times 0.05\% \\&= 2700000 \times \frac{{0.05}}{{100}} \\&= 1350 \\\end{aligned}[/tex]
The difference in the errors can be calculated as follows,
[tex]\begin{aligned}{\text{Difference}} &= 540000 - 1350 \\&= 538650 \\\end{aligned}[/tex]
The difference between manually filed return and the electronically filed return is [tex]\boxed{538650}[/tex]. Option (b) is correct.
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Grade: High School
Subject: Mathematics
Chapter: Tax and Returns
Keywords: Tax, returns, filed, tax return, 20%, chance, errors, electronically, 0.05%, containing errors, chance, same, 2.7 million, each way, manually, manually filed, erroneous, 270575, income tax, salary, tax on salary.
If ƒ(x) = 2x, then ƒ -1(x) =
-2x
½x
x - 2
recall that to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".
[tex]\bf \stackrel{f(x)}{y}=2x\implies \stackrel{\textit{switcheroo}}{x=2y}\implies \cfrac{x}{2}=y\implies \cfrac{1}{2}x=\stackrel{f^{-1}(x)}{y}[/tex]
Linda went to a store and bought 2 items .Each item cost $12. How much money did she spend?
Answer:
24 dollars
Step-by-step explanation:
Linda spends $24 for two items that bought from the store.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Given that,
Cost price of one time = $12.
Also, number of items that Linda bought = 2.
To find the total amount that Linda spends.
Use mathematical operations,
cost of 1 item = $12
Cost of 2 items = 12 x 2 = 24.
Hence, Linda spends $24 for 2 items.
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On a field trip, there was 5 girls for every 8 boys. How many girls attended the 130-student field trip
36?
Bc if you divied 130/5 (girls) you get 36? Im sorry this may not be right, I'm not for sure :P
Calculate the value of the exterior angle
10
95
3.57
1.4
Answer:
95
Step-by-step explanation:
We have been given a diagram triangle in which measurement of few angles in terms of x are given.
Using those we need to find the exterior angle but before that we need to find the value of x.
We know that exterior angle is equal to sum of two distant interior angles of that triangle so we can write:
(8x+15)=(3x+20)+(4x+5)
8x+15=3x+20+4x+5
8x+15=7x+25
8x-7x=25-15
x=10
Now plug x=10 into exterior angle 8x+15
8x+15=8*10+15=80+15=95
Hence final answer is 95.
One number is 3 less than twice another. If their sum is 39, find the numbers.
Which of the following systems of equations represents the word problem?
y = 2x - 3 and y = x + 39
y = 2x - 3 and x + y = 39
y = 2(x - 3) and x + y = 39
Answer with Step-by-step explanation:
Let x and y be two numbers.
One number is 3 less than twice another.
⇒ y=2x-3
Their sum is 39.
⇒ x+y=39
Hence, system of equations are:
y = 2x - 3 and x + y = 39
Putting y=2x-3 in x+y=39
x+2x-3=39
⇒ 3x-3=39
⇒ x-1=13 (dividing both sides by 3)
⇒ x=14
y=2x-3
⇒ y=2×14-3
⇒ y=28-3
⇒ y=25
Hence, Two numbers are:
14 and 25
Please help!!
Which value of y is a solution of the inequality? 2y+9≤11
y = 1
y = 2
y = 11
y = 9
Answer:
y=1 for [tex]y\leq 1[/tex]
Step-by-step explanation:
We can solve an inequality much like we solve an equation. We will use inverse operations to isolate y. If we need to divide by a negative then we will need to flip the inequality.
[tex]2y+9\leq 11\\2y+9-9\leq 11-9\\2y\leq 2\\\frac{2y}{2}\leq \frac{2}{2} \\y\leq 1[/tex]
First, we moved 9 across the equal sign to combine it with 11 by subtracting by 9 from both sides.
Second, we divided both sides by 2.
[tex]y\leq 1[/tex] is the solution. All solutions equal to 1 and less than 1 will work.
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Trisha needs to make at least 50 gift bags for an event. Each gift bag will contain at least 1 thumb drive or 1
key chain. She wants to use at least 5 times as many key chains as thumb drives. She has 25 thumb drives and 200 key chains.
Let x represent the number of key chains. Let y represent the number of thumb drives.
Write an inequality for this situation and graph the inequality.
Answer:
[tex]\ y\geq 5\cdot x\\x+y\geq 50\\y\leq25\\x\leq200\\y\geq0\\x\geq0[/tex]
Step-by-step explanation:
STEP 1 : First we draw the graph for [tex]y\geq 5\cdot x[/tex] by letting [tex]y=5x[/tex]
it is denoted by red colour
STEP 2 : Now we draw the graph for [tex]x+y\geq 50[/tex] by letting [tex]x+y=50[/tex]
It is denoted by orange colour
STEP 3 : Now we draw for [tex]y\leq25[/tex] by letting [tex]y=25[/tex]
It is denoted by green colour.
STEP 4 : Now we draw for [tex]x\leq200[/tex] by letting [tex]x=200[/tex]
It is denoted by blue colour.
Gabriela has dinner at a cafe and the cost of her meal was $45.00 she wants to leave a tip of 15% what is her total bill
45+0.15·45=45+6.75=51.75$
Find the perimeter of the figure:
15 units
30 units
27 units
29 units
Answer:
To find the perimeter, just add up the lengths of the each side.
AB = 13 units
BC = 12 units
CA = 5 units
P = 13 + 12 + 5 = 30 units
Three times one number plus a second number is 40, and the one number minus the second number is 4. Find the numbers.
Answer:
The numbers are 11 and 7
Step-by-step explanation:
To find these, use the statements to create equations in standard form.
3x + y = 40
x - y = 4
Now that we have these two, we can add them together and get the y's to cancel out.
3x + y = 40
x - y = 4
-------------------
4x = 44
x = 11
Now that we have the first number as 11, we can solve for y using either equation.
x - y = 4
11 - y = 4
-y = -7
y = 7
A fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges. They also need $15 for 6 apples and 6 oranges. What is the cost for an apple
Answer:
$1.25
Sorry that i dont have an explanation i just didnt wanna confuse you lol
Show all work plz and answer it quickly
Answer:
x + 4 = 7 + 4 = 11 feet
Step-by-step explanation:
Do you ever have a nice "fist", meaning you have very neat handwriting.
You are told that A to MSG = B to MSG
So
Equation
3x - 10 = x + 4
Solution
Subtract x from both sides
3x - x - 10 = x - x + 4 Simplify
2x - 10 = 4 Add 10 to both sides
2x - 10 + 10 = 4 + 10 Simplify
2x = 14 Divide by 2
2x/2 = 14/2
x = 7
x + 4 = 7 + 4 = 11 feet from A to Madison Square Garden
Tickets for a basketball game cost $2 for students and $5 for adults. The number of students was 3 less than 10 times the number of adults. The total amount of money from ticket sales was $619. How many of each ticket were sold?
Answer:
The no. of adult's tickets sold is 25.
The no. of adult's tickets sold is 247
Step-by-step explanation:
Given :
Tickets for a basketball game cost $2 for students and $5 for adults.
The number of students was 3 less than 10 times the number of adults.
The total amount of money from ticket sales was $619.
To Find : No. of each ticket were sold
Solution :
Let x be the no. of the student's tickets sold
Let y be the no. of adult's tickets sold
Since we are given that The number of students was 3 less than 10 times the number of adults.
⇒ x = 10y -3 --(A)
Now cost of 1 student's ticket is $2
Thus, cost of x student's ticket is $2x
Now cost of 1 adult's ticket is $5
Thus,cost of y adult's ticket is $5y
Since we are given that the total amount of money from ticket sales was $619.
⇒2x +5y =619 ---(B)
Solving equation A and B by substitution method :
putting value of x from (A) in (B)
We get :
⇒2( 10y -3) +5y =619
⇒20y-6+5y= 619
⇒25y = 625
⇒y = 625/25
⇒y=25
Thus, the no. of adult's tickets sold is 25.
Putting value of y in equation A to get value of x .
⇒x = 10(25) -3
⇒x = 247
Thus the no. of adult's tickets sold is 247
Andy Taylor and Ben share their team payment in the ratio 1:3:4. What percentage of the total does Andy recieve?
Answer:
12.5%
Step-by-step explanation:
sum the parts of the ratio 1 + 3 + 4 = 8 parts
8 parts represents 100%, hence
1 part = [tex]\frac{100}{8}[/tex] = 12.5% ← Andy's percentage of the total
Andy Taylor's share in the ratio of 1:3:4 results in him receiving 12.5% of the total team payment.
Explanation:The question is about the sharing of a total team payment between Andy Taylor and Ben in the ratio of 1:3:4. To find out what percentage Andy receives, we first need to establish the total parts in the ratio. The ratio 1:3:4 sums up to 8 parts in total. Andy's share is represented by 1 part out of these 8. To find the percentage, we divide Andy's 1 part by the total 8 parts, multiply by 100, giving us 12.5%. This means that Andy receives 12.5% of the total team payment.
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Which equation shows a line perpendicular to the line
Answer:
The second answer: y= 3/4x + 2
Step-by-step explanation:
Subtract 4x to the other side
Divide by 3 to get y by itself
Make the coefficient of the x term the negative reciprocal, for that is the perpendicular slope of the line
You have performed increasingly well this past year and you are earning a 6% pay increase to your current $62,900 annual salary."
To calculate a new salary after a pay increase, multiply the current salary by the percentage increase and add it to the original salary. In this case, a 6% increase on a $62,900 salary results in a new annual salary of $66,674.
Explanation:The subject of this question is determining the new salary after a pay increase, which is a common problem in mathematics related to percentages. To calculate the new salary after a 6% pay increase to a current salary of $62,900, you multiply the current salary by the percentage increase in decimal form, which is 0.06.
Step-by-Step Calculation
Determine the increase amount by multiplying the current salary by the percentage increase: $62,900 × 0.06 = $3,774.
Add the increase to the current salary to get the new salary: $62,900 + $3,774 = $66,674.
The new annual salary after a 6% increase will therefore be $66,674.
To generalize, the formula to calculate the percentage change or growth rate is given by:
Percentage change = (Change in quantity / Original Quantity) × 100
For example, a $2 per hour raise on a $10 per hour job represents
Percentage change = ($2 / $10) × 100 = 20%